Part 19
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Part-19 Essentials of Options
1
A Quick Recap
Options are by design different from forward and futures contracts.
The buyer of the options contract is called the Holder or the Long, and he has a right. The seller of the contract is called the Writer or the Short and he has an obligation. 2
Recap (Cont…)
Call Options give the holder the right to buy the underlying asset at a pre-specified price. Put Options give the holder the right to sell the underlying asset at a pre-specified price. All option contracts have a specified expiration date after which they become null and void. 3
Recap (Cont…)
Options contract which can be exercised only at the time of expiration are called European options. Contracts which can be exercised at any time, upto and including the time of expiration, are called American options. Most exchange traded options are American.
4
Associated Terms
-
The following terms are important in the context of options. Option Price or Premium Strike Price or Exercise Price Expiration Date or Exercise Date or Strike Date or Maturity Date
5
Price or Premium
This is the cost of acquisition of the option. It is payable by the buyer to the writer at the outset. Thus unlike in the case of a forward or a futures contract, the long has to pay the short to get into an options contract. 6
Price or Premium (Cont…)
The difference is because in the case of a forward/futures contract, both the parties have an equivalent obligation. In the case of an options contract however, one party is acquiring a right from the other. And, no one will give away a right for free. 7
Strike Price or Exercise Price
This is the price payable per unit of the underlying asset, if a call option is exercised by the holder. It is the price receivable per unit of the underlying asset, if a put option is exercised by the holder.
8
Exercise Price (Cont…)
Thus when the buyer of an options contract pays the option premium, he merely acquires the right to transact. If he subsequently decides to go through with the transaction, he must pay to acquire the underlying asset in the case of call options. 9
Exercise Price (Cont…)
Or else he must be paid when he delivers the underlying asset in the case of put options.
10
Expiration Date
This is the point in time after which the contract becomes null and void.
It is the only point in time at which a European option can be exercised. It is the last point in time at which an American option can be exercised
11
Example of a Call Option
Consider European calls on Reliance expiring on the last Thursday of September. Let the exercise price be Rs 400. Let the option premium be Rs 15.
Option premia are always quoted on a per share basis. 12
Example (Cont…)
The contract size, which is the number of shares of stock underlying the contract is 100 shares in the U.S., irrespective of the company on whose shares the contract is written. In India the contract size varies from company to company. 13
Example (Cont…)
In the case of Reliance, the contract size is 300 shares.
Thus the buyer has to pay 15 x 300 =
Rs 4500 to the writer at the outset.
This is a sunk cost and cannot be recovered.
In exchange the buyer acquires the right to buy 300 shares at the time of expiration at a price of Rs 400 per share. 14
Example (Cont…)
What will happen at expiration?
If the stock price is greater than Rs 400, then the option will be exercised.
This is because it is worth paying Rs 400 for an asset that is selling for more than Rs 400. Otherwise the option will simply be allowed to expire worthless. 15
Example (Cont…)
For instance, why pay Rs 400 for an asset that is selling at say Rs 395. Remember that since an option is a right, the holder cannot be forced to exercise. Notice that the spot price at expiration need not be greater than the sum of the exercise price and the premium, in order to 16
Example (Cont…)
That is, the terminal stock price need not exceed Rs 400 + Rs 15 = Rs 415, before the holder opts to exercise.
This is because sunk costs are irrelevant while taking investment decisions.
17
The Irrelevance of Sunk Costs
Assume that the terminal stock price is Rs 405.
If the option is exercised the profit is:
If the option is not exercised
Π = 300(405 – 400) – 4500 = (3000) Π = (4500)
Obviously it is better to lose Rs 3000. 18
The Case of Puts
If the options had been puts instead of calls, then the holder would exercise only if the spot price at expiration were to be less than Rs 400. Obviously, it is attractive to sell the stock for Rs 400, when the prevailing market price is less than Rs 400. 19
Puts (Cont…)
Otherwise it is best to allow the options to expire worthless. For instance if the spot price is Rs 405, why should the option holder deliver under the contract for Rs 400.
20
Profit Bounds
For a call holder the maximum profit is unlimited, since theoretically, there is no upper bound on the price of the asset.
Thus if the call is exercised:
π = (ST – X) – C, which has no upper bound.
ST is the stock price, X is the exercise price and C is the premium. 21
Profit Bounds (Cont…)
If the call is not exercised: π = -C For a call writer the maximum profit is the option premium.
