Problem 6 (Price of Standard Oil contract in a 3-step binomial model). (8 pts) The corittract issued by Standard Oil some time ago worked as follows. At the maturity time T, the company promised to pay $1,000 plus an additional amount based on the price of oil at that time. The additional amount was equal to the product of 170 and the excess (if any) of the price of a barrel of oil at maturity over $25. The maximum additional amount paid was $2,550 (which corresponds to a price of $40 per barrel). Assume that the price St of a barrel of oil now follows a 3-step binomial tree model. Assume that in this binomial tree model, S0=35,u=0.1,d=0.1 and the annual periodic compounding risk-free rate is R=0.05. a) (3 pts) What is the final payoff of this Standard Oil contract? b) (5 pts) Find the initial price of the Standard Oil contract in this 3-step binomial model(i.e., maturity time T=3 )