Financial Derivatives

Centre for Central Banking Studies Bank of England

Financial Derivatives

Simon Gray and Joanna Place

Handbooks in Central Banking no.17

Handbooks in Central Banking

No. 17

FINANCIAL DERIVATIVES

Simon Gray and Joanna Place

Series editor: Robert Heath Issued by the Centre for Central Banking Studies, Bank of England, London EC2R 8AH Telephone 0171 601 5857, Fax 0171 601 5860 March 1999 © Bank of England 1999 ISBN 1 85730 141 2

Foreword The series of Handbooks in Central Banking has grown out of the activities of the Bank of England’s Centre for Central Banking Studies in arranging and delivering training courses, seminars, workshops and technical assistance for central banks and central bankers of countries across the globe. Drawing upon that experience, the Handbooks are therefore targeted primarily at central bankers, or people in related agencies or ministries. The aim is to present particular topics that concern them in a concise, balanced and accessible manner, and in a practical context. This should, we hope, enable someone taking up new responsibilities within a central bank, whether at senior or junior level, and whether transferring from other duties within the bank or arriving fresh from outside, quickly to assimilate the key aspects of a subject, although the depth of treatment may vary from one Handbook to another. We hope they will also be helpful to those with some experience, but who are facing new problems as the economy and markets develop. While acknowledging that a sound analytical framework must be the basis for any thorough discussion of central banking policies or operations, we have generally tried to avoid too theoretical an approach. The Handbooks are not intended as a channel for new research. We have aimed to make each Handbook reasonably self-contained, but recommendations for further reading may be included, for the benefit of those with a particular specialist interest. The views expressed in the Handbooks are those of the authors and not necessarily those of the Bank of England. We hope that our central banking colleagues around the world will continue to find the Handbooks useful. If others with an interest in central banking enjoy them too, we shall be doubly pleased. We would welcome any comments on this Handbook or on the series more generally.

Robert Heath Series Editor

DERIVATIVES Simon Gray and Joanna Place Contents Page Abstract....................................................................................................... 3 1 Introduction................................................................................................ 5 2 Policy aspects of derivatives ..................................................................... 6 a) Monetary policy ..................................................................................... 6 b) Supervision of banks’ derivative risks ................................................... 8 3 Overview of derivative products and arbitrage ..................................... 12 4 Forwards..................................................................................................... 16 a) Foreign exchange forwards ..................................................................... 16 b) Interest rate forwards............................................................................... 18 c) Futures ..................................................................................................... 19 5 Swaps........................................................................................................... 21 i) Interest rate swaps .................................................................................. 23 ii) Currency swaps ...................................................................................... 26 iii) Credit swaps ........................................................................................... 27 6 Options ........................................................................................................ 27 7 Institutional arrangements ....................................................................... 36 8 Accounting standards................................................................................ 39 9 Statistical measurement ............................................................................ 39 Annex 1 The size of global derivatives markets: Survey data from the Bank for International Settlements.............................................. 43 Annex 2 Forward exchange rate calculations................................................... 45 Annex 3 Forward interest rate calculations ...................................................... 46 Annex 4 Swap spreads and government bond yields ....................................... 47 Annex 5 Cash flow and margining ................................................................... 49 Glossary............................................................................................................ 51 Further Reading.............................................................................................. 58 2

ABSTRACT

Derivatives, ranging from relatively simple forward contracts to complicated options products, are an increasingly important feature of financial markets worldwide. They are already being used in many emerging markets, and as the financial sector becomes deeper and more stable, their use is certain to grow. This Handbook provides a basic guide to the different types of derivatives traded, including the pricing and valuation of the products, and accounting and statistical treatment. Also, it aims to highlight the main areas in which derivatives matter to central banks, notably those of monetary policy and banking supervision. It is not intended as a manual for traders, nor to describe in depth the current state of world markets, where changes can happen so rapidly that any description must soon become outdated. But we do hope to provide a clear enough description of derivatives and their relevance to central banks for central bankers to be confident in tackling the issues that arise. Most derivatives traded are, in fact, fairly simple, and well within the grasp of our intended readership.

3

DERIVATIVES 1. Introduction Derivatives are useful for risk management: they can reduce costs, enhance returns and allow investors to manage risks with greater certainty and precision.

But, used

speculatively, they can be very risky instruments as they are highly leveraged and are often more volatile than the underlying instrument. This can mean that, as markets in underlying assets move, speculative derivatives positions can show even greater movements, resulting in large swings to profits and losses.

Recent attention has

focused on large losses (such as Barings, Sumitomo) and has underlined the need to have good management controls in place when dealing with such instruments.

A derivative contract assumes value from the price of an underlying item, such as a commodity, financial asset or an index. The underlying asset could be a physical good, such as wheat, copper or pork bellies, where derivatives pricing is affected by expectations about future supply and demand constraints; or a financial product, such as equities, fixed-income securities or simply a cash balance.

A financial derivative

contract derives a future price for that asset on the basis of its price today (the spot price) and interest rates (the time value of money).

This Handbook considers financial derivatives. The underlying assets are typically a short-term or a long-term loan (normally the three-month interbank interest rate and a long-term government bond yield); foreign currencies; or equities, whether individual equities or an index. Also, credit risk based derivatives have recently emerged in financial markets. Derivative contracts can be subdivided into forward contracts, in which both parties are obliged to conduct the transaction at the specified price and on the agreed date; swaps, which may be viewed as a subset of forwards and involve the exchange of one asset (or liability) against another at a future date (or dates); and options, which give the holder the right but not the obligation to require the other party to buy or sell an underlying asset at the specified price on or by the agreed date. 5

Distinction also needs to be made between exchange-traded contracts, which are standardised, and OTC (over-the-counter) contracts, which typically are non-standard.

Data on the world’s derivatives markets are available from the Bank for International Settlements (BIS). The BIS triennial survey of foreign exchange business in major financial centres around the world was extended in 1995 to include derivatives transactions, and this was repeated in 1998. Also in 1998, the BIS initiated a semiannual survey on open positions in global over-the-counter derivatives markets. The first data - for end-June 1998 - are presented in Annex 1.

The next section discusses the policy issues raised by derivatives. However, as a good understanding of the instruments is necessary to an appropriate central banking response, those readers who are wholly unfamiliar with derivatives will need to return to this section after reading through sections 3-9.

2. Policy Aspects of Derivatives

a) Monetary Policy

There are three main areas in which derivatives may impact monetary policy. These relate to the informational content of the market; any effects on the transmission mechanism; and the possible use of derivatives as monetary policy instruments.

Informational content

Even if derivatives are not traded, the same processes as used for calculating derivative prices such as forward interest and exchange rates can be used to extract information from market prices. For instance, the central bank may calculate implied forward rates to judge whether the market expects interest rates to increase, or whether market 6

expectations of the timing of interest rate changes has altered; or perhaps to estimate a term premium. In interpreting these estimates, the central bank has to remember that the markets will be making (possibly wrong) guesses about future changes in the central bank’s own intervention rates.

If an exchange rate target is being used, the calculation of forward rates can give the central bank a measure of the credibility of the policy. If forward rates are outside a targeted band, this implies the market does not have full confidence that the band can or will be sustained.

If options are traded, then options prices can give an indication not only of the market’s central expectation of future price moves, but also of the distribution of risk. So-called kurtosis analysis can be used to analyse the distribution of expected outcomes (is it normal? Skewed? fat-tailed?).

Transmission mechanism

Since the trading of derivatives allows risk, or market exposure, to be transferred from one person/institution to another, a BIS committee (called the Hannoun committee, after its chairman) studied whether the trading of derivatives affected the transmission mechanism, and concluded that there was no significant effect in the markets studied. A similar conclusion was reached in an IMF paper (“Derivatives Effect on Monetary Policy Transmission”, dated September 1997): “Theoretically, derivatives trading speeds up transmission to financial asset prices, but changes in transmission to the real economy are ambiguous. [In] a study of the UK economy...no definitive empirical support for a change in the transmission mechanism is found.”

7

Use of derivatives as monetary policy instruments

A number of central banks use foreign exchange swaps as a monetary policy instrument; and some will use a broader range of derivatives in managing their foreign exchange reserves, but not for monetary policy purposes. While a theoretical case can be made for using derivatives, including options, to defend a monetary policy stance, they do not have a direct impact on monetary base, and their use is normally considered to be risky and uncertain. We would in general argue that, with the exception of foreign exchange swaps, derivatives should not be used by central banks for monetary policy purposes.

b) Supervision of banks’ derivative risks Derivative instruments give rise to few completely new risks in themselves. Like most products they generate exposures to market risk and to counterparty credit risk, as well as the usual range of operational risks. However, derivatives sometimes can repackage risks in complex ways. This can result in a misunderstanding of the exposure to these risks and to mis-pricing. Derivatives can enable banks to take on large exposures to market risks for relatively small initial cash outlays. This is known as leveraging.

In the UK, banking supervisors tend not to focus specifically on banks’ derivatives activities - because they pose few new risks - but consider them instead as part of banks’ wider treasury and trading activities. When assessing a bank’s treasury and trading activities, supervisors focus on two main areas: the adequacy of internal risk management and control, and capital adequacy.