This is because the best thing that can happen from his standpoint is that the holder does not exercise, and he consequently gets to retain the entire premium. 22
Profit Bounds (Cont…)
Thus if the call is not exercised:
π = C. If the call were to be exercised the writer has to deliver a share, whose price is theoretically unbounded, at the exercise price. That is:
Π = C – (ST – X) 23
Profit Bounds (Cont…)
Thus the maximum possible loss for a call writer is infinite.
24
Puts and Profits
In the case of a put holder the profit is given by: (X – ST) – P The maximum possible value is X – P. This is because the lowest possible stock price is 0, since stocks have limited liability. The maximum possible loss is once 25 again equal to the premium paid:
Puts and profits (Cont…)
For a put writer the maximum possible profit is the premium. This is because the best thing that can happen to him is that the option is not exercised.
His loss if the put is exercised is:
π = P – (X – ST) which has a lower bound of (P – X) = -(X-P) 26
Zero Sum Games
Thus both calls and puts are Zero Sum Games. One man’s profit is always another man’s loss.
27
Payoffs and Profits
Symbolically the payoff from an option for a call holder is: Max[0, ST – X] The profit is Max[0, ST – X] – C The payoff for a call writer is -Max[0, ST – X] = Min[0, X – ST] The profit is Min[0, X – ST] + C 28
Payoffs and Profits (Cont…)
The payoff for a put holder is: Max[0, X – ST] The profit is Max[0, X – ST] – P The payoff for a put writer is: Min[0, ST - X] The profit is Min[0, ST - X] + P 29
Exchange Trade & OTC Options
Exchange traded options were introduced for the first time by the Chicago Board Options Exchange (CBOE) in 1973. Until then options were only traded Over the Counter.
30
Exchange Traded vs. OTC (Cont…)
OTC options are customized, in the sense that the exercise price, the expiration date, and the contract size are negotiated between the buyer and the seller. Exchange traded options are however standardized like futures contracts.
That is the allowable exercise prices and expiration dates are specified by the exchange. 31
Exchange Traded vs. OTC (Cont…)
Individual buyers and sellers can incorporate any of the allowable exercise prices and expiration dates into their agreements, but cannot design their own contracts. The contract size too is specified by the exchange. 32
Exchange Traded Options (Cont…)
The advantage of standardization is that volumes tend to be high and transactions costs tend to be low. Secondly because of high volumes, these markets tend to be liquid. Besides standardized option contracts can be offset by taking counterpositions, without necessarily involving the original counter-party. 33
Counter-Positions
Taking a counter-position means that if you have originally bought a call/put, you now sell an identical call/put.
By identical we mean that the offsetting contract should be on the same asset, and have the same exercise price and time to expiration. 34
Counter-Positions (Cont…)
Similarly if you have sold a call/put, you would now have to buy an identical call/put in order to offset.
35
Illustration
Aditi had bought an options contract on Reliance from Rakesh a week ago. The contract terms have specified an exercise price of Rs 350 and the contract is scheduled to expire at the end of June. Now assume that Aditi wants to get out of her position. 36
Illustration (Cont…)
All she has to do, is to find a person on the floor of the exchange who would like to go long in a contract on Reliance expiring in June, with an exercise price of 350. This person need not be Rakesh, the individual with whom she initially traded.
37
Standardization & Offsetting
Offsetting is easy when the contracts are standardized.
In the case of customized contracts, there is an infinite number of exercise prices and expiration dates that can be specified.
As a consequence of which the odds of finding a third party who is willing to transact as per the original contract are severely reduced. 38
Credit Risk
In the case of exchange traded options, credit risk is minimized because there is a clearinghouse which becomes the effective buyer for every seller and the effective seller for every buyer. However, unlike in the case of a futures contract, the clearinghouse has to guarantee only the 39
Credit Risk (Cont…)
This is because a performance guarantee is required only when a party has an obligation and not when he has a right. And remember both call and put holders have rights, as a consequence of which there is no fear of non-performance. 40
OTC Markets
The OTC market is dominated by institutional investors.
Contracts are entered into privately by
large corporations financial institutions and sometimes even governments.
When buying an OTC option you have to be either familiar with the creditworthiness of the writer or 41 else seek a guarantee.
OTC Markets (Cont…)
Nevertheless OTC markets always carry an element of credit risk. They do offer certain advantages however.
Firstly terms and conditions like expiration dates and exercise prices can be tailored to the specific needs of the two parties. 42
OTC Markets (Cont…)
Often the contract may be on an asset on which an exchange traded contract is not available. Since the market is private, neither the public nor other investors need to know about the transaction taking place.
