The following are prices of options traded on Microsoft Corporation, which pays no dividends.

The stock is trading at $83, and the annualized riskless rate is 3.8%. The standard deviation in ln(stock prices) (based on historical data) is 30%.

a. Estimate the value of a three-month call with a strike price of $85.

b. Using the inputs from the Black-Scholes model, specify how you would replicate this call.

c. What is the implied standard deviation in this call?

d. Assume now that you buy a call with a strike price of $85 and sell a call with a strike price of $90. Draw the payoff diagram on this position.

e. Using put-call parity, estimate the value of a three-month put with a strike price of $85.

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Call Put K=85 K=90 K = 85 K = 90 One-month $2.75 $1.00 $4.50 $ 7.50 Three-month Six-month $4.00 $2.75 $5.75 $ 9.00 $7.75 $6.00 $8.00 $12.00