The stock is trading at $83, and the annualized riskless rate is 3.8%. The stan- dard 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 repli- cate 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.

1. The following are prices of options traded on Microsoft Corporation, which pays no dividends. Call Put K = 85 K = 90 K = 85 K = 90 One-month Three-month Six-month $2.75 $1.00 $4.00 $2.75 $7.75 $6.00 $4.50 $ 7.50 $5.75 $ 9.00 $8.00 $12.00