43
FLEX Options
Their disadvantages not withstanding, customized contracts have an appeal particularly for institutional investors. For many institutions, exchange designed contracts are often inadequate and they desire their freedom to create their own
44
FLEX Options (Cont…)
Traditionally, an institution in need of a tailor-made contract has had to seek out another like minded institution like a commercial bank who is seeking to write an option with similar features. Of late, in response to competition the exchanges have been making an effort to grab a slice of the 45
FLEX Options (Cont…)
To do this, they have created products known as FLEX options for stock indices and E-FLEX options for equity shares, where FLEX stands for FLexible EXchange. In order to trade in these options, an investor has to submit what is called a Request for Quote or RFQ.46
RFQs
The RFQ will contain the details of the contract sought by the investor, namely whether it is a call or a put, the exercise price, the time to maturity, and whether they want a European or an American style contract. The RFQ is then acted upon by market makers who submit quotes47
FLEX Options
Both FLEX and E-FLEX options are cleared by the clearinghouse.
48
Underlying Assets
Equities: The CBOE itself trades options on about 1400 stocks. Indices: Examples include DJIA, S&P 100, and the S&P 500 Interest Rates Foreign Exchange
49
Moneyness
Let us denote the current stock price by St and the exercise price by X. If St > X, the call option is said to be in the money. Example: St = 110; X = 100 If St < X the call option is said to be out of the money. Example: St = 90; X = 100
50
Moneyness (Cont…)
If St = X the call option is said to be at the money. Example: St =100; X = 100 For put options, if St > X, the option is said to be out of the money. Example: St = 110; X = 100 If St < X, the put option is said to be in the money.
51
Moneyness (Cont…)
If St = X, the put option is said to be at the money. If St is very close to X, both call and put options are said to be near the money. Obviously, an option, whether a call or a put will exercised only if it is in the money. 52
Expiration Dates
Stock options contracts in the U.S expire on the Saturday following the third Friday of the expiration month.
That is, if the first day of the month is a Saturday, then the contracts will expire on the fourth Saturday, else they will expire on the third Saturday. The last day of trading is the third Friday. 53
Expiration Dates (Cont…)
In India stock and index options expire on the last Thursday of the expiration month.
If the last Thursday happens to be a market holiday, then the contracts will expire on the previous business day.
54
Available Expiration Months
The methods used in the U.S. and in India are different from each other. In the U.S, a company on whose shares options are allowed for trading, is assigned at the outset to either a January, February, or a March cycle. 55
Expiration Months (Cont…)
The January cycle comprises of: January, April, July, and October The February cycle comprises of: February, May, August, and November. The March cycle comprises of: March, June, September, and December.
56
Expiration Months (Cont…) At any point in time, the available months for a stock will be: the current month, the following month, and the next two months of the cycle to which it has been assigned.
57
Illustration
Assume that today is 1 September 2002 and that XYZ corporation is assigned to a February cycle. Contracts will therefore be available for September 2002, October 2002, November 2002, and February 2003. 58
Illustration (Cont…)
September is the current month, October the following month, and November and February are the next two months from the February cycle. Once the September contracts expire, the available months will be: October 2002, November 2002, February 2003, and May 2003.
59
LEAPS
In addition both the CBOE and the Amex offer long term options with upto two years to maturity called Long Term Equity Anticipation Securities or LEAPS.
60
INDIA
SEBI guidelines permit contracts with upto 12 months to maturity.
But currently we only have contracts with a maximum of three months to expiration. So we have contracts for the current month, and the following two months.
61
INDIA (Cont…)
For instance, on 1 September 2006 we will have the following contracts: September 2006, October 2006, and November 2006.
62
Exercise Prices
The exchange has to specify the allowable exercise prices. There will always be an at the money or near the money contract since these are of the maximum possible interest from the standpoints of both the longs as well as the shorts. 63
Exercise Prices (Cont…)
Consequently at the money contracts have the maximum trading volume. In addition there will be a number of in the money and out of the money contracts available at any point in time. The exchange in India guarantees that a minimum of 7 exercise prices will be provided for contracts with a given expiration date. 64
Exercise Prices (Cont…)
Three of these contracts will be in the money, three out of the money, and one at or near the money. The intervals between exercise prices would depend on the price of the underlying stock, and would be determined as per the following schedule. 65
Exercise Price Intervals Stock Price S < Rs 50 Rs 50 < S < Rs Rs 250250 < S < Rs Rs 500500 < S < Rs 1000 Rs 1000 < S < Rs 2500 S > Rs 2500
Strike Price Interval Rs 2.50 Rs 5 Rs 10 Rs 20 Rs 30 Rs 50
66
Illustration
Assume that the January contracts on Reliance have just expired and that April contracts are being introduced. Let the prevailing share price be Rs 647. Since 647 is in between 500 and 1000, the applicable strike price interval is Rs 20. 67
Illustration (Cont…)
In order to determine the at the money exercise price, the stock price will be rounded off to the nearest multiple of the strike price interval, which in this case is Rs 640.
