Suppose there is a call option on Microsoft (MSFT) stock. The option has an exercise price of $240. At the same time, a US Treasury bill with the same maturity date has an annualized rate of 4%. For simplicity, assume that there are exactly 8 months (or 240 days) to the maturity of the option.

a. Assuming that the correct standard deviation to use in the Black Scholes formula is 30% annually, calculate the price of the call option. Assume that the market price of the MSFT stock is $284 at the time of the option was quoted.

b. Suppose that you believe the historical annual standard deviation of MSFT stock, 25%, is what should be used as the volatility 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 exercise price and maturity as the call above. Use the historical standard deviation in your calculation.