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An Introduction to Options Trading by Frans de Weert

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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 St, the Black – Scholes formula gives that:
(A.1)
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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 ST > K, where K is the strike price. This means:
124
Since y has a standard normal distribution:
(A.2)
125
In the same way one can derive:
(A.3)
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