Varying the Time to Expiration

The impact of changing the time to maturity on American-style options is also fairly obvious. Since an American-style option can be exercised any time, increasing the option's time to expiration can't possibly hurt and, especially for out-of-the-money options, might help. Thus, for both puts and calls, increasing the time to expiration has a positive effect.

For a European-style call option, increasing the time to expiration also never hurts because, as we discussed earlier, the option is always worth more alive than dead and any extra time to expiration only adds to its "alive" value. With a European-style put, however, increasing the time to expiration may or may not increase the value of the option. As we have discussed, for a deep in-the-money put, immediate exercise is often desirable, so increasing the time to expiration only reduces the value of the option. If a put is out-of-the-money, then increasing the time to expiration will probably increase its value.

Figure 24.2 shows the effect of increasing the time to expiration on a put and a call. As in Figure 24.1, the options are exactly at the money. In the figure, notice that once time to maturity reaches about six months, further increases have little impact on the put's value. The call's value, in contrast, just keeps on rising.

The sensitivity of an option's value to the passage of time is called its theta. There is a formula for theta, but it is fairly complicated, so we will not present it. The important thing to realize is that option values are sensitive to the passage of time (especially call option values). To see why this is important, imagine you buy an option today and you hold it for a month. During the month, the stock price never changes. What happens to the value of your option?

The answer is that the value of your option declines because time to expiration has gotten shorter even though the underlying asset has not changed in value. We sometimes say that an option is a "wasting" asset, meaning that its value declines as time goes by, all else held constant. The tendency of an option's value to decline as time passes is also called "time decay." An option's theta is thus a measure of the rate of time decay.

Ross et al.: Fundamentals VIII. Topics in Corporate 24. Option Valuation of Corporate Finance, Sixth Finance

theta

Measures the sensitivity of an option's value to a change in the time to expiration.

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

VIII. Topics in Corporate Finance

24. Option Valuation

© The McGraw-Hill Companies, 2002

PART EIGHT Topics in Corporate Finance

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