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 this information in the following question. The stock was priced at 165.13. The expirations were July 17, August 21, and October 16. The continuously compounded risk-free rates associated with the three expirations were 0.0503, 0.0535, and 0.0571, respectively. Unless otherwise indicated, assume 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 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 Let the standard deviation of the continuously compounded return on the stock be 21 percent. Suppose the stock pays a $1.10 dividend with an ex-dividend date of September 10. What is the theoretical fair value of the October 165 call?