Answer the second “dilemma” in the section on maximum variables, Section 5.3. If the volatility is 20 % and the time to expiration is 2 months, what is the probability that the stock price starting from 100 will rise above 103 over the term of theput option but nevertheless finish below 97.50? In the first case, assume the drift is zero. Write a program to answer the question if the drift is 6 %, if the drift is −4 %.

Data given in Section 5.3

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5.3 Setting Stops: Maximum Variables Consider the following dilemma. A trader sells a 3 month call option struck at $100. The underlying spot price is also currently at $100. At the same time the trader sets an automatic stop to exit the trade if the spot price reaches $105. What is the probability the stop will take out what would have been a profitable trade? In other words, what is the probability the underlying price will rise to