Introduction Or Basic Or Fundamentals Of Derivatives
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Session 2 Introduction to Derivatives
Basics
Finance is the study of risk. How to measure it How to reduce it How to allocate it
All finance problems ultimately boil down to three main questions: What are the cash flows, and when do they occur? Who gets the cash flows? What is the appropriate discount rate for those cash flows?
The difficulty, of course, is that normally none of those questions have an easy answer.
The market “pays” you for bearing non-diversifiable risk only. In general the more nondiversifiable risk that you bear, the greater the expected return
Basics
In this sense, we can view the field of finance as being about two issues: The elimination of diversifiable risk in portfolios; The allocation of systematic (nondiversifiable) risk to those members of society that are most willing to bear it.
What is a Derivative Security?
Derivative securities, more appropriately termed as derivative contracts, are assets which confer the investors who take positions in them with certain rights or obligations.
Why Do We Call Them Derivatives?
They owe their existence to the presence of a market for an underlying asset or portfolio of assets, which may be considered as primary securities. Consequently such contracts are derived from these underlying assets, and hence the name. Thus if there were to be no market for the underlying assets, there would be no derivatives.
Why derivatives and derivatives markets?
Because they somehow allow investors to better control the level of risk that they bear. They can help eliminate idiosyncratic risk. They can decrease or increase the level of systematic risk.
Example
This example illustrates an interesting notion – that insurance contracts (for property insurance) are really derivatives! They allow the owner of the asset to “sell” the insured asset to the insurer in the event of a disaster.
Basics
Positions Buy Position - “LONG” Sell Position – “ SHORT”
Basics
Commissions – Virtually all transactions in the financial markets requires some form of commission payment.
Basics
Bid-Ask spread If you wish to sell, you will get a “BID” quote If you wish to buy you will get an “ASK” quote.
Basics
Bid-ask spread can be a huge factor in determining the profitability of a trade. Many “trading strategies” lose their effectiveness when the bid-ask spread is considered.
Basics
Market Efficiency Discovery and analysis of new information. The limiting factor in this is the transaction costs associated with the market. For this reason, it is better to say that financial markets are efficient to within transactions costs. Some financial economists say that financial markets are efficient to within the bid-ask spread.
Basics
Credit risk – the risk that your trading partner might not honor their obligations. Liquidity risk – the risk that when you need to buy or sell an instrument you may not be able to find a counterparty.
Basics
So now we are going to begin examining the basic instruments of derivatives. In particular we will look at (tonight):
Forwards Futures Options
Forward Contracts The specified price for the sale is known as the delivery price, we will denote this as K.
Note that K is set such that at initiation of the contract the value of the forward contract is 0. Thus, by design, no cash changes hands at time 0.
Forward Contracts As time progresses the delivery price doesn’t change, but the current spot (market) rate does. Thus, the contract gains (or loses) value over time.
Consider the situation at the maturity date of the contract. If the spot price is higher than the delivery price, the long party can buy at K and immediately sell at the spot price ST, making a profit of (ST-K), whereas the short position could have sold the asset for ST, but is obligated to sell for K, earning a profit (negative) of (K-ST).
Forward Contracts Consider the situation at the maturity date of the contract. If the spot price is higher than the delivery price, the long party can buy at K and immediately sell at the spot price ST, making a profit of (ST-K),
Forward Contracts Short position could have sold the asset for ST, but is obligated to sell for K, earning a profit (negative) of (K-ST).
Forward Contracts
If, however, the market price is less than 40, you are not pleased because you are paying more than the market price for the wheat. Indeed, we can determine your net payoff to the trade by applying the formula: payoff = ST – K, since you gain an asset worth ST, but you have to pay K for it. We can graph the payoff function:
Forward Contracts Payoff to Futures Position Delivery Price (K) is 40 4
Payoff to Forwards
3 2 1 0 -1
0
1
2
3
4
5
-2 -3 -4 Spot Price, December 14
6
7
8
Forward Contracts
What about the short party? They have agreed to sell wheat to you for Rs.40 on December 14. Their payoff is positive if the market price is less than Rs.40 – they force you to pay more for the wheat than they could sell it for on the open market.
Indeed, you could assume that what they do is buy it on the open market and then immediately deliver it to you in the forward contract.
Forward Contracts
Their payoff is negative, however, if the market price is greater than Rs.40.
They could have sold for more than Rs.40 had they not agreed to sell it to you.