Thus contracts with an exercise price of 640, which represent near the money options, will be allowed for trading. 68
Illustration (Cont…)
The strike prices for the three in the money contracts and the three out of the money contracts will then be determined with reference to the at the money exercise price, in accordance with the prescribed strike price interval. 69
Illustration (Cont…)
Thus contracts with exercise prices of 580, 600, 620, 660, 680, and 700 will be allowed for trading. Now assume that at the end of the day, the stock price is 695.
The next morning, using the same logic as above, the exercise price for a near the money contract will be set at 700. 70
Illustration (Cont…)
With reference to this exercise price, four in the money contracts are already available.
Thus three new exercise prices which correspond to three out of the money calls, namely 720, 740, and 760 will be allowed for trading.
71
The U.S. System
The exercise prices in the U.S are determined as per the following schedule.
72
The U.S. System (Cont…) Stock Price
Strike Price Interval
S < $ 25
$ 2.50
$ 25 < S < $ 200
$5
S > $ 200
$ 10 73
The U.S. System (Cont…)
For instance if a stock has a price of say $ 21.5, and contracts with a new expiration month are being introduced, then to start with two exercise prices, namely, $ 22.50 and $ 20 will be allowed. If the price moves to $ 24 then automatically an exercise price of $ 25 will be permitted. 74
The U.S. System (Cont…)
Index options have exercise prices in intervals of $ 5. These rules are however flexible and can be modified by the exchange if in its opinion, such changes are necessary to attract larger trading volumes. 75
Exercise Prices
So at any given point in time contracts with many different exercise prices will be trading for each of the expiration months. The number of different exercise prices that are observable at a point in time, would depend on the movement in the price of the underlying stock from the inception of trading in contracts for that expiration month. 76
Cash Settlement
Cash settlement is used for Index options globally. It has also been specified as the method of settlement to be adopted in India, till our markets achieve the desired level of maturity. Indices obviously cannot be delivered.
77
Cash Settlement (Cont…)
For an index represents a portfolio of stocks, which can be large (500 in the case of the S&P 500), weighted in particular proportions. So delivery of an index is technically feasible but practically difficult. 78
Cash Settlement (Cont…)
So if an index option is exercised the holder will receive the difference between the current index value and the exercise price, in the case of call options. In the case of puts, the holder will receive the difference between the exercise price and the current index level, from the writer. 79
Cash Settlement (Cont…)
In India this procedure is currently being followed for stock options as well. For instance assume that the stock price of Reliance is Rs 350, and that an investor is holding a call option with an exercise price of Rs 320. If he decides to exercise, he will receive 80
Cash Settlement (Cont…)
No shares will change hands. Similarly if the current stock price is Rs 350 and an investor is holding put options with an exercise price of Rs 375 on Reliance, he will receive: 300 x (375 – 350) = Rs 7,500 were he to decide to exercise. 81
Intrinsic Value & Time Value
The intrinsic value of an option is equal to the amount by which it is in the money, if it is in the money, else it is equal to zero. Therefore the intrinsic value of a call is:
Max[0, (St – X)]
While that of a put is:
Max[0, (X – St)]
82
I.V & T.V (Cont…)
The difference between an option’s premium and its intrinsic value is called the time value of the option, also known as the speculative value of the option.
83
Determining Option Values
Pricing futures contracts was relatively easy.
All that we had to do was to derive a pricing relationship that would preclude both cash and carry as well as reverse cash and carry arbitrage.
84
Option Values (Cont…)
This was feasible because a futures contract entails an obligation on the part of both the parties. Options however are more complex from a valuation standpoint.
This is because the holder has a right and not an obligation. 85
Option Values (Cont…)
The attractiveness of the right in the case of a European option would depend on the holder’s perception of his being able to exercise the option at maturity, and the corresponding payoff.
86
Option Values (Cont…)
American options are considerably more complex because at every instant the decision has to be taken as to whether or not to exercise. Similarly from a writer’s standpoint, what is important is the possibility of the holder not exercising and of his consequently87
Option Values (Cont…)
Thus in the case of options, valuation entails the postulation of a process for the evolution of the stock price through time. Corresponding to every hypothesis about the price process, we will get a theoretical option premium. 88
Option Values (Cont…)
In certain cases, we will be able to derive precise mathematical formulae for the option price, or what we call closed-form solutions. In other cases we will have to make do with numerical approximations. 89
1
A Quick Recap
Options are by design different from forward and futures contracts.
