(20pt) An airline company needs to buy 10,000 barrels of jet fuel six months later. Due to its price fluctuation over time, the company would like to hedge the risk via the minimum variance hedge using the futures contracts on crude oil price. It is assumed that jet fuel and crude oil prices have a strong correlation p = 0.9 and no futures market exists for the jet fuel. The current jet fuel price So is $80 per barrel, and the 6-month futures price Fo of the crude oil is $70 per barrel today. Suppose that the jet fuel price St (per barrel) follows the process below: dSt = 0.02Stdt + 0.2StdWt, and the standard deviation of the futures price in 6 months is estimated to be $3. Find the optimal amount of the futures contract that should be made to hedge the risk. (20pt) An airline company needs to buy 10,000 barrels of jet fuel six months later. Due to its price fluctuation over time, the company would like to hedge the risk via the minimum variance hedge using the futures contracts on crude oil price. It is assumed that jet fuel and crude oil prices have a strong correlation p = 0.9 and no futures market exists for the jet fuel. The current jet fuel price So is $80 per barrel, and the 6-month futures price Fo of the crude oil is $70 per barrel today. Suppose that the jet fuel price St (per barrel) follows the process below: dSt = 0.02Stdt + 0.2StdWt, and the standard deviation of the futures price in 6 months is estimated to be $3. Find the optimal amount of the futures contract that should be made to hedge the risk