So their payoff function is the mirror image of your payoff function:
Forward Contracts Payoff to Short Futures Position Delivery Price (K) is 40 4
Payoff to Forwards
3 2 1 0 -1
0
1
2
3
4
5
-2 -3 -4 Market (Spot) Price, December 14
6
7
8
Forward Contracts
Clearly the short position is just the mirror image of the long position, and, taken together the two positions cancel each other out:
Forward Contracts Long and Short Positions in a Forward Contract at Rs.40 4 3
Short Position
2
Long Position
Payoff
1 0 -1 -2
0
1
2
3
4
Net Position
-3 -4 Price
5
6
7
8
Futures Contracts
A futures contract is similar to a forward contract in that it is an agreement between two parties to buy or sell an asset at a certain time for a certain price. Futures, however, are usually exchange traded and, to facilitate trading, are usually standardized contracts. This results in more institutional detail than is the case with forwards.
Futures Contracts
Exchange guarantees performance of the contract regardless of whether the other party fails.
Futures Contracts
The exchange will usually place restrictions and conditions on futures. These include:
Daily price (change) limits. For commodities, grade requirements. Delivery method and place. How the contract is quoted.
Note however, that the basic payoffs are the same as for a forward contract.
Options Contracts
A Call option is the right, but not the obligation, to buy the underlying asset by a certain date for a certain price. A Put option is the right, but not the obligation, to sell the underlying asset by a certain date for a certain price.
Options Contracts
The date when the option expires is known as the exercise date, the expiration date, or the maturity date. The price at which the asset can be purchased or sold is known as the strike price.
Options Contracts
European - Holder can exercise only on the maturity date. American - Holder can exercise on any date up to and including the exercise date. An options contract is always costly to enter as the long party. The short party always is always paid to enter into the contract
Looking at the payoff diagrams you can see why…
Comparison of Futures/Forwards versus Options Instrument
Nature of Long’s Commitment
Nature of Short’s Commitment
Forward/Futures Obligation to buy Obligation to Contract sell Call Options
Right to buy
Obligation to sell
Put Options
Right to sell
Obligation to buy
Options Contracts
Let’s say that you entered into a call option on a stock:
Today the stock is selling for roughly Rs.78.80/share, so let’s say you entered into a call option that would let you buy the stock in December at a price of Rs.80/share.
Options Contracts
If in December the market price were greater than 80, you would exercise your option, and purchase the share for 80.
Options Contracts
If, in December the stock were selling for less than 80, you could buy the stock for less by buying it in the open market, so you would not exercise your option. Thus your payoff to the option is Rs.0 if the stock is less than 80 It is (ST-K) if stock is worth more than 80
Thus, your payoff diagram is:
Options Contracts Long Call with Strike Price (K) = 80 80
Payoff
60 40 20 0 0
20
40
60
K = 80
100
-20 Terminal Stock Price T
120
140
160
Options Contracts
What if you had the short position? Well, after you enter into the contract, you have granted the option to the long-party. If they want to exercise the option, you have to do so. Of course, they will only exercise the option when it is in there best interest to do so – that is, when the strike price is lower than the market price of the stock.
Options Contracts
If STK, Long party will exercise their option and you will have to sell them an asset that is worth ST for K.
Your payoff:
payoff = min(0,ST-K), which has a graph that looks like:
Options Contracts
Short Call Position with Strike Price (K) = 80
Payoff to Short Position
21.25 0 0
20
40
60
80
100
-21.25
-42.5 -63.75 -85 Ending Stock Price
120
140
160
Options Contracts
This is obviously the mirror image of the long position. Notice, however, that at maturity, the short option position can NEVER have a positive payout – the best that can happen is that they get 0.
Options Contracts
This is why the short option party always demands an up-front payment – it’s the only payment they are going to receive. Option premium or price.
Once again, the two positions “net out” to zero:
Options Contracts Long and Short Call Strike Prices of 80 100 80 60
Long Call
40 Payoff
20 0 -20 0 -40
Net Position 20
40
60
80
100
Short Call
-60 -80 -100 Ending Stock Price
120
140
160
Options Contracts
Recall that a put option grants the long party the right to sell the underlying at price K. Returning to our example, if K=80, the long party will only elect to exercise the option if the price of the stock in the market is less than 80, otherwise they would just sell it in the market.
