Let the standard deviation of the continuously compounded return on the stock is 21 percent. Use the Black-Scholes-Merton European put option pricing formula for the October 165 put option. a) What is the theoretical fair value of the October 165 put? b) Based on your answer in part a, recommend a riskless strategy. c) If the stock price decreases by $1, how will the option position offset the loss on the stock?

The following option prices were observed for calls and puts on a stock for the trading day of July 6 of a articular year. Use this information in problems 7 through 14. The stock was priced at 165.13 The expirations were July 17, August 21, and October 16. The continuously compounded risk-free rates asso- ciated with the three expirations were 0.0503, 0.0535, and 0.0571, respectively. Unless otherwise indicated, assume that the options are European Calls Puts Strike Jul Aug Oct Jul Aug Oct 155 10.50 11.75 14.00 0.19 1.25 2.75 160 6.00 4.50 2.75 8.13 11.13 0.75 165 2.69 8.13 2.38 4.75 6.75 5.25 170 0.81 6.00 5.75 7.50 9.00 3.25