Internal risk management and control

Supervisors undertake on-site visits to the whole range of banks which have treasury and trading operations - whether they are engaged in balance sheet hedging, or trading for 8

own account or customers - including to banks which use internal pricing and risk aggregation models to calculate market risk capital requirements (see below). These visits, which typically last 1-3 days, focus very much on internal controls and risk management in the treasury and/or trading area, as well as on the technical aspects of pricing and risk models. Internal controls and risk management are judged against supervisors’ assessment of market best practice, with the onus on banks to justify any divergence.

Managing the market risk of derivatives can be more challenging than managing the underlying assets because of the sometimes complex relationship between changes in the value of derivatives and changes in the underlying asset price. This is particularly true for options: as the price of the underlying asset changes, option values change in a nonlinear way, making them sometimes very sensitive to small changes in the price of the underlying asset. For some products, e.g. barrier or digital options1, there are also discontinuities in the relationship between an options’ value and the price of the underlying asset.

And discontinuities are not confined to exotic products, since a

portfolio of “vanilla” options can closely approximate exotic options: sudden changes in the value of a portfolio of vanilla options are therefore quite possible.

Risk

identification and timely measurement of exposures are therefore crucial to effective risk management. Typically, many banks use Value-at Risk (VaR) models to manage their market risk exposure. These VaR models estimate the potential loss of a portfolio over a given time interval at a given confidence interval; normal market conditions are usually assumed.

Independent valuation of positions is an important aspect of internal control in any trading area, including one that uses derivatives. Where a bank is marking to market, valuing any OTC product can be difficult if market prices are not readily available, e.g. from brokers’ screens. OTC derivatives are no exception and, in fact, the problem can be greater for OTC options, whose value depends on implied volatilities that are hard to

9

estimate, particularly for options that are away from the money. Losses can therefore easily be concealed in a portfolio (deliberately or otherwise) and so it is important for middle and back office staff to be as familiar with derivatives risks and pricing issues as traders, and to undertake a rigorous comparison of profit and loss against risks taken.

Capital requirements

Both the EU and BIS have established capital requirements for market and credit risks for on- and off-balance sheet items, including derivatives. Capital requirements for foreign-exchange and commodity price risk on all positions, and interest rate and equity risk on trading positions, are set out in the EU Capital Adequacy Directive (1993) (as subsequently amended) and the BIS Amendment to the Capital Accord to incorporate market risks (1996). Capital requirements for counterparty credit risks are set out in the EU Capital Adequacy and Solvency Ratio Directives (as subsequently amended) and the Basle Capital Accord (as subsequently amended).

None of these make special

provisions for derivatives except where the risks differ from those on the underlying assets. So, capital is charged for options risks to capture their non-linearity (gamma) and sensitivity to changes in volatility (vega), and a special calculation is made for counterparty risk. Banks’ internal models may be used to calculate options’ risk requirements, with their supervisor’s prior agreement.

The counterparty risk on a derivative contract depends on the size of the exposure, the probability of the counterparty defaulting, and the recovery value in the event of default. The size of the exposure is typically only a small proportion of the notional amount underlying the contract but can change quite substantially over the life of the contract as the underlying asset price changes. For capital adequacy purposes, the size of the exposure is measured as the current value of a contract - how much it would cost to replace a contract today if the bank’s counterparty defaulted today - plus an “add-on” to capture potential future exposure. To see the need for this add-on consider an interest 1

A glossary of terms is provided at the end of this Handbook. 10

rate swap. At the time the contract is entered into, its market value is usually zero. But clearly a bank has an exposure to its counterparty because it expects the counterparty to make payments to it over the life of the contract. So, its counterparty exposure is not zero and an “add-on” is required to capture the full exposure (note that there is no counterparty exposure of this sort arising on written options, as the holder will not exercise an out-of-the money option). The net value to a bank of the payments which are payable and receivable over the life of a swap are uncertain at the outset and will depend upon the path of interest and exchange rates over the swap’s life. The add-on must therefore reflect the expected path of the underlying interest and exchange rates over the life of the contract.

The EU and BIS capital requirements distinguish between contracts of different maturities, and contracts with different underlying asset prices, with larger amounts of capital (larger add-ons) held against contracts where the underlying price is more volatile, e.g. more for options based on commodity prices than on interest rates. Capital requirements for derivatives are finally calculated using the usual counterparty credit risk weights, but with the maximum risk weight reduced from 100% to 50%.

Derivatives clearing houses reduce their counterparty exposures through initial and daily margining. There are a number of ways to reduce counterparty exposures on OTC contracts, including bilateral netting, collateralisation, margining, guarantees or letters of credit, but these will only be effective if the arrangements are legally enforceable in relevant jurisdictions. A number of other risks should also be considered in relation to derivatives 2:

2

In September 1998, the Basle Committee on Banking Supervision and the Technical Committee of the International Organisation of Securities Commission (IOSCO) published Framework for Supervisory Information about Derivatives and Trading Activities, a document that provides a framework for the collection of data for supervisory purposes. 11

Liquidity - Derivatives can give rise to large and unpredictable cashflows, particularly margin calls for exchange-traded products, and this should be considered as part of a bank’s overall liquidity position, if material.

Legal and settlement risks - For exchange-traded products, provided the exchange is well set up, the legal and settlement risks may be small. But, for OTC contracts, where there is not usually a clearing house, and where legal contract documentation may not be standardised, risks may be considerably greater.

For banks selling OTC derivatives to clients, there is also a need to take account of suitability. There have been a number of court cases in the UK and the USA where nonfinancial clients have entered into derivatives transactions, lost money and subsequently sued the bank in question for selling them an inappropriate product. Banks need not only to take account of the sophistication of the client and ensure that derivative products are properly explained, but also to be able to demonstrate that they have done so in the event of a subsequent dispute. 3. Overview of derivative products and arbitrage

Forwards may be related to interest rates, bond prices, foreign currency, a basket of equities, a commodity or, more recently, credit risk.

For instance, a forward rate

agreement (FRA) fixes the interest rate for a deposit or loan transaction commencing on an agreed future date. Futures3 are exchange traded forwards, and consequently are traded in a standardised format e.g. traded in predetermined bundles for settlement only on certain fixed dates, and settled through a clearing house. Some traders use the futures market as a proxy for the market in the underlying asset. Forwards are bilateral contracts whose terms can be decided by the parties involved. As OTC contracts, forwards may provide a more exact match of the needs of the parties involved than is possible with a 3

In this Handbook, we will refer to an OTC forward simply as a "forward" and an exchange traded forward as a "future". 12

standardised exchange-traded product, but with this flexibility comes potentially greater counterparty risk4 because of the lack of a clearing house arrangement (although some clearing houses are discussing the possibility of clearing some OTC contracts). While the OTC market is bigger than that for exchange-traded products, it is often thought of as less liquid in that there is less trading in each contract.

Options can be either exchange traded (like futures) or OTC. A call option gives the holder the right (but not the obligation) to buy an underlying item - an interest rate, foreign exchange, a security or other assets - at a predetermined price on or before the agreed expiry date of the option. A put option gives the holder the right (but not the obligation) to sell an underlying item.

Swaps are almost exclusively traded OTC; they are virtually never exchange-traded. They can be related to interest rates, exchange rates, commodities, equities or credit risk. A swap is an agreement to exchange cash flows based on a given principal amount (usually notional) for a given time period.

Interest rate swaps represent an agreement to exchange cash flows related to interest rates - normally at least one of which is on a floating basis - at a future date, based on a notional principal amount. Foreign exchange swaps are in effect a spot transaction coupled with a reverse forward transaction (an agreement to transact at a fixed price at a future date). These instruments may also involve an exchange of interest payments during the life of the contract, if the underlying assets involved are loans (liabilities) rather than cash balances (assets).

“Long” and “short” positions can be measured in different ways. A “long” position is associated with an obligation to purchase an asset (foreign exchange, securities, commodities, and loans), and a “short” position an obligation to sell. The position is usually looked at on a net basis by type of risk category e.g a net forward foreign 4

The risk that a counterparty fails to make all of the payments over the life of the contract. 13

exchange position will take into account future obligations to purchase sterling against obligations to sell it (including swaps). But it could be divided by time periods, or added to an underlying cash position. Traders will tend to take a long position if they expect asset prices to rise, and a short position if they expect prices to fall.

The table below summaries the different derivative types and how they are traded. Exchange -Traded (= standardised contracts) Purchase/Sale of Asset at specified price on agreed future date Exchange of assets at specified prices and on agreed date(s) Right but not the obligation to conduct one of the above transactions

Over-the-Counter (OTC) (= non-standardised contracts)

Future

Forward

-

Swap

Option

OTC Option Swaption5

Pricing In order to value a financial derivative it is essential to have an active market in the underlying item. The market pricing of derivatives also assumes a well-arbitraged market. If this is not the case, perhaps because of segmentation in the market or an inefficient payments system, it may prove difficult for the market to price derivatives; and market liquidity will consequently be reduced.

If the market is well arbitraged, participants in the markets should be indifferent between comparable transactions. For instance, a borrower needing finance for six months could borrow for 6 months, or could borrow for three months and roll over the finance for a

5

An option to transact in a swap. 14

further 3 months, or any other combination of periods which totalled the required 6 months. Ex ante, the expected cost of any of these options should be the same.

