© 2003 The McGraw-Hill Companies, Inc. All rights reserved. Basics of Financial Options

14.1 What is a financial option? An option is a contract which gives its holder the right, but not the obligation, to buy (or sell) an asset at some predetermined price within a specified period of time. It does not obligate its owner to take any action. It merely gives the owner the right to buy or sell an asset. Stock and index option contracts in the U.S. typically gives rights to 100 shares.

14.2 Option Terminology Call option: An option to buy a specified number of shares of a security within some future period. Put option: An option to sell a specified number of shares of a security within some future period. Exercise (or strike) price: The price stated in the option contract at which the security can be bought or sold. (X)

14.3 Call Option Basics You own a call option that gives you the right to buy 100 shares of Apple for $75.00 per share (strike price). Shares of Apple closed to day at $ Should you exercise your option? What if you own a put option, rather than a call option?

14.4 Option Terminology Option price: The market price of the option contract. Premium: The value of the option. Expiration date: The date the option matures. Exercise value: The value of an option if it were exercised today Exercise Value = Current stock price - Strike price Note: The exercise value is zero if the stock price is less than the strike price.

14.5 Option Terminology In-the-money: An option that currently has a positive exercise value. Out-of-the-money: An option that currently has no exercise value. Writer: The investor who sells the option (opposite of the buyer). American option: can be exercised anytime up to the maturity date. European option: can only be exercised on the maturity date.

14.6 More on (Call) Option Premiums Example: Prices and premiums for options on a stock with a strike price of $25.

14.7 Call Premium Diagram Stock Price Option value Market price Exercise value Strike price = $25

14.8 Profit from buying a Call Option

14.9 Profit from buying a Put Option

14.10 Profit from writing a Put Option

14.11 Profit from writing a Call Option

14.12 Why would an investor ever write a call?

14.13 Put-Call Parity Put and call prices are not independent. If you know the value of the call with strike price X, you can solve for the value of the put with strike price X, and vice versa. A portfolio holding one call option and cash (equal to the PV(X) ) must have the same value as a portfolio holding one put option and one share.

14.14 Put-Call Parity Example Let P 0 =$31, X =$30, r f =10%, t=3 mo. If the call is priced at $3, find the price of the put.

14.15 Pricing Options The price (not premium) of non-dividend paying European options can be found using the Black-Scholes Model Inputs: P 0 = stock price today X = strike price t = time to expiration σ 2 = variance of the stock’s returns r f

14.16 Black-Scholes Formula

14.17 What the N(d 1 )?!?! The function N(d) is the probability that a normally distributed variable with a mean of 0 and standard deviation of 1 will be less than d. For example, N(0) = ½ Typically, you will look up these probabilities in a table. You can also find them with Excel using the formula: =Normdist(d,0,1,true)

14.18 Example P 0 =$50, X = $49, r f =7%, t = 199 days, σ 2 = 0.09

14.19 Black-Scholes Formula for Puts