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The Chicago Board Options Exchange website shows that there is a call option on Microsoft stock. The option has a strike price of $35. At the same time, a US Treasury Bill with the same maturity date has an annualized return of 1.25%. You may assume that the correct standard deviation to use in the Black-Scholes formula is 36.5% annually. For simplicity, you can assume that there are exactly 7 months (or 210 days) to the maturity of the option.
a) Calculate the price of the call option described above assuming that the option has a European exercise structure. The price of the Microsoft stock is $27 at the time the option was quoted.
b) Suppose that you believe the historical annual standard deviation of Microsoft stock, 34.5%, should be used as the volatility variable in the formula when calculating the Black-Scholes price. What will be the price of the same option under this new volatility measure?
c) Calculate the price of a put option that has the same strike price and maturity as the above call option. Use the historical volatility in your calculation.
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