20-3 What determines Option Values?

Point A:

When the stock is worthless, the option is worthless.

A stock price of zero means that there is no possibility the stock will ever have any future value.13 If so, the option is sure to expire unexercised and worthless, and it is worthless today. That brings us to our first important point about option value:

The value of an option increases as stock price increases, if the exercise price is held constant.

That should be no surprise. Owners of call options clearly hope for the stock price to rise and are happy when it does.

Point B As the stock price increases, the option price approaches the stock price less the present value of the exercise price. The reason is as follows: The higher the stock price, the higher is the probability that the option will eventually be exercised. If the stock price is high enough, exercise becomes a virtual certainty; the probability that the stock price will fall below the exercise price before the option expires becomes trivially small.

Thus, the value of an option increases with both the rate of interest and the time to maturity.

Thus the value of an option increases with both the volatility of the share price and the time to maturity.