1. Mechanics of Options Markets
Chapter 8
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

2. Review of Option Types
A call is an option to buy an asset at a fixed price
A put is an option to sell an asset at a fixed price
Important: Unlike for forwards/futures, the purchaser of an option is not obliged to buy or sell the asset – it is his or her option
The holder will not exercise unless his or her payoff is positive.
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

3. Review of Option Types
A European option can be exercised only at the end of its life (when the contract expires)
An American option can be exercised at any time up to the expiration
All exchange traded options are American. All index options are European except for the S&P 100 Index.
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

4. Option Positions Long position in a call. Payoff: max(ST-K,0)
Long position in a put. Payoff:
max(K-ST,0)
Short position in a call. Payoff:
- max(ST-K,0) = min(K-ST,0)
Short position in a put. Payoff:
- max(K-ST,0) = min(ST-K,0)
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

5. Terminology Current time t Maturity at expiration T
Price of the underlying S(t)
Exercise price K (or X)
Value of a European Call c(S,K,t,T)
Value of an American Call C(S,K,t,T)
Value of a European Put p(S,K,t,T)
Value of an American Pall P(S,K,t,T)
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

6. Moneyness:
A call is in-the-money (ITM) if the asset price is greater than the exercise price (i.e. it would be worth something exercised)
A put is in-the-money if the asset price is less than the exercise price (i.e. it would be worth something exercised)
A call is out-of-the-money (OTM) if the asset price is less than the exercise price (i.e. it would be worth nothing exercised)
A put is out-of-the-money if the asset price is greater than the exercise price (i.e. it would be worth nothing exercised)
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

7. Moneyness:
A call is at-the-money (ATM) if the asset price is equal with the exercise price
A put is at-the-money (ATM) if the asset price is equal with the exercise price
S<K S=K S>K
Call
Put
Out-of-the money At-the-money In-the-money
In-the-money At-the-money Out-of-the-money
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

8. Long Call on eBay (Figure 8.1, Page 182)
Profit from buying one eBay European call option: option price = $5, strike price = $100, option life = 2 months 30 20 10 -5 70 80 90
100
110
120
130
Profit ($)
Terminal
stock price ($)
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

9. Short Call on eBay (Figure 8.3, page 184)
Profit from writing one eBay European call option: option price = $5, strike price = $100
-30
-20
-10 5 70 80 90
100
110
120
130
Profit ($)
Terminal
stock price ($)
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

10. Long Put on IBM (Figure 8.2, page 183)
Profit from buying an IBM European put option: option price = $7, strike price = $70 30 20 10 -7 70 60 50 40 80 90
100
Profit ($)
Terminal
stock price ($)
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

11. Short Put on IBM (Figure 8.4, page 184)
Profit from writing an IBM European put option: option price = $7, strike price = $70
-30
-20
-10 7 70 60 50 40 80 90
100
Profit ($)
Terminal
stock price ($)
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

12. Payoffs from Options What is the Option Position in Each Case?
K = Strike price, ST = Price of asset at maturity
Payoff
Payoff K K ST ST
Payoff
Payoff K K ST ST
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

13. Assets Underlying Exchange-Traded Options
Stocks. Each option contract represents 100 shares.
Foreign Currency. Both American and European contracts are traded
Stock Indices. One contract is for 100 times the index. Settlement is for cash. Example: if K=560 and S(T)=590, the writer pays the buyer 30*100=$3.000
Futures. Deliverable is a futures contract plus the difference between the futures price and exercise price. Settlement based on futures price
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

14. Specification of Exchange-Traded Options
Expiration date (usually the Saturday immediately following the third Friday of the expiration month
Strike price
European or American
Call or Put (option class)
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

15. Terminology Option class :calls or puts
Option series :All options of a given class with the same expiration date and strike price
Intrinsic value :max(K-S,0), if it were exercised immediately
Time value :wait rather than exercise immediately
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

