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6. [20 points) The CFO of Refinery Co. is afraid of potentially high volatility in the price of crude oil (Price). High crude oil prices can lower the profits of the company. On the other hand, low crude oil prices may imply an economic recession. The CFO decides to buy a 2-year (T = 2) American straddle with strike price K = $40 to protect the profits of the company. The payoff of the American straddle is given by max {Price - K, 0} + max {K Price, 0}. What is the value today (t = 0) of the 2-year American crude oil straddle? Assume there are no arbitrage opportunities, the storage cost of crude oil is $0, crude oil barrels can easily be bought or sold, and the annual risk-free rate is equal to 1%. The future dynamics of the price of crude oil is as follows: 80 60 40 40 25 15 t=0 t-2 Hint: notice that u and d are not constant; you can use the broad replicating portfolio definition or the broad risk-neutral probability definition