Business, 12.03.2021 15:30 carlosiscr7

The following option prices were observed for calls and puts on a stock for the trading day of July 6 of a particular year. Use the information for the following problem. The stock was priced at $165.13, and the expirations on the options were July 17, August 21, and October 16. The continuously compounded risk-free rate associated with the three expirations were 0.0503, 0.0535, and 0.0571, respectively. The standard deviation of the continuously compounded return on the underlying is 21%. Assume that these are all European options. 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 8.13 11.13 0.75 2.75 4.50
165 2.69 5.25 8.13 2.38 4.75 6.75
170 0.81 3.25 6.00 5.75 7.50 9.00

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?

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The following option prices were observed for calls and puts on a stock for the trading day of July...

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