The buyer of the options contract is called the Holder or the Long, and he has a right. The seller of the contract is called the Writer or the Short and he has an obligation. 2
Recap (Cont…)
Call Options give the holder the right to buy the underlying asset at a pre-specified price. Put Options give the holder the right to sell the underlying asset at a pre-specified price. All option contracts have a specified expiration date after which they become null and void. 3
Recap (Cont…)
Options contract which can be exercised only at the time of expiration are called European options. Contracts which can be exercised at any time, upto and including the time of expiration, are called American options. Most exchange traded options are American.
4
Associated Terms
-
The following terms are important in the context of options. Option Price or Premium Strike Price or Exercise Price Expiration Date or Exercise Date or Strike Date or Maturity Date
5
Price or Premium
This is the cost of acquisition of the option. It is payable by the buyer to the writer at the outset. Thus unlike in the case of a forward or a futures contract, the long has to pay the short to get into an options contract. 6
Price or Premium (Cont…)
The difference is because in the case of a forward/futures contract, both the parties have an equivalent obligation. In the case of an options contract however, one party is acquiring a right from the other. And, no one will give away a right for free. 7
Strike Price or Exercise Price
This is the price payable per unit of the underlying asset, if a call option is exercised by the holder. It is the price receivable per unit of the underlying asset, if a put option is exercised by the holder.
8
Exercise Price (Cont…)
Thus when the buyer of an options contract pays the option premium, he merely acquires the right to transact. If he subsequently decides to go through with the transaction, he must pay to acquire the underlying asset in the case of call options. 9
Exercise Price (Cont…)
Or else he must be paid when he delivers the underlying asset in the case of put options.
10
Expiration Date
This is the point in time after which the contract becomes null and void.
It is the only point in time at which a European option can be exercised. It is the last point in time at which an American option can be exercised
11
Example of a Call Option
Consider European calls on Reliance expiring on the last Thursday of September. Let the exercise price be Rs 400. Let the option premium be Rs 15.
Option premia are always quoted on a per share basis. 12
Example (Cont…)
The contract size, which is the number of shares of stock underlying the contract is 100 shares in the U.S., irrespective of the company on whose shares the contract is written. In India the contract size varies from company to company. 13
Example (Cont…)
In the case of Reliance, the contract size is 300 shares.
Thus the buyer has to pay 15 x 300 =
Rs 4500 to the writer at the outset.
This is a sunk cost and cannot be recovered.
In exchange the buyer acquires the right to buy 300 shares at the time of expiration at a price of Rs 400 per share. 14
Example (Cont…)
What will happen at expiration?
If the stock price is greater than Rs 400, then the option will be exercised.
This is because it is worth paying Rs 400 for an asset that is selling for more than Rs 400. Otherwise the option will simply be allowed to expire worthless. 15
Example (Cont…)
For instance, why pay Rs 400 for an asset that is selling at say Rs 395. Remember that since an option is a right, the holder cannot be forced to exercise. Notice that the spot price at expiration need not be greater than the sum of the exercise price and the premium, in order to 16
Example (Cont…)
That is, the terminal stock price need not exceed Rs 400 + Rs 15 = Rs 415, before the holder opts to exercise.
This is because sunk costs are irrelevant while taking investment decisions.
17
The Irrelevance of Sunk Costs
Assume that the terminal stock price is Rs 405.
If the option is exercised the profit is:
If the option is not exercised
Π = 300(405 – 400) – 4500 = (3000) Π = (4500)
Obviously it is better to lose Rs 3000. 18
The Case of Puts
If the options had been puts instead of calls, then the holder would exercise only if the spot price at expiration were to be less than Rs 400. Obviously, it is attractive to sell the stock for Rs 400, when the prevailing market price is less than Rs 400. 19
Puts (Cont…)
Otherwise it is best to allow the options to expire worthless. For instance if the spot price is Rs 405, why should the option holder deliver under the contract for Rs 400.
20
Profit Bounds
For a call holder the maximum profit is unlimited, since theoretically, there is no upper bound on the price of the asset.
Thus if the call is exercised:
π = (ST – X) – C, which has no upper bound.
ST is the stock price, X is the exercise price and C is the premium. 21
Profit Bounds (Cont…)
If the call is not exercised: π = -C For a call writer the maximum profit is the option premium.
