## Quick Discussion of Factors Determining Put Option Values

Given our extended discussion of the factors influencing a call's value, we can examine the effect of these factors on puts very easily. Table 22.2 summarizes the five factors influencing the prices of both American calls and American puts. The effect of three factors on puts are the opposite of the effect of these three factors on calls:

1. The put's market value decreases as the stock price increases because puts are in the money when the stock sells below the exercise price.

2. The value of a put with a high exercise price is greater than the value of an otherwise identical put with a low exercise price for the reason given in (1).

3. A high interest rate adversely affects the value of a put. The ability to sell a stock at a fixed exercise price sometime in the future is worth less if the present value of the exercise price is diminished by a high interest rate.

The effect of the other two factors on puts is the same as the effect of these factors on calls:

4. The value of an American put with a distant expiration date is greater than an otherwise identical put with an earlier expiration.8 The longer time to maturity gives the put holder more flexibility, just as it did in the case of a call.

Probability

The call on stock B is worth more than the call on stock A because stock B is more volatile. At expiration, a call that deep in the money is more valuable than a call that is only slightly in the money. However, at expiration, a call way out of the money is worth zero, just as is a call only slightly out of the money.

Exercise price

Price of common stock at expiration

Exercise price

8Though this result must hold in the case of an American put, it need not hold for a European put.

Ross-Westerfield-Jaffe: I VI. Options, Futures, and I 22. Options and Corporate I I © The McGraw-Hill

Corporate Finance, Sixth Corporate Finance Finance: Basic Concepts Companies, 2002

Edition

Chapter 22 Options and Corporate Finance: Basic Concepts 625

■ TABLE 22.2 Factors Affecting American Option Values

Increase in Call Option* Put Option*

Value of underlying asset (stock price) +

Stock volatility + +

Interest rate +

Time to exercise date + +

In addition to the preceding, we have presented the following four relationships for American calls:

1. The call price can never be greater than the stock price (upper bound).

2. The call price can never be less than either zero or the difference between the stock price and the exercise price (lower bound).

3. The call is worth zero if the stock is worth zero.

4. When the stock price is much greater than the exercise price, the call price tends toward the difference between the stock price and the present value of the exercise price.

*The signs (+, —) indicate the effect of the variables on the value of the option. For example, the two + s for stock volatility indicate that an increase in volatility will increase both the value of a call and the value of a put.

5. Volatility of the underlying stock increases the value of the put. The reasoning is analogous to that for a call. At expiration, a put that is way in the money is more valuable than a put only slightly in the money. However, at expiration, a put way out of the money is worth zero, just as is a put only slightly out of the money.

List the factors that determine the value of options.

Why does a stock's variability affect the value of options written on it?

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