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.
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