Problem A1 and its solution

A1. Assume the Black-Scholes framework. Consider a 9-month at-the-money European put option on a futures contract. You are given: (i) The continuously compounded risk-free interest rate is 10%. (ii) The strike price of the option is 20. (iii) The price of the put option is 1.625. If three months later the futures price is 17.7, what is the price of the put option at that time? (A) 2.09 (B) 2.25 (C) 2.45 (D) 2.66 (E) 2.83