Derivatives allow traders to take advantage of different expectations of forward interest rates from that implied in the yield curve. For instance if one trader thought that interest rates were likely to remain flat but the yield curve implied a sharp rise, the trader could take a position in a forward contract such that he would profit if his expectation turned out to be correct. For instance, if the three month interest rate is 10%6 and the six month rate 12%, implying that the three months rate in three months’ time will rise to 14% (see Annex 2 for forward yield calculations), a trader who thought interest rates would not rise might borrow for three months and lend for six. He could then refinance after three months at a rate lower than 14% to lock in a profit. Assets Loan Interest rate 12% for six months

Total

Liabilities 100 Borrowing

100 * 12% * 182/365 = 6

Interest rate: 10% for 3 months 10% for 3 months

100 100*10%*91/3657 = 100*10%*91/365 =

2.5 2.5

Profit

1.0

106 Total

106

But this would tend to increase demand for three month money, pushing up that interest rate, and increase supply of six month money, pulling that rate down. If enough traders or other market participants took this position, then as traders positioned themselves to take advantage of the perceived anomalies, they would shift the pattern of supply and demand in a way that would tend to remove those anomalies. The yield curve would flatten out until the implied futures rates reflected market opinion. Any trader can take a

6

Annualised basis. The market convention for money market calculations in the UK is actual/365. However, other countries may have different conventions e.g. for the Euro area countries the recommended market convention in actual/360. 7

15

different view to the market, but the market as a whole can only have internally inconsistent pricing if arbitrage is weak.

4. Forwards

A forward agreement is an agreement made between two counterparties to sell/buy an underlying item at a certain future time for a certain price. The price agreed is referred to as the delivery price. It allows both the buyer and seller to lock in a certain price and therefore protects them from price movements in the period ahead of delivery. The reason for entering into such an agreement may be to ensure certainty of price. For example, if a manufacturer has agreed a certain price for his products with his customers, he may want to guard against increases in the price of raw materials for the period in which his output prices are set. It may also be used as a speculative instrument, where the buyer/seller anticipates future price movements and hopes to gain from them; or as an arbitrage against other markets where an opportunity exists.

An OTC forward agreement can be for any size, amount and period. It will be bilaterally negotiated between two counterparties and credit risk will remain with the counterparties themselves.

a) Foreign Exchange forwards “A contract for the exchange of one currency against another, at an agreed rate, for a specified settlement date in the future” Foreign exchange forwards are often the first derivatives to be traded in an emerging market, as it tends to be the forex market that develops first. In some cases, capital controls mean that there are problems, particularly for non- residents, in taking or providing delivery of the underlying currency. Sometimes foreign markets will trade “non-deliverable forwards” (NDFs), allowing non-residents to take or hedge exposures against the currency in question, but settling the contract in another currency such as the 16

US dollar. The bank or other entity which trades in such NDFs cannot always hedge its own net position easily in the cash market, however. This will tend to mean that spreads are relatively wide, and pricing may reflect localised demand and supply rather than being a good proxy for the domestic market.

Forward rates are based on the spot exchange rate and the interest rate differential between the two countries in question. The calculation is detailed in Annex 2. The calculation of foreign exchange forwards can be shown pictorially:

‘Y’ units of domestic currency

plus domestic interest rate, Id

times implied forward FX rate

times spot FX rate

plus foreign interest rate, If

‘X’ units of FX at future date

(1 + Id ) * (implied) forward rate = Spot rate * (1 + If ); (implied) forward rate = Spot rate * (1 + If ) / (1 + Id ) This can be approximated as : (Implied) forward rate = Spot rate * (1 +( If - Id ))

17

b) Interest rate forwards The pricing of interest rate forwards is taken from the forward yield curve. The forward yield curve can, in turn, be derived from the yield curve as follows:

Current interest rates No. of days

A 3 month 91 6 month 182

Implied 3 month forward

(i) annual (ii) period rate rate

B

C

10% 12%

2.4% 5.8%

(iii) period (iv) rate annual rate

now in 3 months’ time

D

E

2.4% 3.3%

10.0% 14.0%

Strictly speaking, the longer-term rate should be divided by the shorter term, rather than the latter subtracted from the former. For example, using the number in the example above, the forward rate of 14% - column E - is 1.058 / 1.024, annualised (i.e. figures from col. C) - rather than 1.058 - 1.024, annualised (see Annex 3). The difference becomes significant if the annualised rate is much over 10%.

It is vital to remember that forward rates are arithmetical calculations based on the market yield curve and not an individual trader’s opinion of what the spot rate will be at the settlement date quoted.

If the yield curve is reasonably robust - i.e. it reflects real transactions in the money markets - then it should be possible for banks and others to calculate implied forward rates.

18

Upward sloping yield curve 25.00% 20.00% 15.00% 10.00% annual rates 5.00%

one month forward, ar

0.00% 1 2 3 4 5 6 7 8 9 10 11 12

“Synthetic” forward positions can be created using cash market instruments. For instance, borrowing for 6 months and lending for 3 results in an exposure to the 3 months interest rate in 3 months time. This gives the same result as using a forward/future contract to take a “long” position in the three month interest rate. The opposite could be done to take a short position.

As a rule, derivatives are

administratively simpler and cheaper to use than such synthetic positions (which expand the balance sheet).

c) Futures A futures contract is an exchange traded forward contract. It is an agreement to deliver or receive a specified amount of a particular asset on a fixed future date at a price agreed today. The instruments underlying financial futures contracts are typically government bonds, money market instruments or foreign exchange. To this extent they are exactly the same at OTC forwards. Exchange trading is only possible where most of the features of the asset are standardised. A future will be for a set contract size; a fixed maturity and a limited number of settlement dates; and the responsibility for credit risk control will normally rest with a clearing house (see section 7), which is the counterparty to each outstanding position (counterparty risk is standardised). The exchange also needs

19

to specify certain details about the futures contract: i.e. how prices will be quoted, and when and how delivery will be made.

Because of the liquidity of the futures markets - which is facilitated by the standardisation and the speed and safety of transactions - it often leads the cash market; and is used as proxy for the market as a whole. It can therefore be thought of as, and is often used as, a barometer of market sentiment in the underlying instrument. Many investors will use futures rather than the cash market in order to e.g., change the duration8 of their portfolio or their asset allocation or for hedging purposes. Futures are often more liquid than cash bonds, there are low ‘up-front’ payments (just the initial margin), and the purchase/sale is very quick.

However, although, under ‘normal’

circumstances, derivatives markets are often more liquid than the underlying cash market, liquidity in derivatives markets is more easily lost at times of crisis, partly as there are no market makers in derivatives (as there may be in the underlying assets) and therefore liquidity can not be guaranteed.

It is relatively rare for the futures contract to be held to maturity and for the underlying asset to be delivered: usually investors/traders buy and sell the contract without wishing to receive/deliver the underlying asset. They simply want to take on an exposure (or hedge) for a particular period. If the contract is held to delivery, it is the seller of the contract who will deliver the underlying asset. In the case of a government bond future, the seller chooses which specific bond – from a basket of “deliverable” bonds – to deliver.

When the asset is a short-term interest rate (rather than, say, a long-term bond) the contract will be cash settled: this is easier than trying to standardise the credit risk of short-term loans. For example, the three-month “short [i.e. relatively short-term] sterling future” traded in the London market uses as a reference point the three month LIBOR 8

Weighted average term to maturity. Duration provides a measure of price sensitivity: the longer the duration of the portfolio the more sensitive its value to interest rate changes. 20

quote for the relevant day as set by the British Bankers Association. Interest futures prices are usually quoted as “100 minus the annualised interest rate”. If the expected interest rate at the futures settlement date is 7.5%, the future will trade at 92.5; and the value of each basis point move in the futures price is fixed in relation to a notional loan size. If the notional loan is 1 million currency units and a three month interest rate is being traded, the value of a one basis point move in the future will be 25 currency units (1,000,000 * 0.01% * [3/12]; the “3/12” factor is because a three month notional loan is being traded, but the future is priced as 100 minus the annualised interest rate). It is assumed that a borrower’s actual costs will move in parallel with the LIBOR quote.

Futures can be used as a proxy for the broader position of a bank or other company . If I wish to borrow money for a three month period in two months’ time at today’s implied forward rate, I could sell a three month futures contract for delivery in, say, four months’ time. In two months’ time I buy the equivalent number of contracts, closing out my position. If the yield curve has moved upwards (interest rates have risen), the price of the futures contract will fall and I will make a profit on my futures trading which offsets the higher cost of my borrowing. But if the yield curve changes shape, the hedge will turn out to be imperfect. In contrast, a forward contract is more flexible and would give me a perfect hedge, thus reducing market risk, but could be less liquid and potentially could expose me to potentially greater counterparty risk unless it was settled through a clearing house. 5. Swaps A “Swap” can be related to interest rates, foreign exchange rates, equities, commodities or, more recently, credit risk.

