The following option prices were observed for calls and puts on a stock for the trading day of July 6 of a year. Use this information in the problems 7 through 14. The stock was priced at 165.13. the expirations were July 17, August 21, and October 16. The continuous compounded risk-free rates associated with the three expirations were 0.0503, 0.0535, and 0.0571, respectively. Unless otherwise indicated, assume that the options are European

		Call			Put
strike	july	Aug	Oct	jul	Aug	Oct
155	10.5	11.75	14	0.19	1.25	2.75
160	6	8.13	11.13	0.75	2.75	4.5
165	2.69	5.25	8.13	2.38	4.75	6.75
170	0.81	3.25	6	5.75	7.5	9

Use the Black-Scholes-Merton European put option pricing formula for the October 165 put option. Repeat parts a, b, and of the previous problem with respect to put.

What is the theoretical fair value of the October 165 Put?

Based on your answer in part a recommend a riskless strategy

If the stock price decreases by $1 how will the option position offset the loss on the stock