The current price of a stock share that pays no dividend is \(€ 50\). The price follows a GBM with drift \(12 \%\) and volatility \(35 \%\); the continuously compounded risk-free rate is \(5 \%\). Consider a call and a put options, both European-style, with strike \(€ 55\), maturing in nine months. Which option is more likely to be exercised?

The probability of exercising the call is), which is given by , provided that we use the true drift. Hence, we should compute  as

Since, there is no need for further calculations, as this implies . Hence, the put is more likely to be exercised.

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