Today is june 8th. an airline company wants to purchases 2,000,000 gallons jet fuel on december 8th (of the same year). they fear that the price of jet fuel will rise and thus would like to hedge the purchase of jet fuel by a futures contract. unfortunately, there exists no jet fuel futures contract. however, a futures contract for heating oil trades at the nymex (new york mercantile exchange) and, it is known that jet fuel is a derivative of heating oil. the spot price of jet fuel is $0.95 per gallon on june 8th. we assume that the spot price follows a geometric brownian motion with the expected annual log-return 2%, and annual volatility 10%. on june 8th, a futures contract specifies $1.03 per gallon for 500,000 gallons of heating oil for delivery on december 8th. we assume this price also follows a geometric brownian motion with the expected annual log-return 2%, and annual volatility 8%. we also assume that the correlation between the futures contract price of heating oil and the spot price of jet fuel is 0.94 on december 8th. what is the minimum variance hedge ratio? equivalently, how many future contracts of heating oil the airline company should buy?