Options Contracts
The payoff to the holder of the long put position, therefore is simply payoff = max(0, K-ST)
Options Contracts Payoff to Long Put Option with Strike Price of 80 80 70 60 Payoff
50 40 30 20 10 0 -10 0
20
40
60
80
100
Ending Stock Price
120
140
160
Options Contracts
The Short granted the option to the Long. The short has to buy the stock at price K, when long wants. Long will only do this when the stock price is less than the strike price. Thus, the payoff function for the short put position is: payoff = min(0, ST-K)
Options Contracts Short Put Option Strike Price of 80
0 0
20
40
60
80
100
Payoff
-21.25
-42.5
-63.75
-85 Ending Stock Price
120
140
160
Options Contracts
Since the short put party can never receive a positive payout at maturity, they demand a payment up-front from the long party – that is, they demand that the long party pay a premium to induce them to enter into the contract.
Once again, the short and long positions net out to zero: when one party wins, the other loses.
Options Contracts
Since the short put party can never receive a positive payout at maturity, they demand a payment up-front from the long party – that is, they demand that the long party pay a premium to induce them to enter into the contract.
Options Contracts
Once again, the short and long positions net out to zero: when one party wins, the other loses.
Options Contracts
Long and Short Put Options Strike Prices of 80
100 80
Long Position
60
Payoff
40
Net Position
20 0 -20
0
20
40
60
80
100
-40 -60
Short Position
-80 -100 Ending Stock Price
120
140
160
Options Contracts
For a European call, the payoff to the option is:
For a European put it is
Max(0,ST-K) Max(0,K-ST)
The short positions are just the negative of these:
Short call: -Max(0,ST-K) = Min(0,K-ST)
Short put: -Max(0,K-ST) = Min(0,ST-K)
Options Contracts
Traders frequently refer to an option as being “in the money”, “out of the money” or “at the money”.
Options Contracts
An “in the money” option means one where the price of the underlying is such that if the option were exercised immediately, the option holder would receive a payout.
For a call option this means that St>K For a put option this means that St
Options Contracts
An “at the money” option means one where the strike and exercise prices are the same.
Options Contracts
An “out of the money” option means one where the price of the underlying is such that if the option were exercised immediately, the option holder would NOT receive a payout.
For a call option this means that StK.
Options Contracts Long Call with Strike Price (K) = 80 80
Payoff
60
At the money
40
Out of the money
In the money
20 0 0
20
40
60
K = 80
100
-20 Terminal Stock Price T
120
140
160
Options Contracts
One interesting notion is to look at the payoff from just owning the stock – its value is simply the value of the stock:
Options Contracts Payout Diagram for a Long Position 180 160 140
Payoff
120 100 80 60 40 20 0 0
20
40
60
80
100
Ending Stock Price
120
140
160
Options Contracts
What is interesting is if we compare the payoff from a portfolio containing a short put and a long call with the payoff from just owning the stock:
Options Contracts Payoff Diagram for a Long Position 200 150 Stock 100 Long Call f o y a P
50 0 0
20
40
60
80
100
-50 Short Put -100 Ending Stock Price
120
140
160
Options Contracts
Notice how the payoff to the options portfolio has the same shape and slope as the stock position – just offset by some amount? This is hinting at one of the most important relationships in options theory – Put-Call parity.
Options Contracts Payoff Diagram for a Long Position 200 150 100
f o y a P
50 0 0
20
40
60
80
100
-50 -100 Ending Stock Price
120
140
160
Swaps
A swap is a contractual agreement between two parties to exchange specified cash flows at pre-defined points in time. There are two broad categories of swaps – Interest Rate Swaps and Currency Swaps.
Interest Rate Swaps
In the case of these contracts, the cash flows being exchanged, represent interest payments on a specified principal, which are computed using two different parameters. For instance one interest payment may be computed using a fixed rate of interest, while the other may be based on a variable rate such as LIBOR.
Interest Rate Swaps (Cont…)
There are also swaps where both the interest payments are computed using two different variable rates – For instance one may be based on the LIBOR and the other on the Prime Rate of a country. Obviously a fixed-fixed swap will not make sense.
Interest Rate Swaps Since both the interest payments are denominated in the same currency, the actual principal is not exchanged. Consequently the principal is known as a notional principal. Also, once the interest due from one party to the other is calculated, only the difference or the net amount is exchanged.
Currency Swaps
These are also known as cross-currency swaps. In this case the two parties first exchange principal amounts denominated in two different currencies. Each party will then compute interest on the amount received by it as per a pre-defined yardstick, and exchange it periodically.
Currency Swaps
At the termination of the swap the principal amounts will be swapped back. In this case, since the payments being exchanged are denominated in two different currencies, we can have fixedfloating, floating-floating, as well as fixedfixed swaps.