This is because the best thing that can happen from his standpoint is that the holder does not exercise, and he consequently gets to retain the entire premium. 22
Profit Bounds (Cont…)
Thus if the call is not exercised:
π = C. If the call were to be exercised the writer has to deliver a share, whose price is theoretically unbounded, at the exercise price. That is:
Π = C – (ST – X) 23
Profit Bounds (Cont…)
Thus the maximum possible loss for a call writer is infinite.
24
Puts and Profits
In the case of a put holder the profit is given by: (X – ST) – P The maximum possible value is X – P. This is because the lowest possible stock price is 0, since stocks have limited liability. The maximum possible loss is once 25 again equal to the premium paid:
Puts and profits (Cont…)
For a put writer the maximum possible profit is the premium. This is because the best thing that can happen to him is that the option is not exercised.
His loss if the put is exercised is:
π = P – (X – ST) which has a lower bound of (P – X) = -(X-P) 26
Zero Sum Games
Thus both calls and puts are Zero Sum Games. One man’s profit is always another man’s loss.
27
Payoffs and Profits
Symbolically the payoff from an option for a call holder is: Max[0, ST – X] The profit is Max[0, ST – X] – C The payoff for a call writer is -Max[0, ST – X] = Min[0, X – ST] The profit is Min[0, X – ST] + C 28
Payoffs and Profits (Cont…)
The payoff for a put holder is: Max[0, X – ST] The profit is Max[0, X – ST] – P The payoff for a put writer is: Min[0, ST - X] The profit is Min[0, ST - X] + P 29
Exchange Trade & OTC Options
Exchange traded options were introduced for the first time by the Chicago Board Options Exchange (CBOE) in 1973. Until then options were only traded Over the Counter.
30
Exchange Traded vs. OTC (Cont…)
OTC options are customized, in the sense that the exercise price, the expiration date, and the contract size are negotiated between the buyer and the seller. Exchange traded options are however standardized like futures contracts.
That is the allowable exercise prices and expiration dates are specified by the exchange. 31
Exchange Traded vs. OTC (Cont…)
Individual buyers and sellers can incorporate any of the allowable exercise prices and expiration dates into their agreements, but cannot design their own contracts. The contract size too is specified by the exchange. 32
Exchange Traded Options (Cont…)
The advantage of standardization is that volumes tend to be high and transactions costs tend to be low. Secondly because of high volumes, these markets tend to be liquid. Besides standardized option contracts can be offset by taking counterpositions, without necessarily involving the original counter-party. 33
Counter-Positions
Taking a counter-position means that if you have originally bought a call/put, you now sell an identical call/put.
By identical we mean that the offsetting contract should be on the same asset, and have the same exercise price and time to expiration. 34
Counter-Positions (Cont…)
Similarly if you have sold a call/put, you would now have to buy an identical call/put in order to offset.
35
Illustration
Aditi had bought an options contract on Reliance from Rakesh a week ago. The contract terms have specified an exercise price of Rs 350 and the contract is scheduled to expire at the end of June. Now assume that Aditi wants to get out of her position. 36
Illustration (Cont…)
All she has to do, is to find a person on the floor of the exchange who would like to go long in a contract on Reliance expiring in June, with an exercise price of 350. This person need not be Rakesh, the individual with whom she initially traded.
37
Standardization & Offsetting
Offsetting is easy when the contracts are standardized.
In the case of customized contracts, there is an infinite number of exercise prices and expiration dates that can be specified.
As a consequence of which the odds of finding a third party who is willing to transact as per the original contract are severely reduced. 38
Credit Risk
In the case of exchange traded options, credit risk is minimized because there is a clearinghouse which becomes the effective buyer for every seller and the effective seller for every buyer. However, unlike in the case of a futures contract, the clearinghouse has to guarantee only the 39
Credit Risk (Cont…)
This is because a performance guarantee is required only when a party has an obligation and not when he has a right. And remember both call and put holders have rights, as a consequence of which there is no fear of non-performance. 40
OTC Markets
The OTC market is dominated by institutional investors.
Contracts are entered into privately by
large corporations financial institutions and sometimes even governments.
When buying an OTC option you have to be either familiar with the creditworthiness of the writer or 41 else seek a guarantee.
OTC Markets (Cont…)
Nevertheless OTC markets always carry an element of credit risk. They do offer certain advantages however.
Firstly terms and conditions like expiration dates and exercise prices can be tailored to the specific needs of the two parties. 42
OTC Markets (Cont…)
Often the contract may be on an asset on which an exchange traded contract is not available. Since the market is private, neither the public nor other investors need to know about the transaction taking place.
