An Introduction to Options Trading

Appendix A

PROBABILITY THAT AN OPTION EXPIRES IN THE MONEY

Whenever the stock price movement is only known up to time t and the price at time t is S_t, the Black – Scholes formula gives that:

(A.1)

provided it is a non-dividend paying stock. In the above formula y is normally distributed with mean 0 and variance 1. Now it is easy to calculate the probability that an option expires in the money. Take a call option. A call option expires in the money when S_T > K, where K is the strike price. This means:

Since y has a standard normal distribution:

(A.2)

In the same way one can derive:

(A.3)