The two most common types of swap are interest rate swaps and currency swaps. The former typically swaps a floating rate payment for a fixed rate payment; the latter swaps currency A for currency B. It is also possible to use swaps to change the frequency or timing of payments, even if interest type or currency remains the same. Swaps can 21

change either the net liability or the net asset and are therefore sometimes referred to as an “asset swap” or “liability swap”. The structure is the same in both cases; it is simply the motivation behind the swap that gives it this name.

Essentially the swap market provides a means of converting cash flow, changing the amount of payments and/or the type, frequency or currency.

Swaps are used by

investors to match more closely their assets/liabilities (which may change over time); by traders to exploit arbitrage opportunities; to hedge exposures; to take advantage of better credit ratings in different markets; to speculate 9; and to create certain synthetic products.

For example, if a British company wishes to borrow in Deutschmarks, it does not need to issue a Deutschmark-denominated security. It may find it cheaper to issue in, say, sterling – where its name is better known in the market - and then to swap into Deutschmarks. The company’s borrowing (ie its net liability) will be in DM, but it has ‘tapped’ the investor base in sterling. Similarly, an investor could purchase a fixed-rate asset, perhaps a government security, and swap into a floating rate asset if he wanted to change his type of income stream.

The market in swaps has grown over the past few years for a number of reasons. Global deregulation has meant access to new markets and greater choice for investors and borrowers; financial innovation has allowed more advanced products to be developed, so matching borrower and investor needs more closely; interest from traders has helped boost liquidity; and the attraction of their off-balance-sheet nature, which can free up capital to be used elsewhere. Banking supervisors will, of course, aim to take account of the risks involved in swaps, even though they are off balance sheet.

9

For instance, a lender may want to pay floating and receive fixed payments if he expects rates to fall.

22

In some developing and transitional economies, the futures market is significantly larger than the swaps market (ie. the opposite case to developed markets). This may be because futures, being exchange traded, are likely to have a standard counterparty risk and a margining mechanism, which helps to protect against the greater uncertainties of counterparty risk.

(i)

Interest rate swaps

An interest rate swap is defined as an agreement between two parties to exchange cash flows related to interest payments. The most common type of interest rate swap is a liability swap where the parties swap a stream of future fixed rate payments for floating rate payments. A counterparty may want to swap fixed for floating payments if he holds floating rate assets or if, with fixed-rate liabilities, he expects rates to fall and does not want to be locked in at high rates.

“A” has an existing fixed rate liability and “B” has a floating rate liability. They then enter into a swap transaction to alter the nature of their net cash flows (ie to alter their exposure to interest rate movements); the arrows show the direction of the cash payments under the swap transaction.

A

Floating →

B

↓

← Fixed

↓

Fixed

Floating

A now makes a net floating rate cash payment and B a net fixed rate cash payment. A’s original fixed rate loan remains A’s direct liability (eg to its bondholders), regardless of whether B keeps his side of the agreement. But provided B does so, then A’s net liability is now in floating rate rather than fixed rate money.

23

The amount of the interest payments exchanged is based on a notional principal amount: only the interest payments are exchanged; principal is not. (For supervisory purposes, however, the notional amount is important in providing an indication of the potential exposure to adverse price movements and is also relevant for determining capital requirements.)

Using swaps as an arbitrage opportunity will exist if one party has a comparative advantage and if each party borrows in the market where they have a relative advantage. An example of this is shown below.

Credit

Cost of 10 year

Cost of 10 year

rating

fixed debt

floating debt

Firm 1

AA

8%

Libor + 25bp

Firm 2

BB

10%

Libor + 100bp

200bp

75bp

Credit Differential Arbitrage available for a Swap

125bp

An arbitrage will exist if there is a difference in the ‘credit differential’ between borrowing in fixed or floating. In order to take advantage of this differential, each firm will have to borrow in the market where it has the comparative advantage. In this example the difference in credit differentials between the two markets is 125bp and therefore this is the amount available for arbitrage. Firm 1 can borrow more cheaply perhaps because of better credit rating, or perhaps because it is a better known name. Obviously the comparative advantage of Firm 1 gives it a certain negotiating power. Sources of comparative advantage include better credit rating, name recognition, regulatory constraints, and currency constraints. 24

So: • Firm 1 wants floating rate debt, but issues fixed rate debt at 8%; while Firm 2 wants fixed rate debt, but issues floating debt at Libor + 100bp. • The two firms enter into an interest rate swap, and (jointly) save 125bp (the difference between the fixed and floating rate credit differentials): this is divided up in agreement between them.

Say, Firm 1 saves 75bp. In other words, its

costs are 75bp cheaper than if it issued directly into the floating rate market. Its net interest-related payments will therefore be Libor - 50bp. Firm 2 saves 50bp, paying a net 9.5%

Payments under the Swap Transaction Firm 1

8.50% fixed

Firm 2

Libor

8% fixed to bondholders

Libor + 100bp floating bondholders

Although the diagram shows the gross payments under the swap transaction, it may be possible to settle only the net flows, if the interest payment dates coincide. Because of this, and the fact that no principal is exchanged, the counterparty credit risk is often considered not as important as the market risk, ie exposure to changes in interest rates.

If the benefit was smaller, it may not be considered worth doing the swap due to the extra transactions cost, supervisory capital (if a bank) and credit risk which both firms take on. (A further example on an interest rate swap is contained in Annex 4).

25

(ii)

Currency swaps

An issuer may find it difficult (or even impossible on account of legal or other restrictions) to issue in a particular currency. However, it may be important - eg for hedging purposes or for asset/liability management for the company - to have its liability in that particular currency. It therefore may choose to borrow in another currency (currency B) and swap the proceeds; this allows the borrower to raise the necessary funds and have the net liability in the chosen currency (currency A). The chart sets the payments under this currency swap transaction. ← Currency B Borrower

Currency A →

Swap Counterparty

↓ ↓ Currency B to investor At its simplest, a currency swap is equivalent to a spot forex transaction coupled with a forward forex agreement. (Forex swap rates are calculated on this basis.) This simple version is usually referred to as a FX swap; and (unlike an interest rate swap) involves exchange of principal at the start and at end of the transaction - but no cash flow in between. Alternatively, the two counterparties may exchange a series of interest flows throughout the swap; this is usually referred to as a currency swap.

For instance, two counterparties may agree to a swap of DEM150 mn at 6% DEM (Deutschemark) against USD100 mn at 5% USD (US dollar) for 5 years, with an exchange of principal at the beginning and end of the period, and annual interest payments of DEM 9mn and $5mn. There is, therefore, greater risk on a currency swap

26

than an interest rate swap, as the principal is exchanged (credit risk and Herstatt risk 10 are both higher).

(iii)

Credit Swaps

It is also possible to swap credit risks by exchanging payments received from two different income streams relating to different credit risks. A ‘credit default swap’ is a credit derivative in which the counterparties swap the risk premium inherent in an interest rate on a bond or loan – on an ongoing basis – for a cash payment in the event of default by the debtor. A total return swap is a credit derivative under which the cash flows and capital gains/losses related to the liability of a lower rated entity are swapped for cash flows related to a guaranteed interest rate such as inter-bank rate plus a margin.

6. Options

An options contract confers on the holder the right, but not the obligation, to conduct a transaction on or by a future date at a pre-determined price. Options may be either puts or calls. A put gives the holder of the option the right to sell the underlying item at the specified price, and a call gives him the right to buy the item. As the contract is asymmetric - the writer of the option is obliged to complete the transaction if the holder chooses, but not vice versa - the writer will always receive a premium11, for writing it (whereas for forwards, the contract is symmetric and no premium is paid). This means that a bank can write options in order to generate “fee” income/cash flows, believing that the income will more than offset any future losses, on average.

By contrast,

forwards/ futures allow a bank to take a position, but do not generate cash flow. Options contracts can be either exchange-traded or OTC. Exchange – traded options relate to 10

“Herstatt risk” refers to the June 1974 bankruptcy of Herstatt Bank: large losses arose when Herstatt Bank collapsed after receiving settlement of European currencies in forex transactions but before paying out the dollar counterpart (because of time differences between settlement in Europe and the USA). 11 This has some similarities to an insurance premium in concept. 27

(exchange-traded) futures contracts; OTC options relate directly to the underlying financial item.

Call options on some assets - equities and commodities - have, in theory, unlimited potential for notional profit, as there is no limit to price increases, although there is of course an expected maximum likely profit. If an investor has a call option to buy crude oil or Microsoft shares, at a given price, then unexpected events - political problems in the Middle East, or technological breakthrough - could result in very sharp increases in the value of the assets involved.

This does not hold true for securities: a zero coupon bond will not trade for more than nominal/face value, for instance, as investors will hold cash rather than receive a negative interest rate. A similar argument holds for coupon-bearing bonds. Likewise with foreign exchange. Assume a bank sells a call option to buy US$100 for Thai baht 4,000. Even if there is a catastrophic collapse in the value of the baht, say to Thai baht 1 million = US$1, the bank’s loss cannot exceed US$100. In baht terms its percentage loss may be astronomic; but in the face of a currency depreciation of this order, the bank’s whole balance sheet would have changed substantially. That said, a written option on a currency can, in extremis, result in a loss equivalent to the notional value (in terms of the stronger currency) of the option.