43
FLEX Options
Their disadvantages not withstanding, customized contracts have an appeal particularly for institutional investors. For many institutions, exchange designed contracts are often inadequate and they desire their freedom to create their own
44
FLEX Options (Cont…)
Traditionally, an institution in need of a tailor-made contract has had to seek out another like minded institution like a commercial bank who is seeking to write an option with similar features. Of late, in response to competition the exchanges have been making an effort to grab a slice of the 45
FLEX Options (Cont…)
To do this, they have created products known as FLEX options for stock indices and E-FLEX options for equity shares, where FLEX stands for FLexible EXchange. In order to trade in these options, an investor has to submit what is called a Request for Quote or RFQ.46
RFQs
The RFQ will contain the details of the contract sought by the investor, namely whether it is a call or a put, the exercise price, the time to maturity, and whether they want a European or an American style contract. The RFQ is then acted upon by market makers who submit quotes47
FLEX Options
Both FLEX and E-FLEX options are cleared by the clearinghouse.
48
Underlying Assets
Equities: The CBOE itself trades options on about 1400 stocks. Indices: Examples include DJIA, S&P 100, and the S&P 500 Interest Rates Foreign Exchange
49
Moneyness
Let us denote the current stock price by St and the exercise price by X. If St > X, the call option is said to be in the money. Example: St = 110; X = 100 If St < X the call option is said to be out of the money. Example: St = 90; X = 100
50
Moneyness (Cont…)
If St = X the call option is said to be at the money. Example: St =100; X = 100 For put options, if St > X, the option is said to be out of the money. Example: St = 110; X = 100 If St < X, the put option is said to be in the money.
51
Moneyness (Cont…)
If St = X, the put option is said to be at the money. If St is very close to X, both call and put options are said to be near the money. Obviously, an option, whether a call or a put will exercised only if it is in the money. 52
Expiration Dates
Stock options contracts in the U.S expire on the Saturday following the third Friday of the expiration month.
That is, if the first day of the month is a Saturday, then the contracts will expire on the fourth Saturday, else they will expire on the third Saturday. The last day of trading is the third Friday. 53
Expiration Dates (Cont…)
In India stock and index options expire on the last Thursday of the expiration month.
If the last Thursday happens to be a market holiday, then the contracts will expire on the previous business day.
54
Available Expiration Months
The methods used in the U.S. and in India are different from each other. In the U.S, a company on whose shares options are allowed for trading, is assigned at the outset to either a January, February, or a March cycle. 55
Expiration Months (Cont…)
The January cycle comprises of: January, April, July, and October The February cycle comprises of: February, May, August, and November. The March cycle comprises of: March, June, September, and December.
56
Expiration Months (Cont…) At any point in time, the available months for a stock will be: the current month, the following month, and the next two months of the cycle to which it has been assigned.
57
Illustration
Assume that today is 1 September 2002 and that XYZ corporation is assigned to a February cycle. Contracts will therefore be available for September 2002, October 2002, November 2002, and February 2003. 58
Illustration (Cont…)
September is the current month, October the following month, and November and February are the next two months from the February cycle. Once the September contracts expire, the available months will be: October 2002, November 2002, February 2003, and May 2003.
59
LEAPS
In addition both the CBOE and the Amex offer long term options with upto two years to maturity called Long Term Equity Anticipation Securities or LEAPS.
60
INDIA
SEBI guidelines permit contracts with upto 12 months to maturity.
But currently we only have contracts with a maximum of three months to expiration. So we have contracts for the current month, and the following two months.
61
INDIA (Cont…)
For instance, on 1 September 2006 we will have the following contracts: September 2006, October 2006, and November 2006.
62
Exercise Prices
The exchange has to specify the allowable exercise prices. There will always be an at the money or near the money contract since these are of the maximum possible interest from the standpoints of both the longs as well as the shorts. 63
Exercise Prices (Cont…)
Consequently at the money contracts have the maximum trading volume. In addition there will be a number of in the money and out of the money contracts available at any point in time. The exchange in India guarantees that a minimum of 7 exercise prices will be provided for contracts with a given expiration date. 64
Exercise Prices (Cont…)
Three of these contracts will be in the money, three out of the money, and one at or near the money. The intervals between exercise prices would depend on the price of the underlying stock, and would be determined as per the following schedule. 65
Exercise Price Intervals Stock Price S < Rs 50 Rs 50 < S < Rs Rs 250250 < S < Rs Rs 500500 < S < Rs 1000 Rs 1000 < S < Rs 2500 S > Rs 2500
Strike Price Interval Rs 2.50 Rs 5 Rs 10 Rs 20 Rs 30 Rs 50
66
Illustration
Assume that the January contracts on Reliance have just expired and that April contracts are being introduced. Let the prevailing share price be Rs 647. Since 647 is in between 500 and 1000, the applicable strike price interval is Rs 20. 67
Illustration (Cont…)
In order to determine the at the money exercise price, the stock price will be rounded off to the nearest multiple of the strike price interval, which in this case is Rs 640.