16. Exercise price spacing:
$2 ½ spacing for S(t) < $25
$5 spacing for $25 < S(t)
$10 spacing for S(t) > $200
Example: Suppose S(t)=$84. The exercise prices offered are of $80, $85 and $90.
If the stock price rose above $90, a strike price of $95 may be offered.
If the stock price fell bellow $80, a strike price of $75 may be offered.
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

17. Dividends & Stock Splits (Page 188-190)
Suppose you own N options with a strike price of K :
No adjustments are made to the option terms for cash dividends
When there is an n-for-m stock split,
the strike price is reduced to mK/n
the no. of shares is increased to nN/m
Stock dividends are handled in a manner similar to stock splits
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

18. Dividends & Stock Splits (continued)
Consider a call option to buy 100 shares for $30/share
How should terms be adjusted for a for-1 stock split?
The terms of the option contract are changed so that it gives the holder the right to purchase 200 shares for $15 per share.
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

19. Dividends & Stock Splits (continued)
Consider a call option to buy 100 shares for $30/share
How should terms be adjusted for a % stock dividends?
This is equivalent to a 5-for-4 stock split. The terms of the option contract are changed so that it gives the holder the right to sell 125 shares for $24.
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

20. Market Makers
Most exchanges use market makers to facilitate options trading
A market maker quotes both bid and ask prices when requested
The market maker does not know whether the individual requesting the quotes wants to buy or sell
Market makers add liquidity to the market.
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

21. Commissions:
Dollar amount of trade Commission
< $ $20 + 2% of dollar amount
$2.500 to $ $45 + 1% of dollar amount
> $ $ % of dollar amount
Maximum commission is $30 per contract for the first 5 contracts plus $20 per contract for each additional contract
Minimum commission is $30 per contract for the first contract plus $2 per contract for each additional contract
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

22. Commissions: Example:
Consider an investor who buys a call with K=$50, S0=$49, and c=$4.5, so the cost of the contract is $450.
Suppose the stock price is $60 when the option is exercised. The investor pays 1.5% commission on stock trades. The commission payable is therefore:
0.015*60*100+$30=$120
Net profit:
$1000-$450-$120=$430
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

23. Margins (Page 194-195) Margins are required when options are sold
When a naked option is written the margin is the greater of:
A total of 100% of the proceeds of the sale plus 20% of the underlying share price less the amount (if any) by which the option is out of the money
A total of 100% of the proceeds of the sale plus 10% of the underlying share price
For other trading strategies there are special rules
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

24. Example
An investor writes 4 naked call option contracts with K=$40, S0=$38, and c=$5.
Because the options is $2 OTM, the first calculation gives:
400*(5+0.2*38-2)=$4.240
The second calculation gives
400*(5+0.1*38)=$3.520
The initial requirement is therefore $4.240.
If the option had been a put, it would be $2 ITM and then:
400*(5+0.2*38)=$5.040
In both cases the proceeds of the sale, $2000, can be used to form part of the margin account
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

25. Warrants
Warrants are options that are issued by a corporation or a financial institution
The number of warrants outstanding is determined by the size of the original issue and changes only when they are exercised or when they expire
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

26. Warrants (continued)
The issuer settles up with the holder when a warrant is exercised
When call warrants are issued by a corporation on its own stock, exercise will lead to new treasury stock being issued
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

27. Executive Stock Options
Executive stock options are a form of remuneration issued by a company to its executives
They are usually at the money when issued
When options are exercised the company issues more stock and sells it to the option holder for the strike price
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

28. Executive Stock Options continued
They become vested after a period of time (usually 1 to 4 years)
They cannot be sold
They often last for as long as 10 or 15 years
Accounting standards now require the expensing of executive stock options
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

29. Convertible Bonds
Convertible bonds are regular bonds that can be exchanged for equity at certain times in the future according to a predetermined exchange ratio
Very often a convertible is callable
The call provision is a way in which the issuer can force conversion at a time earlier than the holder might otherwise choose
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005