There is a maximum profit for all put options, as asset values will not turn negative. A put option to sell crude oil at $15 per barrel cannot be worth more than $15 (even if the oil could be obtained free, it could only be sold for $15 pb); whereas a call option to buy crude oil at a strike price of $15 pb could be worth much more, for instance if spot prices rose to $50 pb when the option would be worth around $35.

The potential loss for a buyer of options is limited to the premium paid; but the potential loss for a writer can be much greater (although limited to the price of the underlying asset). 28

Strike Price The strike price (or exercise price) is the pre-specified price at which the underlying asset position is taken if the option is exercised: a long position in the case of exercising a call option, or a short position with a put option. The intrinsic value of the option is the difference between the underlying futures contract (or the underlying item, in the case of an OTC option) and the strike price. An option cannot have negative intrinsic value. The intrinsic value is a measure of the amount by which an option is in-themoney.

At the money: an option is “at the money” if the strike price of an option is the same as the spot price, so that exercise of the contract does not imply a gain or a loss to holder of the option. (This does not include the gain/loss caused by the premium paid, as this is a sunk cost.) For instance, if in September the short sterling future12 December contract is trading at 93.00 (i.e. the market is on balance expecting the three month interest rate in December to be 7% - see page 21 for explanation of futures pricing), an "at the money” option on the December contract would have a strike-price of 93.00. If on the last trading day of the life of an option, the futures price were (still) 93.00, the option with strike price of 93.00 would have no value.

In the money: for a call option, if the strike price is lower than the underlying, then the contract is in-the-money; in other words, a profit is implied for the holder of the option because he will be able buy the underlying item for a lower price than in the spot market currently. For example, if the strike price of call was 92.50, then if the contract was trading at 93.00 it would have positive value, since a exercising the option would allow a future to be bought for 92.50 and sold immedately for 93.00 (or, as is more likely, the position could be closed out by selling call options). For a put option, if the strike price

12

The short sterling future relates to the three-month sterling interbank rate. A long position in this contract protects the holder who wishes to invest cash at a future date against a fall in interest rates, since a fall in future interest rates will be offset by a rise in the value of the future. 29

is above that of the underlying, the option is also in-the-money because the holder can sell the underlying item for more than in the spot market.

Out of the money: for a call option, if the strike price is higher than the underlying, this implies a loss for the holder of the option if it were exercised (i.e. no intrinsic value); in other words, if he exercised the option, the holder would have to buy the underlying item at a higher price than available in the spot market. In such a case, the holder would simply allow the option to expire worthless, and the cost would be the option premium paid in the first place. For a put option, a strike price below the underlying means that the put would be "out of the money", since there would be no point in exercising a right to sell the future at 92.50 if the open market price was higher than that. The opposite would apply if the strike price were 93.50 with the underlying item (the future) still at 93.00. A put would be worth exercising, but a call would expire worthless (‘out of the money’).

The above does not mean that an out-of-the-money option necessarily means a loss for the holder. It may still have some value as a hedge. Even if it expires worthless, the holder has still benefited from the hedge provided during its lifetime, which may have facilitated treasury management or even reduced capital costs (since regulators of financial institutions typically require less capital to be held for a well-hedged portfolio).

Types of options

Options can also be divided into American and European style. This does not refer to the location of trading, but to the period when the option may be exercised. Europeanstyle options can be exercised only on a specific day i.e. the last trading day of the option’s life. For instance, at the end of September you could buy a European-style option with an end November expiry date; the option could only be exercised on the last trading day of November. By contrast, American-style options can be exercised at any point during their life. In the above example, this would be on any trading day from the 30

day the option was purchased until the last trading day of November, at the choice of the holder.

For call options, it makes little difference whether the option is European or American. Options have time-value (see below), and it normally makes sense for the call option holder to realise this value by selling the option (for “intrinsic value plus time value”) rather than exercising it before the end of its life, as exercise will only ever yield intrinsic value. The time value of money is also a factor here, since the option gives the holder the right to purchase an asset at a fixed price in the future. Consider an investor with 100 of cash and an option to purchase an asset (securities, forex etc) for 100 at any time in the next three months. It will be more profitable to invest the cash for three months and then pay 100 for the asset than to exercise the option today and lose three months interest income.

This is not, however, the case with put options. Again, the time value of money is a factor here. If an investor can exercise a put option today and invest the cash received from selling the asset involved, rather than waiting three months to sell the asset at the same price, he will earn interest income over the period and so be better off. This means that American style put options do have an advantage over European style, and will therefore have greater value.

Valuation

Pricing an option is much more complex that pricing a forward or swaps contract. The value of an option is a function of its intrinsic value, its maturity and market price volatility. This Handbook does not go into detail on the pricing, but offers an intuitive guide to the way that an options price behaves.

31

Option prices are a function of:

Option price = f (V, T, S p - St ; 0] ),

where V is volatility, T is time to expiry, St is strike price, S p is spot price. Since the value of an option cannot be below zero, the intrinsic value – discussed above - is shown as the greater of zero or spot minus strike price. (For a put option, it is the greater of zero or strike minus spot.)

Consider the issue of market price volatility. If the three-month interbank rate is currently 10% p.a., the central bank has declared its intention to keep market rates at this level for at least 30 days and there is no expectation whatever that the rate will move over this period, then an “at-the-money” option with a 30 day maturity would have no value. No-one would pay a premium for an option to enter into a future transaction if there was certainty that an equivalent transaction could be undertaken without payment of the premium. But if market rates were volatile, the picture would change. With the same spot interest rate, strike rate and maturity, but no central bank commitment to hold the rate and a history of interest rate volatility, the option would have value. The more volatile the market - both as regards “historic volatility” (i.e. past performance) and “expected volatility” (a matter of judgement), the greater the value of the option.

The intuition to this is straightforward. An option may be used to hedge risk exposure. The greater the perceived risk (expected volatility) the more expensive the hedge; and if there is no (perceived) risk, then the market value of an option will be zero.

If

volatility/risk increases, then the value of an options portfolio increases for the holder; and a writer of options, facing a greater chance of payout, should hold more capital.

32

A similar analysis holds for the time value of an option. For a given underlying price, strike price and level of volatility, the value of an option will increase with the length of its life. Again, considering that an option can be used to hedge risk exposure, the longer the time to maturity, ceteris paribus, the greater the option’s value to the buyer/seller as there is a greater chance that the option will be exercised. This means that, as a given options portfolio ages, its value will tend to decrease. The holder will have less value and the writer less risk (other things being equal).

T im e v a lu e o f a 3 0 d a y o p tio n

Price

1 .0 0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

T im e

Time decay - the loss of time value (or theta, see below) as the option ages - is not a linear function. This is simply because, as the time to expiry approaches, a one-day change in lifetime represents a greater proportion of the remaining life. If there are 30 days to expiry and one day passes, 1/30th of the time value has eroded. But with two days left to expiry, when one day passes then 1/2 of the remaining time value has eroded. Theta is calculated in relation to the remaining time to expiration, rather than the original maturity of the option; this means that the theta value of two options with 33

identical terms and the same expiry date will be the same, even if the original life of one was longer. Synthetics

To create a synthetic short position in securities using options, a trader could sell a call and buy a put at the same (current market) strike price (the net premium should be very small). If the price rises, the call will be exercised, leaving a short position; if the price falls, the bought put will be exercised, again leaving a short position. (Vice versa for a long position). This may allow traders to take the equivalent of a short position even if short selling itself is not permitted under local trading regulations.

“Greeks”

Certain Greek letters are often used to denote the risk of changes in underlying prices or market conditions to the value of an options portfolio.

Delta: the delta of an option portfolio is the change in value implied by a one point move in the price of the underlying asset.

Delta factor = change in the price of the option change in the price of the underlying

For an option that is at the money, the delta is typically around 50% i.e. if the value of the underlying moves by £1:00, the value of the option will change by £0.50.

34

Price of underlying asset

Delta of a call option

at the money

0 1

2

3

4

5

6

7

8

9

Value of option

Delta values range from 0% for deep out-of-the-money options to 100% for deep in-themoney options. If an option is deeply out-of-the-money - for instance, if the strike price on a call option is 100 and the spot price for the underlying is 50, the option will have little value (unless the market is extremely volatile), since the underlying price would have to more than double for the option to move into the money. An increase in the underlying price from 50 to 51 would have little effect on the option value. At the other extreme, if the strike price were 50 and that of the underlying 100, then an increase in the price of the underlying from 100 to 101 would be fully reflected in the value of the option.

An increase in volatility will tend to flatten the delta curve for a given price range. The delta may be viewed as a probability estimate that the option will expire in-the-money. A deep in-the-money option is virtually certain to expire in-the-money, and delta is 100%. Vice versa for a deep out-of-the-money option. As volatility increases, the probability of expiring in-the-money tends to 50% (i.e. uncertainty increases with volatility; 50% probability represents the highest level of uncertainty). 35

Gamma: denotes the change in the delta for a one-point move in the underlying price. Since delta is not a linear function, gamma too is non-linear. Gamma decreases as certainty increases.

Vega: is used to denote the sensitivity of the option price for a 1% change in volatility (easy to remember because both begin with V). If volatility increases, so does the value of the option. Vega may vary depending on whether the option is at, in or out of the money. In major OECD government securities markets, implied volatility for at-themoney options is usually between 5-10%, but has in recent years jumped to around 15% in periods of market uncertainty.