Thus contracts with an exercise price of 640, which represent near the money options, will be allowed for trading. 68
Illustration (Cont…)
The strike prices for the three in the money contracts and the three out of the money contracts will then be determined with reference to the at the money exercise price, in accordance with the prescribed strike price interval. 69
Illustration (Cont…)
Thus contracts with exercise prices of 580, 600, 620, 660, 680, and 700 will be allowed for trading. Now assume that at the end of the day, the stock price is 695.
The next morning, using the same logic as above, the exercise price for a near the money contract will be set at 700. 70
Illustration (Cont…)
With reference to this exercise price, four in the money contracts are already available.
Thus three new exercise prices which correspond to three out of the money calls, namely 720, 740, and 760 will be allowed for trading.
71
The U.S. System
The exercise prices in the U.S are determined as per the following schedule.
72
The U.S. System (Cont…) Stock Price
Strike Price Interval
S < $ 25
$ 2.50
$ 25 < S < $ 200
$5
S > $ 200
$ 10 73
The U.S. System (Cont…)
For instance if a stock has a price of say $ 21.5, and contracts with a new expiration month are being introduced, then to start with two exercise prices, namely, $ 22.50 and $ 20 will be allowed. If the price moves to $ 24 then automatically an exercise price of $ 25 will be permitted. 74
The U.S. System (Cont…)
Index options have exercise prices in intervals of $ 5. These rules are however flexible and can be modified by the exchange if in its opinion, such changes are necessary to attract larger trading volumes. 75
Exercise Prices
So at any given point in time contracts with many different exercise prices will be trading for each of the expiration months. The number of different exercise prices that are observable at a point in time, would depend on the movement in the price of the underlying stock from the inception of trading in contracts for that expiration month. 76
Cash Settlement
Cash settlement is used for Index options globally. It has also been specified as the method of settlement to be adopted in India, till our markets achieve the desired level of maturity. Indices obviously cannot be delivered.
77
Cash Settlement (Cont…)
For an index represents a portfolio of stocks, which can be large (500 in the case of the S&P 500), weighted in particular proportions. So delivery of an index is technically feasible but practically difficult. 78
Cash Settlement (Cont…)
So if an index option is exercised the holder will receive the difference between the current index value and the exercise price, in the case of call options. In the case of puts, the holder will receive the difference between the exercise price and the current index level, from the writer. 79
Cash Settlement (Cont…)
In India this procedure is currently being followed for stock options as well. For instance assume that the stock price of Reliance is Rs 350, and that an investor is holding a call option with an exercise price of Rs 320. If he decides to exercise, he will receive 80
Cash Settlement (Cont…)
No shares will change hands. Similarly if the current stock price is Rs 350 and an investor is holding put options with an exercise price of Rs 375 on Reliance, he will receive: 300 x (375 – 350) = Rs 7,500 were he to decide to exercise. 81
Intrinsic Value & Time Value
The intrinsic value of an option is equal to the amount by which it is in the money, if it is in the money, else it is equal to zero. Therefore the intrinsic value of a call is:
Max[0, (St – X)]
While that of a put is:
Max[0, (X – St)]
82
I.V & T.V (Cont…)
The difference between an option’s premium and its intrinsic value is called the time value of the option, also known as the speculative value of the option.
83
Determining Option Values
Pricing futures contracts was relatively easy.
All that we had to do was to derive a pricing relationship that would preclude both cash and carry as well as reverse cash and carry arbitrage.
84
Option Values (Cont…)
This was feasible because a futures contract entails an obligation on the part of both the parties. Options however are more complex from a valuation standpoint.
This is because the holder has a right and not an obligation. 85
Option Values (Cont…)
The attractiveness of the right in the case of a European option would depend on the holder’s perception of his being able to exercise the option at maturity, and the corresponding payoff.
86
Option Values (Cont…)
American options are considerably more complex because at every instant the decision has to be taken as to whether or not to exercise. Similarly from a writer’s standpoint, what is important is the possibility of the holder not exercising and of his consequently87
Option Values (Cont…)
Thus in the case of options, valuation entails the postulation of a process for the evolution of the stock price through time. Corresponding to every hypothesis about the price process, we will get a theoretical option premium. 88
Option Values (Cont…)
In certain cases, we will be able to derive precise mathematical formulae for the option price, or what we call closed-form solutions. In other cases we will have to make do with numerical approximations. 89
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