part b is as follow:

Let S(t) denote the spot price of an asset at time t. Let r 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. (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 answer. (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? Let S(t) denote the spot price of an asset at time t. Let r 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. (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 answer. (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