Simple Model Part I

Option pricing can be a complex subject, and we defer a detailed discussion to a later chapter. Fortunately, as is often the case, many of the key insights can be illustrated with a simple example. Suppose we are looking at a call option with one year to expiration and an exercise price of \$105. The stock currently sells for \$100, and the risk-free rate, Rf, is 20 percent.

The value of the stock in one year is uncertain, of course. To keep things simple, suppose we know that the stock price will be either \$110 or \$130. It is important to note that

Ross et al.: Fundamentals of Corporate Finance, Sixth Edition, Alternate Edition

V. Risk and Return

14. Options and Corporate Finance

PART FIVE Risk and Return we don't know the odds associated with these two prices. In other words, we know the possible values for the stock, but not the probabilities associated with those values.

Because the exercise price on the option is \$105, we know that the option will be worth either \$110 - 105 = \$5 or \$130 - 105 = \$25, but, once again, we don't know which. We do know one thing, however: Our call option is certain to finish in the money.

The Basic Approach Here is the crucial observation: It is possible to exactly duplicate the payoffs on the stock using a combination of the option and the risk-free asset. How? Do the following: buy one call option and invest \$87.50 in a risk-free asset (such as a T-bill).

What will you have in a year? Your risk-free asset will earn 20 percent, so it will be worth \$87.50 X 1.20 = \$105. Your option will be worth \$5 or \$25, so the total value will be either \$110 or \$130, just like the value of the stock:

 Stock Value vs. Risk-Free Asset Value + Call Value = Total Value \$110 130

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