Let S(t) denote the spot price of an asset at time t. Letr denote the risk-free rate of return. Let F(t) denote the futures price at time t for a futures contract with delivery date T. (a) (4 points) If we are at time t = 0, one unit of the asset costs $100, the risk-free rate is 4% per year (continuously compounded) for the year period, and the we plan to hedge a long position in the asset worth $100,000 for 1 year, what is the value of the basis at this time? (b) (4 points) Suppose that at time t = 0 we entered a short futures contract (100 units per contract) to hedge our asset. Now suppose that nine months have passed, and we want to close out our position. If the spot price of the asset is now $110, what is the basis, and what is the gain/loss on the hedge upon closing out? (c) (4 points) If we knew at time t = 0 that our asset followed a stock model with Gaussian steps, and that u = 0.1, 0 = 0.08, then find the probability distribution for the basis in nine months. What is its mean and its variance? Did the hedge in part (b) perform better or worse than expected? Justify your