Theta (sometimes called zeta or kappa): denotes the time value of an option (easy to remember because both begin with T). The longer the time period until the strike date, the greater is Theta: this is because there is more time for the price of the underlying to move in a direction favourable to the holder.

7. Institutional Arrangements

Clearing Houses

In order to standardise counterparty risk in exchange-traded derivatives, a clearing house is typically interposed between traders. If a trader belonging to firm “A” sells a contract to a trader belonging to firm “B”, then at the end of the trading day, the clearing house will stand in between the two, buying (for future settlement) from “A” and selling (for future settlement) to “B”. As long as the clearing house is reliable, then neither “A” nor ”B” need worry about credit risk. But the clearing house needs to protect itself against credit risk of both A and B. If prices rise and “A” defaults, the clearing house will still need to sell to “B” at the pre-agreed lower price; and vice-versa if prices fall and “B”

36

defaults. The clearing house protects itself by margining (see Annex 5 for detailed description).

The exchange or clearing house will take initial margin at the start of the contracts, and will call for variation margin each day. The counterparties will realise profits or losses on the contracts on a daily basis by “marking-to-market” (see below). The clearing house not only has responsibility for credit risk control (i.e. for ensuring that the margining system is correctly applied) but also for the administration of closing out contracts and for the delivery procedures.

Margining Practices Margin is taken to protect against counterparty exposure. It is regularly used in repo operations, and by derivatives exchanges. Initial margin is taken by a clearing house at the start of the agreement, to protect against any sudden price changes or future failure to provide (daily) variation margin. Variation margin is taken on a daily basis and is related to the movement in price of the contract each day.

Further examples of

margining are found in Annex 5.

Margining in derivative exchanges has the same basic function as with repo, but is different in some important respects. First, margin is paid by both seller and purchaser of the futures or options contract, as it is to protect the clearing house, which stands in between the two parties. Second, the payment of variation margin is different from repo variation margin in that it is not like “collateral” which is returned at the end of the period if the “loan” is repaid; rather, the traders’ positions (usually their overall position on all exchanges served by the relevant clearing house) are marked-to-market daily, with any losses paid over and any profits withdrawn on a daily basis. Thus on any day, including the settlement day for cash settled contracts, traders pay/receive their net profit for that day’s price movements. This daily cash flow minimises the exposure of the

37

clearing house to traders, and by putting the clearing house in a strong position, means that traders’ exposure to the clearing house does not constitute a large risk.

Margining is being increasingly used in OTC markets.

The deliverable basket

Given the homogeneity of government bonds, there needs to be some criteria as to what bonds could be delivered in a futures contact for bonds and there needs to be some form of “standardisation” between the bonds that can be delivered.

In deciding which bonds are eligible for delivery, the first criteria to decide is the maturity of the underlying asset(s) in the contract, for example, if it is a long bond futures contract the exchange will assign a notional maturity for a deliverable bond (a real bond will, of course, only have that exact maturity for a single day). The exchange will provide a “contract specification” as shown below:

Contract specification for long gilt future on LIFFE (London International Financial Futures Exchange)

Nominal Value

£50,000

Notional coupon

7%

Range of deliverable bonds

8.75 to 13 years residual maturity

The notional coupon is set to approximate the yield that is expected to prevail over the long term.

The fewer deliverable bonds in the contract, then the greater the homogeneity but the less the liquidity of the basket. Obviously, the exchange could decide to have only one 38

deliverable bond but, whilst this would mean homogeneity, it would not provide a very liquid basket which could cause problems for delivery. In this case, all bonds in the maturity range are eligible for delivery in the long gilt futures contract on LIFFE.

Having established a basket of deliverable bonds, the exchange must then find a mechanism by which these securities can all be valued and traded at one unique price prevailing on the futures exchange. Whilst this Handbook does not go into the details of this formula, the aim is to “standardise” the pricing of the deliverable bonds. A price factor system is used to “reprice” all bonds falling within the relevant maturity range – which will have different maturities, coupons and accrued interest – into a unified scale.

8. Accounting Standards

At the time of writing, international accounting standards are not yet fully agreed. The general principle that is emerging is that all derivatives should be recognised on the balance sheet and valued at fair value i.e. marked-to-market. There is an argument that, where derivatives are being used to hedge a specific risk, then either both sides of the balance sheet should be marked-to-market, or neither. But while the theoretical case for this is strong, practical implementation can be difficult.

9. Statistical Measurement

Measurement in Economic Statistics of Activity in Financial Derivatives Set out below is an outline of the IMF’s recommendations for the measurement of financial derivatives in the economic accounts. Fuller detail is provided in the IMF working paper entitled “The Statistical Measurement of Financial Derivatives” (March 1998).

39

For economic statistics purposes, financial derivatives are defined as follows:

Financial derivatives are financial instruments that are linked to a specific financial instrument or indicator or commodity, and through which specific financial risks can be traded in financial markets in their own right. Transactions in financial derivatives should be treated as separate transactions rather than as integral parts of the value of underlying transactions to which they may be linked. The value of a financial derivative derives from the price of an underlying item, such as an asset or index. Unlike debt instruments, no principal amount is advanced to be repaid and no investment income accrues. Financial derivatives are used for a number of purposes including risk management, hedging, arbitrage between markets, and speculation.

If a financial derivative instrument meets the above definition and there is an observable market price for the underlying item from which the derivative can acquire value, transactions in the instrument should be recorded in the financial account and any positions in the position statement. Among arrangements that are not to be classified as financial derivatives are fixed price contracts for goods and services, unless standardised in such a way as to be traded as a futures contract, insurance, which involves the pooling rather than the trading of risk, contingencies, and embedded derivatives.

Transactions Data

Forwards: At inception, risk exposures of net zero value are exchanged so there are no transactions to record in the financial account, although any fees associated with the creation of a forward should be recorded as a service payment. As forwards are not traded in the sense of ownership changing hands, no transactions are recorded during the life of the contract. The one exception is for contracts, such as interest rate swaps and futures, where there is on-going settlement: transactions are to be recorded in the financial account as either assets or liabilities depending on the net position of the 40

contract at the time the transaction occurs, although in the absence of information on the net position, net payments are recorded as a reduction in financial derivative liabilities and any net receipts as a reduction in financial derivative assets. The latter is also the recording practice for a forward that is settled at maturity or through mutual agreement to extinguish it. If the underlying item is delivered at the time of settlement, such as with many foreign exchange derivatives, the transaction in the underlying should be recorded at its prevailing market price, and any difference between the contract and prevailing market price, times quantity, should be recorded as a transaction in financial derivatives.

Options: The creation of an option involves the payment of a premium that is recorded as an increase in financial assets by the buyer and an increase in financial derivative liabilities by the writer of the option. Any trading in an option during its life is recorded and valued at the price agreed, like any other financial asset. At maturity, the option may expire worthless in which case no transactions are recorded. If there is a net cash settlement, or the underlying item is delivered, the treatment in the economic accounts is the same as described above for forwards.

Margins: Any margin that is paid but remains in the ownership of the depositor is termed repayable margin. If this margin is in the form of a security, no transactions are recorded because the depositor still has a claim on the same entity – the issuer of the security. On the other hand, if the margin is paid in currency then two transactions are recorded: a reduction in claims on the original depository and an increase in claims on the new depository. If margin is paid to meet a liability in financial derivatives, that is ownership of the margin changes hands, a transaction in financial derivative is recorded in accordance with the recommendations set out above. This type of margin is known as nonrepayable margin.

41

Position Data

Forwards: The value of a forward derives from the discounted net present value of expected receipts or payments. Because the market price of the item underlying the derivative contract can change between end reporting periods, so a position in a forward may switch from a net asset to a net liability position, or vice versa, between end periods. This change in value is recorded as a revaluation gain or loss in the position statement.

Options: The value of an option derives from the relationship between the contract and prevailing market price for the underlying item, the time to maturity of the contract, the time value of money, and the volatility of the price of the underlying item. The buyer of the option always has an asset and the writer a liability. If an option expires worthless but had value at the end of the previous reporting period, the writer records a revaluation gain and the holder a revaluation loss in the position statement.

42

Annex 1

The Size of Global Derivatives Markets: Survey Data from the Bank for International Settlements (BIS) At end-June 1998, the G-10 countries under the auspices of the BIS conducted a survey of the over-the-counter financial derivatives market. The data include both the notional amounts and gross market values outstanding of the world-wide consolidated OTC derivatives exposure of 75 large market participants that account for 90% of global market activity in financial derivatives. The survey covered four main categories of market risk: foreign exchange, interest rate, equity and commodity. After adjustment for double counting resulting from positions between reporting institutions the total estimated notional amount 13of outstanding OTC contracts stood at $70 trillion at end-June 1998. This was 47% higher than the estimate for end-March 1995, which was obtained from a supplementary survey to the triennial foreign exchange and derivatives turnover survey. However, adjusting for differences in exchange rates and the change from locational reporting in 1995 to consolidated reporting in 1998, the BIS estimates the increase between the two dates at about 130%. These data also confirm the predominance of the OTC market over organised exchanges in financial derivatives business. The data show that interest rate instruments are the largest OTC component (67% mainly swaps), followed by foreign exchange products (30%, mostly outright forwards and forex swaps) and those based on equities and commodities (with 2% and 1% respectively). At end-June 1998, estimated gross market values 14stood at $2.4 trillion, or 3.5% of the reported notional amounts. The BIS stressed that such values exaggerate actual credit exposure, since they exclude netting and other risk reducing arrangements. Allowing for netting lowered the derivatives-related credit exposure of reporting institutions to $1.2 trillion, or to 11% of on-balance sheet international banking assets. As might be expected, the ratio of gross market values to notional amounts varied considerably across individual market segments, ranging from less than 1% for FRAs to more than 15% for equity-linked options. Interestingly, the ratio was of the same order of magnitude in the two major individual market segments: outright forwards and forex swaps (3.9%), and interest rate swaps (3.5%). This stands in sharp contrast to the results of the 1995 survey, which had founds a considerably higher value of replacement costs for foreign exchange contracts.