Actors in the Market
There are three broad categories of market participants: Hedgers Speculators Arbitrageurs
Hedgers
These are people who have already acquired a position in the spot market prior to entering the derivatives market. They may have bought the asset underlying the derivatives contract, in which case they are said to be Long in the spot.
Hedgers (Cont…)
Or else they may have sold the underlying asset in the spot market without owning it, in which case they are said to have a Short position in the spot market. In either case they are exposed to Price Risk.
Hedgers (Cont…)
Price risk is the risk that the price of the asset may move in an unfavourable direction from their standpoint. What is adverse depends on whether they are long or short in the spot market. For a long, falling prices represent a negative movement.
Hedgers (Cont…)
For a short, rising prices represent an undesirable movement. Both longs and shorts can use derivatives to minimize, and under certain conditions, even eliminate Price Risk. This is the purpose of hedging.
Speculators
Unlike hedgers who seek to mitigate their exposure to risk, speculators consciously take on risk. They are not however gamblers, in the sense that they do not play the market for the sheer thrill of it.
Speculators (Cont…)
They are calculated risk takers, who will take a risky position, only if they perceive that the expected return is commensurate with the risk. A speculator may either be betting that the market will rise, or he could be betting that the market will fall.
Hedgers & Speculators
The two categories of investors complement each other. The market needs both types of players to function efficiently. Often if a hedger takes a long position, the corresponding short position will be taken by a speculator and vice versa.
Arbitrageurs
These are traders looking to make costless and risk-less profits. Since derivatives by definition are based on markets for an underlying asset, it is but obvious that the price of a derivatives contract must be related to the price of the asset in the spot market.
Arbitrageurs (Cont…)
Arbitrageurs scan the market constantly for discrepancies from the required pricing relationships. If they see an opportunity for exploiting a misaligned price without taking a risk, and after accounting for the opportunity cost of funds that are required to be deployed, they will seize it and exploit it to the hilt.
Arbitrageurs (Cont…)
Arbitrage activities therefore keep the market efficient. That is, such activities ensure that prices closely conform to their values as predicted by economic theory.
Why Use Derivatives
Derivatives have many vital economic roles in the free market system. Firstly, not every one has the same propensity to take risks. Hedgers consciously seek to avoid risk, while speculators consciously take on risk. Thus risk re-allocation is made feasible by active derivatives markets.
Why Derivatives? (Cont…)
In a free market economy, prices are everything. It is essential that prices accurately convey all pertinent information, if decision making in such economies is to be optimal. How does the system ensure that prices fully reflect all relevant information?
Why Derivatives? (Cont…)
It does so by allowing people to trade. An investor whose perception of the value of an asset differs from that of others, will seek to initiate a trade in the market for the asset. If the perception is that the asset is undervalued, there will be pressure to buy.
Why Derivatives? (Cont…)
On the other hand if there is a perception that the asset is overvalued, there will be pressure to sell. The imbalance on one or the other side of the market will ensure that the price eventually attains a level where demand is equal to the supply.
Why Derivatives? (Cont…)
When new information is obtained by investors, trades will obviously be induced, for such information will invariably have implications for asset prices. In practice it is easier and cheaper for investors to enter derivatives markets as opposed to cash or spot markets.
Why Derivatives? (Cont…)
This is because, the investor can trade in a derivatives market by depositing a relatively small performance guarantee or collateral known as the margin. On the contrary taking a long position in the spot market would entail paying the full price of the asset.
Why Derivatives? (Cont…)
Similarly it is easier to take a short position in derivatives than to short sell in the spot markets. In fact, many assets cannot be sold short in the spot market. Consequently new information filters into derivatives markets very fast.
Why Derivatives? (Cont…)
Thus derivatives facilitate Price Discovery. Because of the high volumes of transactions in such markets, transactions costs tend to be lower than in spot markets. This in turn fuels even more trading activity. Also derivative markets tend to be very liquid.
Why Derivatives? (Cont…)
That is, investors who enter these markets, usually find that traders who are willing to take the opposite side are readily available. This enables traders to trade without having to induce a transaction by making major price concessions.
Why Derivatives? (Cont…)
Derivatives improve the overall efficiency of the free market system. Due to the ease of trading, and the lower associated costs, information quickly filters into these markets. At the same time spot and derivatives prices are inextricably linked.
Why Derivatives? (Cont…)
Consequently, if there is a perceived misalignment of prices, arbitrageurs will move in for the kill. Their activities will eventually lead to the efficiency of spot markets as well. Finally derivatives facilitate speculation. And speculation is vital for the free market system.
