Today is September 1. A futures contract on crude oil expiring on December 20 of the same year has a futures price of $44.70. The volatility on the futures contract is 23%, and the continuously compounded risk-free rate is 2%. Assume that there are 365 days in a year.

a. What is the Black model price of a European call option on this futures contract, expiring on December 20 and with an exercise price of $46? (5 marks)

b. What is the Black model price of a European put option on this futures contract, expiring on December 20 and with an exercise price of $50? (5 marks)