1 Chapter 16 Options Markets u Derivatives are simply a class of securities whose prices are determined from the prices of other (underlying) assets u Options, futures, and swaps are just some examples of derivatives u Options are traded on various underlying assets. –Individual stocks as well as stock indexes –Futures –Foreign currency –Interest rates

2 Option Contracts u A call option gives the holder the right (but not the obligation) to buy an asset for a specified price (strike price) on or before a specified expiration date. –Example: A MSFT July 120 call would give the buyer the right to purchase 100 shares of MSFT stock at $120 per share on or before the third Friday in July. u Why would someone want to buy this option?

3 Option Contracts u A put option gives the holder the right (but not the obligation) to sell an asset for a specified price (strike price) on or before a specified expiration date. –Example: An INTC September 95 put would give the buyer the right to sell 100 shares of INTC stock at $95 per share on or before the third Friday in September. u Why would someone want to buy this option?

4 Some Terminology u In order for someone to buy an option, someone must be willing to sell it. The seller of an option is called the writer of the option. u An option is in the money when its exercise would produce a positive payoff. u An option is out of the money when its exercise would produce a negative payoff. u The option is at the money when the price of the underlying asset equals the strike price of the option.

5 Terminology u The price paid for an option contract is called the premium. u Option contracts are generally for 100 shares. u An American option allows its holder to exercise it on or before the expiration date. u A European option can only be exercised on the expiration date. u However, both American and European options can be sold prior to expiration.

6 Quick Review u When would a call option be in the money? Out of the money? At the money? u What about a put option? u Why would investors write (sell) options? u If you wanted to have the option to purchase 800 shares of MSFT, how many calls would you need to buy?

7 Value of Call Options at Expiration u Recall that call options give the holder the right to purchase a security at the exercise price. We denote the price of the underlying security as S T and the exercise price as X u Since the option need not be exercised, the value is contingent on the relative values of S T and X. u Recall that to purchase the call, an investor must pay the premium (to the writer) which we will denote by C (for calls) or P (for puts).

8 Value of Call Options at Expiration

9 u Suppose you bought a MSFT 120 call for $13. What are the payoffs and profits at expiration for certain stock prices?

10 Value of Call Options at Expiration

11 Value of Put Options at Expiration

12 Value of Put Options at Expiration u Suppose you bought a INTC 95 put for $9. What are the payoffs and profits at expiration for certain stock prices?

13 Value of Put Options at Expiration

14 Put-Call Parity u We discussed the idea of arbitrage and said that two assets with the same payoff must sell for the same price. u We can use put and call options and the underlying stock to establish a relationship between the pricing of the put and call options. u The equation representing the proper relationship between put and call prices is known as the put-call parity theorem.

15 Put-Call Parity u Suppose we consider 2 investments. One is to buy a call and write a put with the same exercise price (X) and the same expiration date (T). u The other is to borrow a certain amount of money and buy the underlying stock. u We borrow enough so that when we pay back the loan at time T, we have to repay X dollars. u Assuming that we can borrow at the risk-free rate, this means we will borrow X/(1+r f ) T.

16 Put-Call Parity

17 Put-Call Parity u Since those two investments have the same payoffs, they must have the same prices. u The cost of buying a call and writing a put is C - P. u The cost of buying stock and borrowing is where S 0 is the current stock price u Thus, the put-call parity relationship is

18 Option Strategies u Naked u Protective put u Covered call u Straddle –Strips and straps u Spread –Vertical or horizontal –Butterfly

19 Options in Other Securities u Callable bonds u Convertible bonds u Warrants u Collateralized loans –Mortgage u Levered equity –The firm can be valued with option pricing

20 Exotic Options u Asian u Barrier –Knock-out and knock-in u Lookback u Currency-translated u Binary