Basics
Finance is the study of risk. How to measure it How to reduce it How to allocate it
All finance problems ultimately boil down to three main questions: What are the cash flows, and when do they occur? Who gets the cash flows? What is the appropriate discount rate for those cash flows?
The difficulty, of course, is that normally none of those questions have an easy answer.
The market “pays” you for bearing non-diversifiable risk only. In general the more nondiversifiable risk that you bear, the greater the expected return
Basics
In this sense, we can view the field of finance as being about two issues: The elimination of diversifiable risk in portfolios; The allocation of systematic (nondiversifiable) risk to those members of society that are most willing to bear it.
What is a Derivative Security?
Derivative securities, more appropriately termed as derivative contracts, are assets which confer the investors who take positions in them with certain rights or obligations.
Why Do We Call Them Derivatives?
They owe their existence to the presence of a market for an underlying asset or portfolio of assets, which may be considered as primary securities. Consequently such contracts are derived from these underlying assets, and hence the name. Thus if there were to be no market for the underlying assets, there would be no derivatives.
Why derivatives and derivatives markets?
Because they somehow allow investors to better control the level of risk that they bear. They can help eliminate idiosyncratic risk. They can decrease or increase the level of systematic risk.
Example
This example illustrates an interesting notion – that insurance contracts (for property insurance) are really derivatives! They allow the owner of the asset to “sell” the insured asset to the insurer in the event of a disaster.
Basics
Positions Buy Position - “LONG” Sell Position – “ SHORT”
Basics
Commissions – Virtually all transactions in the financial markets requires some form of commission payment.
Basics
Bid-Ask spread If you wish to sell, you will get a “BID” quote If you wish to buy you will get an “ASK” quote.
Basics
Bid-ask spread can be a huge factor in determining the profitability of a trade. Many “trading strategies” lose their effectiveness when the bid-ask spread is considered.
Basics
Market Efficiency Discovery and analysis of new information. The limiting factor in this is the transaction costs associated with the market. For this reason, it is better to say that financial markets are efficient to within transactions costs. Some financial economists say that financial markets are efficient to within the bid-ask spread.
Basics
Credit risk – the risk that your trading partner might not honor their obligations. Liquidity risk – the risk that when you need to buy or sell an instrument you may not be able to find a counterparty.
Basics
So now we are going to begin examining the basic instruments of derivatives. In particular we will look at (tonight):
Forwards Futures Options
Forward Contracts The specified price for the sale is known as the delivery price, we will denote this as K.
Note that K is set such that at initiation of the contract the value of the forward contract is 0. Thus, by design, no cash changes hands at time 0.
Forward Contracts As time progresses the delivery price doesn’t change, but the current spot (market) rate does. Thus, the contract gains (or loses) value over time.
Consider the situation at the maturity date of the contract. If the spot price is higher than the delivery price, the long party can buy at K and immediately sell at the spot price ST, making a profit of (ST-K), whereas the short position could have sold the asset for ST, but is obligated to sell for K, earning a profit (negative) of (K-ST).
Forward Contracts Consider the situation at the maturity date of the contract. If the spot price is higher than the delivery price, the long party can buy at K and immediately sell at the spot price ST, making a profit of (ST-K),
Forward Contracts Short position could have sold the asset for ST, but is obligated to sell for K, earning a profit (negative) of (K-ST).
Forward Contracts
If, however, the market price is less than 40, you are not pleased because you are paying more than the market price for the wheat. Indeed, we can determine your net payoff to the trade by applying the formula: payoff = ST – K, since you gain an asset worth ST, but you have to pay K for it. We can graph the payoff function:
Forward Contracts Payoff to Futures Position Delivery Price (K) is 40 4
Payoff to Forwards
3 2 1 0 -1
0
1
2
3
4
5
-2 -3 -4 Spot Price, December 14
6
7
8
Forward Contracts
What about the short party? They have agreed to sell wheat to you for Rs.40 on December 14. Their payoff is positive if the market price is less than Rs.40 – they force you to pay more for the wheat than they could sell it for on the open market.
Indeed, you could assume that what they do is buy it on the open market and then immediately deliver it to you in the forward contract.
Forward Contracts
Their payoff is negative, however, if the market price is greater than Rs.40.
They could have sold for more than Rs.40 had they not agreed to sell it to you.