13 14

The amount used to calculate payments or receipts – for interest rate contracts, for instance, this amount is not exchanged. A measure of the cost of replacing the contract at prevailing market prices.

43

Table 1 The global over-the-counter (OTC) derivatives markets1 Positions at end-June 1998, in billions of US dollars

Notional amounts

Gross market values

A. Foreign exchange contracts Outright forwards and forex swaps Currency swaps Options

18,719 12,149 1,947 4,623

799 476 208 115

B. Interest rate contracts2 FRAs Swaps Options

42,368 5,147 29,363 7,858

1,160 33 1,018 108

C. Equity-linked contracts Forwards and swaps Options

1,274 154 1,120

190 20 170

451 192 259 153 106

38 10 28 -

E. Estimated gaps in reporting

7,100

240

GRAND TOTAL GROSS CREDIT EXPOSURE3

69,912

2,427 1,203

98 14,256

3

D. Commodity Contracts Gold Other Forwards and swaps Options

Memorandum items: Credit -linked and other OTC contracts4 Exchange-traded contracts5 Source: BIS 1

All figures are adjusted for double-counting. Notional amounts outstanding have been adjusted by halving positions vis-àvis other reporting dealers. Gross market values have been calculated as the sum of the total gross positive market value of contracts and the absolute value of the gross negative market value of contracts with non-reporting counterparties. 2 Single-currency contracts only 3 Gross market values after taking into account legally enforceable bilateral netting agreements. 4 Gross market values not adjusted for double-counting 5 Sources: Futures Industry Association and various futures and options exchanges

44

Annex 2 Forward exchange rate calculations Forward exchange rates are priced from interest rate differentials. For instance, UK interest rates less US interest rates determine the forward rate for a £-$ future (or swap). As with interest rate forwards, it is vital to remember that forward rates are arithmetical calculations and not an individual trader’s opinion of what the spot rate will be at the settlement date quoted.

Spot One month Three months

Spot/forward Current interest rates DM/$ exchange rate DM A B C

Dollar D

E

1.565 1.562 1.556

5.31% 5.42%

0.44% 1.36%

3.08% 0.26% 3.00% 0.75%

Implied forward rate is spot rate plus (spot rate multiplied by the interest rate differential)

Column A = One and three month forward rates are Spot rate (col. A) + [spot rate * (col.C - col. E)] e.g. 1.565 + [1.565 * (0.0026-0.0044)] = 1.565 + [1.565 * -0.0018] = 1.565 - .0028 = 1.562 Columns B and D = Annualised interest rates for relevant currency Columns C and E = Period rate for relevant currency e.g. 0.26% = 3.08%/12 and 0.75% = 3.00%/4

45

Annex 3 Forward interest rate calculations This table shows the calculation, using compound interest, for forward interest rates.

Current interest rates No. of days

3 month 6 month 9 month 12 month

(i) annual rate

Implied 3 month forward

(ii) period rate

A

B

C

91 182 273 365

10% 12% 14% 16%

2.4% 5.8% 10.3% 16.0%

(iii) period rate

now in 3 months’ time in 6 months’ time in 9 months’ time

(iv) annual rate

D

E

2.4% 3.3% 4.2% 5.2%

10.0% 14.0% 18.1% 22.1%

Column B = interest rates from the yield curve Column C = Col.B to the power of (days in period/365) e.g. 1.024 = 1.10^(91/365) Column D = Col. C / Col.C T-1 e.g. 1.033 = 1.058/1.024 Column E = Col. D to the power of (365/days in period) e.g. 1.14 = 1.033^(365/91)

Using simple interest rates, then If interest rate for period X is A%, and for period Y is B%, then the forward rate for the period from end of X to end of Y is Forward rate = B% / (1-[X/Y]) - ([X/Y]*A%)/(1-[X/Y]) This looks difficult; but when Y = 2*X (e.g X is 3 months, Y is 6 months) then [X/Y] is 0.5, giving (simplified) Forward rate = 2*B% - A%

(or B% + (B-A)).

e.g. 2 * 12% - 10% = 24% - 10% = 14% or 12% + (12%-10%) = 12% + 2% = 14% 46

Annex 4

Swap spreads and government bond yields

FIXED RATE

FLOATING RATE

Government bond yield + swap

=

LIBOR

spread

Swap spreads are quoted in reference to Libor ie the quoted spread is the fixed side of the swap and will be priced off the government bond yield. For example, a 5 year government bond yield has a yield of 6.35%, and the 5 year swap spread is 23bp/25bp. A fixed yield of 6.58/6.60% would then swap into LIBOR flat (depending which way the swap counterparty wants to swap).

In the table below 25/21 refers to bid/offer, eg you pay a fixed rate of T + 25bp in order to receive US equivalent of LIBOR; or pay LIBOR equivalent to receive T + 21bp. The spread is the turn which the swap broker makes ie the difference between his buying and selling rates. In the UK, swap rates are sometimes quoted in absolute terms; but they are still priced off government bond yields.

USD ($)

GBP (£)

2 year

Treasury + 25/21

5.54 – 5.49

3 year

Treasury + 34/29

5.90 – 5.85

5 year

Treasury + 32/27

6.52 – 6.47

Quoting of Swap Rates in US and UK

47

Cashflows for issuer

Assume a company issues a fixed rate three year bond, but wants a floating rate liability and wants to make payments on a semi-annual basis. ( - indicates the company is making a payment, + indicates the company is receiving a payment).

Year

Swap fixed

Swap floating

receipts

payments

0.5 1.0

- 6m LIBOR - 20bp +10.0%

1.5 2.0

- 6m LIBOR - 20bp

+10.0%

- 6m LIBOR - 20bp

-10.0%

- 6m LIBOR - 20bp

48

- 6m LIBOR – 20bp - 6m LIBOR – 20bp

-10.0%

- 6m LIBOR - 20bp +10.0%

Net

- 6m LIBOR – 20bp

- 6m LIBOR - 20bp

2.5 3.0

Bond coupon

- 6m LIBOR – 20bp - 6m LIBOR – 20bp

-10.0%

- 6m LIBOR – 20bp

Annex 5 Cash flow and margining

In the UK the short sterling contract traded on the exchange (LIFFE) refers to the 3 month interbank rate on settlement date. One contract is for a notional amount of £500,000 and the minimum price movement is one “tick” - in the case of this contract, 0.01%. The price traded is “100 less the expected (annualised) interest rate”. For instance, if the interest rate on the next settlement date is expected to be 10%, the contract will trade for 90. The value of a tick movement is £500,000 * 0.01% * 0.25 (0.25 because it is a three month contract but the interest rate is quoted on an annualised basis) = £12.50. If the expected interest rate on settlement date falls to 9%, the contract price rises to 91 and a purchaser would therefore receive a cash payment of £12,500 (£12.50 * 100 ticks); the person who had sold a contract would pay this amount. This means that any profit or loss is paid over throughout the life of the contract rather than at its maturity.

The daily cash flows involved in a futures contract, a forward, a repo and a cash position in the underlying security will be different. Assume a long position is taken on a security worth 100, and over the next fortnight its secondary market value drops to 92. The cash flows for different contracts will be: Market Price

Cash holding

Forward

-

Future (with 2.5% margin) -2.5

Repo (with 2.5% cash margin1) -2.5

Day 1

100

-100

5

98

-

-

-2.0

-2.0

8

95

-

-

-2.9

-2.9

12

93

-

-

-2.0

-2.0

13

92

-

-100

-90.7

-90.7

-100

-100

-100

-100

Total

Market value of security at end of day 13 is 92

1

The precise margining requirements depend on the maturity of the underlying securities.

49

In the “cash” column, the security is purchased on day 1; whereas using a forward, the price is agreed on day 1, but settlement is delayed until day 13. Using a future, or a spot purchase financed by repo for 13 days, margin is paid out each day, and the spot price less margin paid on day 13.

In practice, market pricing of these different contracts will be slightly different in order to take account of the different timing of cash flows, so that the net present value of the flows will be equalised (ex ante).

50

GLOSSARY1

B Barrier Option: An option, which is only exercised when the underlying item reaches a predetermined price.

Black Scholes options pricing model: A mathematical formula used to value options.

C Call option: An option that gives the holder the right, but not the obligation, to buy an underlying item.

