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The following option prices were observed for calls and puts on a stock for the

ID: 2784805 • Letter: T

Question

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

On July 6, the dividend yield on the stock is 2.7 percent. What is the theoretical fair value of the October 165 call?

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

Explanation / Answer

The Black-Scholes Option pricing formula for put option can be derived from put-call parity relationship and the formula is : P = X * EXP(-r *t) * (1- N(d2)) - S * (1-N(d1) Where X is Put Exercise Price = 165 S = Current Price = 165.13.