So their payoff function is the mirror image of your payoff function:
Forward Contracts Payoff to Short Futures Position Delivery Price (K) is 40 4
Payoff to Forwards
3 2 1 0 -1
0
1
2
3
4
5
-2 -3 -4 Market (Spot) Price, December 14
6
7
8
Forward Contracts
Clearly the short position is just the mirror image of the long position, and, taken together the two positions cancel each other out:
Forward Contracts Long and Short Positions in a Forward Contract at Rs.40 4 3
Short Position
2
Long Position
Payoff
1 0 -1 -2
0
1
2
3
4
Net Position
-3 -4 Price
5
6
7
8
Futures Contracts
A futures contract is similar to a forward contract in that it is an agreement between two parties to buy or sell an asset at a certain time for a certain price. Futures, however, are usually exchange traded and, to facilitate trading, are usually standardized contracts. This results in more institutional detail than is the case with forwards.
Futures Contracts
Exchange guarantees performance of the contract regardless of whether the other party fails.
Futures Contracts
The exchange will usually place restrictions and conditions on futures. These include:
Daily price (change) limits. For commodities, grade requirements. Delivery method and place. How the contract is quoted.
Note however, that the basic payoffs are the same as for a forward contract.
Options Contracts
A Call option is the right, but not the obligation, to buy the underlying asset by a certain date for a certain price. A Put option is the right, but not the obligation, to sell the underlying asset by a certain date for a certain price.
Options Contracts
The date when the option expires is known as the exercise date, the expiration date, or the maturity date. The price at which the asset can be purchased or sold is known as the strike price.
Options Contracts
European - Holder can exercise only on the maturity date. American - Holder can exercise on any date up to and including the exercise date. An options contract is always costly to enter as the long party. The short party always is always paid to enter into the contract
Looking at the payoff diagrams you can see why…
Comparison of Futures/Forwards versus Options Instrument
Nature of Long’s Commitment
Nature of Short’s Commitment
Forward/Futures Obligation to buy Obligation to Contract sell Call Options
Right to buy
Obligation to sell
Put Options
Right to sell
Obligation to buy
Options Contracts
Let’s say that you entered into a call option on a stock:
Today the stock is selling for roughly Rs.78.80/share, so let’s say you entered into a call option that would let you buy the stock in December at a price of Rs.80/share.
Options Contracts
If in December the market price were greater than 80, you would exercise your option, and purchase the share for 80.
Options Contracts
If, in December the stock were selling for less than 80, you could buy the stock for less by buying it in the open market, so you would not exercise your option. Thus your payoff to the option is Rs.0 if the stock is less than 80 It is (ST-K) if stock is worth more than 80
Thus, your payoff diagram is:
Options Contracts Long Call with Strike Price (K) = 80 80
Payoff
60 40 20 0 0
20
40
60
K = 80
100
-20 Terminal Stock Price T
120
140
160
Options Contracts
What if you had the short position? Well, after you enter into the contract, you have granted the option to the long-party. If they want to exercise the option, you have to do so. Of course, they will only exercise the option when it is in there best interest to do so – that is, when the strike price is lower than the market price of the stock.
Options Contracts
If ST
Your payoff:
payoff = min(0,ST-K), which has a graph that looks like:
Options Contracts
Short Call Position with Strike Price (K) = 80
Payoff to Short Position
21.25 0 0
20
40
60
80
100
-21.25
-42.5 -63.75 -85 Ending Stock Price
120
140
160
Options Contracts
This is obviously the mirror image of the long position. Notice, however, that at maturity, the short option position can NEVER have a positive payout – the best that can happen is that they get 0.
Options Contracts
This is why the short option party always demands an up-front payment – it’s the only payment they are going to receive. Option premium or price.
Once again, the two positions “net out” to zero:
Options Contracts Long and Short Call Strike Prices of 80 100 80 60
Long Call
40 Payoff
20 0 -20 0 -40
Net Position 20
40
60
80
100
Short Call
-60 -80 -100 Ending Stock Price
120
140
160
Options Contracts
Recall that a put option grants the long party the right to sell the underlying at price K. Returning to our example, if K=80, the long party will only elect to exercise the option if the price of the stock in the market is less than 80, otherwise they would just sell it in the market.