Cap: An option that sets a ceiling on the rate paid on an underlying item. Most commonly, caps are written on interest rates. The purchase of a cap option protects the purchaser from increases in interest rates. If the agreed contract (strike) price or rate is exceeded on the settlement date, the writer pays the purchaser the difference between market and contract price, times the notional principal.

Caption: An option to purchase a cap.

Collar: A combination of the purchase of a cap option and the sale of a floor option, creating a price boundary for the underlying item. Most commonly, collars are written on interest rates. Sometimes a collar is termed a corridor.

Collateral: An asset, usually a financial asset, provided by one counterparty to another to reduce the latters’ credit risk.

Contract price: See also "strike price." 1

This glossary is drawn primarily from the IMF Working Paper WP/98/24: "The Statistical Measurement of Financial Derivatives".

51

Credit Default Swap: A credit derivative in which the counterparties swap the risk premium inherent in an interest rate on a bond(s) or loan(s) – on an ongoing basis – for a cash payment in the event of default by the debtor.

Credit Derivative: A financial derivative whose primary purpose is to trade credit risk.

Credit (or counterparty) risk: The risk that the entity on which a financial claim is held will default.

Cross-Currency Interest Rate (Currency) swap:

An exchange of specified amounts of

two different currencies of equal net present value, with subsequent repayments, both interest and repayment flows, made according to predetermined rules.

D Digital Option: These options are only exercised when the underlying item reaches a pre-determined price and then only pay a fixed amount regardless of how far in-themoney the option was.

E Equity option: An option which gives the purchaser the right, but not the obligation to buy (call) or sell (put) an individual equity, a basket of equities, or an equity index at an agreed contract (strike) price on or before a specified date.

Equity swap: A swap in which one party exchanges a rate of return linked to an equity investment for either the rate of return on another equity investment, (such as swapping rates of return on different equity indices), or for the rate of return on a non-equity investment, such as an interest rate. Net cash settlement payments may be made.

52

F Floor: An option that sets a floor on the rate paid on an underlying item. Most commonly, floors are written on interest rates. The purchase of a floor option protects the purchaser from declines in interest rates. If the market rate falls below the contract (strike) price or rate, the writer pays the purchaser the difference between market and contract price, times the notional principal.

Foreign Exchange swaps: A sale/purchase of currencies and a simultaneous forward purchase/sale of the same currencies.

Forward foreign exchange contracts: A forward contract whereby the counterparties commit to transact in foreign currencies at an agreed exchange rate in a specified amount on some agreed date.

Forward rate agreements (FRA): A forward contract in which two counterparties agree on a specified interest rate to be paid, at a specified settlement date, on a notional amount of principal of a specified maturity in one currency, that is never exchanged. At settlement, a net cash payment is made equal to the difference between the specified rate and the actual market interest rate times the notional amount of principal. Which counterparty pays and which receives depends on whether the actual market rate is above or below the specified rate.

Futures: Forward contracts traded on an organised exchange. Futures contracts are highly standardised in order to facilitate the creation of liquid markets.

G

Gross Market Value: A measure of the cost of replacing a financial derivative contract at prevailing market prices. The value may be positive or negative.

53

H Hedging: A method of reducing financial risk by acquiring a position in one instrument which offsets, either partially or entirely, a risk inherent in another position held or anticipated to be held.

I Initial margin:

Margin payments that are made on the acquisition of a financial

derivative contract. Initial margin is most commonly associated with transactions on organised exchanges, because the clearing house acts as the counterparty to all transactions, and requires initial margin to protect it against the credit risk of its counterparties.

Interest rate swap: Interest rate swaps involve an exchange of cash flows related to interest payments, or receipts, on a notional amount of principal in one currency over a period of time. For example, payments based on a floating rate of interest are swapped for payments based on a fixed rate of interest. Typically, on each settlement date net cash settlement payments are made by one counterparty to the other reflecting the difference between the fixed and floating rates of interest, times the notional amount of principal.

L Leverage: Having exposure to the full benefits arising from holding a position in a financial asset, without having had to fund the entire purchase price.

Liquid market: A market in which individual market participants can transact quickly and efficiently without, in normal circumstances, significantly altering the prevailing market price. Characteristics of a liquid market include a small spread between buying and selling prices, and the ability to transact in large amounts.

54

M Marked to market: Revaluing the price of a financial asset or liability to the prevailing market price.

N Net cash settlement payments: Payments made in cash on the exercise of a financial derivative by one counterparty to meet its net liability to another counterparty.

Net present value: The net present value of any financial instrument is the discounted value of expected net future receipts (that is, gross receipts less gross payments) associated with the instrument.

Non-deliverable forward (NDF): A foreign currency forward contract, usually traded offshore, which is settled on a net basis in a major currency such as dollars. An NDF typically allows a non-resident to have an exposure to a currency without needing to receive or pay that currency.

Notional amount: The principal amount of a financial derivatives contract necessary for calculating payments or receipts but which is not itself exchange.

O Option: A contract that gives the purchaser the right but not the obligation to buy (call option) or sell (put option) a specified underlying item – real or financial – at an agreed contract (strike) price on or before a specified date from the writer of the option.

Option premium: The payment by the purchaser of the option to the writer of the option. The value of the option premium, at inception, reflects the market price of the option.

Option writer: The seller of an option contract.

55

Over-the-counter (OTC) financial derivatives:

Financial derivatives in which

transactions occur outside of an organised exchange (off-exchange) and involve major market participants, such as financial institutions.

P Put option: An option that gives the holder the right, but not the obligation, to sell an underlying item.

S Strike price: The price agreed in a financial derivative contract at which transactions, if any, in the underlying asset take place. Also called contract price.

Swaps: A forward-type financial derivative contract in which two counterparties agree to exchange cash flows determined with reference to prices of, say, currencies or interest rates, according to pre-determined rules.

T Total return swap: A credit derivative under which the cash flows and capital gains and losses related to the liability of a lower rated entity are swapped for cash flows related to a guaranteed interest rate such as an inter-bank rate plus a margin.

V Variation margin: Margin that is paid during the life of the financial derivative contract, and is affected by its price. As the price of the financial derivative contract moves against one counterparty, and his/her liability position increases, variation margin is paid by that counterparty. Variation margin is most commonly associated with transactions on organised exchanges, because the clearing house acts as the counterparty to all transactions, and requires variation margin to protect it against the credit risk of its counterparties. On some markets, variation margin is paid over from the counterparty

56

with the net liability position, to the counterparty with the net asset position, as a form of on-going settlement of liabilities.

Volatility: The measure of the variability of the price of a financial asset or liability over a specified time period.

W Warrants: Option-type tradeable instruments giving the holder the right to buy, at an agreed contract (strike) price for a specified period of time, from the issuer of the warrant, a specified amount of the underlying asset, such as equities and bonds.

57

Further Reading

Hull, John C, “Options, Futures and other Derivatives”, Prentice Hall International (1997)

Hong Kong Monetary Authority, “Derivatives in Plain Words”, (1997)

BIS, “Macroeconomic and monetary policy issues raised by the growth of derivatives markets (Hanoun Report)”, (November 1994)

BIS, “Report on OTC derivatives: settlement procedures and counterparty risk management”, (September 1998) BIS and IOSCO, "Framework for Supervisory Information about Derivatives and Trading Activities", (September 1998)

BIS, “Proposals for improving global derivatives market statistics (Yoshikuni report)”, (July 1996)

(Recent BIS papers can be found on the web-site www.bis.org/publ/index.htm

58

Handbooks in this series

No

Title

Author

1 2 3

Glenn Hoggarth Tony Latter Lionel Price

7 8 9 10

Introduction to monetary policy The choice of exchange rate regime Economic analysis in a central bank: Models versus judgement Internal audit in a central bank The management of government debt Primary dealers in government securities Markets Basic principles of banking supervision Payment systems Deposit insurance Introduction to monetary operations

11 12 13 14

Government securities: primary issuance Causes and management of banking crises The retail market for government debt Capital flows

15 16 17

Consolidated Supervision of Banks Repo of Government Securities Financial Derivatives

4 5 6

Christopher Scott Simon Gray Robin McConnachie Derrick Ware David Sheppard Ronald MacDonald Simon Gray and Glenn Hoggarth Simon Gray Tony Latter Robin McConnachie Glenn Hoggarth and Gabriel Sterne Ronald MacDonald Simon Gray Simon Gray and Joanna Place

The text of the Handbooks can be found on the Bank of England’s web site www.bankofengland.co.uk

59

Handbooks: Lecture Series As financial markets have become increasingly complex, central bankers’ demands for specialised technical assistance and training has risen. This has been reflected in the content of lectures and presentations given by CCBS and Bank staff on technical assistance and training courses. In order to give wider distribution to the material developed in these lectures, in 1999 we have introduced new series of Handbooks: Lecture Series.

The aim of this new series is to give wider exposure to lectures and presentations that address topical and technically advanced issues of relevance to central banks. The intention is both to spread ideas and knowledge and to add to the debate in the particular subject.

No

Titles

Author

1

Inflation Targeting: The British Experience

William A Allen

The text of the Handbooks can be found on the Bank of England’s web site www.bankofengland.co.uk

60