A firm wants to buy an average strike call option on crude oil. As the name

suggests, the strike price for this type of option is equal to the average crude oil price per barrel during the options life. The call options payoff is max[0, ST AVGt,T], where ST is the crude oil price per barrel at time T and AVGt,T is the average crude oil price per

barrel between time t and time T. The option is European exercise.

Suppose crude oil is priced at $45 per barrel and has a volatility of 40%. The riskless

interest rate for continuous compounding is 5%. Using a binomial tree model with two

time steps, what is the price per barrel at time t for an average strike call option with 0.5

years until expiration?

Note that with two time steps, there are three prices along each price path. Thus for a

given price path, AVGt,T is equal to (1/3) [St + St+0.25 + ST].