Options Contracts
The payoff to the holder of the long put position, therefore is simply payoff = max(0, K-ST)
Options Contracts Payoff to Long Put Option with Strike Price of 80 80 70 60 Payoff
50 40 30 20 10 0 -10 0
20
40
60
80
100
Ending Stock Price
120
140
160
Options Contracts
The Short granted the option to the Long. The short has to buy the stock at price K, when long wants. Long will only do this when the stock price is less than the strike price. Thus, the payoff function for the short put position is: payoff = min(0, ST-K)
Options Contracts Short Put Option Strike Price of 80
0 0
20
40
60
80
100
Payoff
-21.25
-42.5
-63.75
-85 Ending Stock Price
120
140
160
Options Contracts
Since the short put party can never receive a positive payout at maturity, they demand a payment up-front from the long party – that is, they demand that the long party pay a premium to induce them to enter into the contract.
Once again, the short and long positions net out to zero: when one party wins, the other loses.
Options Contracts
Since the short put party can never receive a positive payout at maturity, they demand a payment up-front from the long party – that is, they demand that the long party pay a premium to induce them to enter into the contract.
Options Contracts
Once again, the short and long positions net out to zero: when one party wins, the other loses.
Options Contracts
Long and Short Put Options Strike Prices of 80
100 80
Long Position
60
Payoff
40
Net Position
20 0 -20
0
20
40
60
80
100
-40 -60
Short Position
-80 -100 Ending Stock Price
120
140
160
Options Contracts
For a European call, the payoff to the option is:
For a European put it is
Max(0,ST-K) Max(0,K-ST)
The short positions are just the negative of these:
Short call: -Max(0,ST-K) = Min(0,K-ST)
Short put: -Max(0,K-ST) = Min(0,ST-K)
Options Contracts
Traders frequently refer to an option as being “in the money”, “out of the money” or “at the money”.
Options Contracts
An “in the money” option means one where the price of the underlying is such that if the option were exercised immediately, the option holder would receive a payout.
For a call option this means that St>K For a put option this means that St
Options Contracts
An “at the money” option means one where the strike and exercise prices are the same.
Options Contracts
An “out of the money” option means one where the price of the underlying is such that if the option were exercised immediately, the option holder would NOT receive a payout.
For a call option this means that St
Options Contracts Long Call with Strike Price (K) = 80 80
Payoff
60
At the money
40
Out of the money
In the money
20 0 0
20
40
60
K = 80
100
-20 Terminal Stock Price T
120
140
160
Options Contracts
One interesting notion is to look at the payoff from just owning the stock – its value is simply the value of the stock:
Options Contracts Payout Diagram for a Long Position 180 160 140
Payoff
120 100 80 60 40 20 0 0
20
40
60
80
100
Ending Stock Price
120
140
160
Options Contracts
What is interesting is if we compare the payoff from a portfolio containing a short put and a long call with the payoff from just owning the stock:
Options Contracts Payoff Diagram for a Long Position 200 150 Stock 100 Long Call f o y a P
50 0 0
20
40
60
80
100
-50 Short Put -100 Ending Stock Price
120
140
160
Options Contracts
Notice how the payoff to the options portfolio has the same shape and slope as the stock position – just offset by some amount? This is hinting at one of the most important relationships in options theory – Put-Call parity.
Options Contracts Payoff Diagram for a Long Position 200 150 100
f o y a P
50 0 0
20
40
60
80
100
-50 -100 Ending Stock Price
120
140
160
Swaps
A swap is a contractual agreement between two parties to exchange specified cash flows at pre-defined points in time. There are two broad categories of swaps – Interest Rate Swaps and Currency Swaps.
Interest Rate Swaps
In the case of these contracts, the cash flows being exchanged, represent interest payments on a specified principal, which are computed using two different parameters. For instance one interest payment may be computed using a fixed rate of interest, while the other may be based on a variable rate such as LIBOR.
Interest Rate Swaps (Cont…)
There are also swaps where both the interest payments are computed using two different variable rates – For instance one may be based on the LIBOR and the other on the Prime Rate of a country. Obviously a fixed-fixed swap will not make sense.
Interest Rate Swaps Since both the interest payments are denominated in the same currency, the actual principal is not exchanged. Consequently the principal is known as a notional principal. Also, once the interest due from one party to the other is calculated, only the difference or the net amount is exchanged.
Currency Swaps
These are also known as cross-currency swaps. In this case the two parties first exchange principal amounts denominated in two different currencies. Each party will then compute interest on the amount received by it as per a pre-defined yardstick, and exchange it periodically.
Currency Swaps
At the termination of the swap the principal amounts will be swapped back. In this case, since the payments being exchanged are denominated in two different currencies, we can have fixedfloating, floating-floating, as well as fixedfixed swaps.
