Analysis of Financial Time Series, Third Edition

6.1 Options

A stock option is a financial contract that gives the holder the right to trade a certain number of shares of a specified common stock by a certain date for a specified price. There are two types of options. A call option gives the holder the right to buy the underlying stock; see Chapter 3 for a formal definition. A put option gives the holder the right to sell the underlying stock. The specified price in the contract is called the strike price or exercise price. The date in the contract is known as the expiration date or maturity. American options can be exercised at any time up to the expiration date. European options can be exercised only on the expiration date.

The value of a stock option depends on the value of the underlying stock. Let K be the strike price and P be the stock price. A call option is in-the-money when P > K, at-the-money when P = K, and out-of-the-money when P < K. A put option is in-the-money when P < K, at-the-money when P = K, and out-of-the-money when P > K. In general, an option is in-the-money when it would lead to a positive cash flow to the holder if it were exercised immediately. An option is out-of-the-money when it would lead to a negative cash flow to the holder if it were exercised immediately. Finally, an option is at-the-money when it would lead to zero cash flow if it were exercised immediately. Obviously, only in-the-money options are exercised in practice. For more information on options, see Hull (2007).