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Probability and Statistics for Finance by Svetlozar T. Rachev, Markus Höechstöetter, Sergio M. Focardi, Frank J. Fabozzi CFA

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Appendix D. Application of the Log-Normal Distribution to the Pricing of Call Options

In Chapter 11, we described the log-normal distribution and applied it to the return distribution for a stock's price. In this appendix, we illustrate the application of this distribution to price a derivative instrument. More specifically, we illustrate an application to the pricing of a European call option.

Call Options

A call option is a contract that entitles the holder to purchase some specified amount of a certain asset at a predetermined price some time in the future. The predetermined price is called the strike price or exercise price. The date when the option expires is called the expiration date or maturity date. A call option has an exercise style that means when the option can be exercised by the holder of the option. If the call option can be exercised any time up to and including the maturity date, it is called an American call option. If it can only be exercised on the maturity date, it is referred to as a European call option. A call option is said to be a Bermuda call option if it exercised on designated dates throughout the option's life. In this appendix, our focus is on European call options.

The underlying asset for a call option can be a stock, bond, or any other financial instrument. Our focus in this appendix is a European call option on a stock. We will assume that the stock in this illustration is stock A.

The buyer of an option must pay the seller (or writer) of that option ...

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