We can identify at least six factors that should affect the value of a call option: the stock price, the exercise price, the volatility of the stock price, the time to expiration, the interest rate, and the dividend rate of the stock. The call option should increase in value with the stock price and decrease in value with the exercise price because the payoff to a call, if exercised, equals ST - X. The magnitude of the expected payoff from the call increases with the difference S0 - X.
Call option value also increases with the volatility of the underlying stock price. To see why, consider circumstances where possible stock prices at expiration may range from $10 to $50 compared to a situation where stock prices may range only from $20 to $40. In both cases, the expected, or average, stock price will be $30. Suppose the exercise price on a call option is also $30. What are the option payoffs?
Option payoff 0 0 0 10 20
Option payoff 0 0 0 5 10
If each outcome is equally likely, with probability 0.2, the expected payoff to the option under high-volatility conditions will be $6, but under the low-volatility conditions, the expected payoff to the call option is half as much, only $3.
Despite the fact that the average stock price in each scenario is $30, the average option payoff is greater in the high-volatility scenario. The source of this extra value is the limited loss an option holder can suffer, or the volatility value of the call. No matter how far below $30 the stock price drops, the option holder will get zero. Obviously, extremely poor stock price performance is no worse for the call option holder than moderately poor performance.
Part FIVE Derivative Markets
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