Actors in the Market
There are three broad categories of market participants: Hedgers Speculators Arbitrageurs
Hedgers
These are people who have already acquired a position in the spot market prior to entering the derivatives market. They may have bought the asset underlying the derivatives contract, in which case they are said to be Long in the spot.
Hedgers (Cont…)
Or else they may have sold the underlying asset in the spot market without owning it, in which case they are said to have a Short position in the spot market. In either case they are exposed to Price Risk.
Hedgers (Cont…)
Price risk is the risk that the price of the asset may move in an unfavourable direction from their standpoint. What is adverse depends on whether they are long or short in the spot market. For a long, falling prices represent a negative movement.
Hedgers (Cont…)
For a short, rising prices represent an undesirable movement. Both longs and shorts can use derivatives to minimize, and under certain conditions, even eliminate Price Risk. This is the purpose of hedging.
Speculators
Unlike hedgers who seek to mitigate their exposure to risk, speculators consciously take on risk. They are not however gamblers, in the sense that they do not play the market for the sheer thrill of it.
Speculators (Cont…)
They are calculated risk takers, who will take a risky position, only if they perceive that the expected return is commensurate with the risk. A speculator may either be betting that the market will rise, or he could be betting that the market will fall.
Hedgers & Speculators
The two categories of investors complement each other. The market needs both types of players to function efficiently. Often if a hedger takes a long position, the corresponding short position will be taken by a speculator and vice versa.
Arbitrageurs
These are traders looking to make costless and risk-less profits. Since derivatives by definition are based on markets for an underlying asset, it is but obvious that the price of a derivatives contract must be related to the price of the asset in the spot market.
Arbitrageurs (Cont…)
Arbitrageurs scan the market constantly for discrepancies from the required pricing relationships. If they see an opportunity for exploiting a misaligned price without taking a risk, and after accounting for the opportunity cost of funds that are required to be deployed, they will seize it and exploit it to the hilt.
Arbitrageurs (Cont…)
Arbitrage activities therefore keep the market efficient. That is, such activities ensure that prices closely conform to their values as predicted by economic theory.
Why Use Derivatives
Derivatives have many vital economic roles in the free market system. Firstly, not every one has the same propensity to take risks. Hedgers consciously seek to avoid risk, while speculators consciously take on risk. Thus risk re-allocation is made feasible by active derivatives markets.
Why Derivatives? (Cont…)
In a free market economy, prices are everything. It is essential that prices accurately convey all pertinent information, if decision making in such economies is to be optimal. How does the system ensure that prices fully reflect all relevant information?
Why Derivatives? (Cont…)
It does so by allowing people to trade. An investor whose perception of the value of an asset differs from that of others, will seek to initiate a trade in the market for the asset. If the perception is that the asset is undervalued, there will be pressure to buy.
Why Derivatives? (Cont…)
On the other hand if there is a perception that the asset is overvalued, there will be pressure to sell. The imbalance on one or the other side of the market will ensure that the price eventually attains a level where demand is equal to the supply.
Why Derivatives? (Cont…)
When new information is obtained by investors, trades will obviously be induced, for such information will invariably have implications for asset prices. In practice it is easier and cheaper for investors to enter derivatives markets as opposed to cash or spot markets.
Why Derivatives? (Cont…)
This is because, the investor can trade in a derivatives market by depositing a relatively small performance guarantee or collateral known as the margin. On the contrary taking a long position in the spot market would entail paying the full price of the asset.
Why Derivatives? (Cont…)
Similarly it is easier to take a short position in derivatives than to short sell in the spot markets. In fact, many assets cannot be sold short in the spot market. Consequently new information filters into derivatives markets very fast.
Why Derivatives? (Cont…)
Thus derivatives facilitate Price Discovery. Because of the high volumes of transactions in such markets, transactions costs tend to be lower than in spot markets. This in turn fuels even more trading activity. Also derivative markets tend to be very liquid.
Why Derivatives? (Cont…)
That is, investors who enter these markets, usually find that traders who are willing to take the opposite side are readily available. This enables traders to trade without having to induce a transaction by making major price concessions.
Why Derivatives? (Cont…)
Derivatives improve the overall efficiency of the free market system. Due to the ease of trading, and the lower associated costs, information quickly filters into these markets. At the same time spot and derivatives prices are inextricably linked.
Why Derivatives? (Cont…)
Consequently, if there is a perceived misalignment of prices, arbitrageurs will move in for the kill. Their activities will eventually lead to the efficiency of spot markets as well. Finally derivatives facilitate speculation. And speculation is vital for the free market system.
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