Problem 3. Weather is very important for farmers. Suppose that you are approached by a farmer who is worried about warm temperatures and wishes to purchase a call option on the average weather temperature over the next year. Specifically, the weather (in Fahrenheit) follows the process and the farmer wants a payoff equal to max (X K, 0) (1) You observe that call options on the weather follow the following process dC a) Use Exercise 15.1 in ATC to prove that A (at) 0 for all weather derivatives. (Hint: Observe that the average return from investing in weather derivatives is just the riskless rate b) Provide an analytical price for the option with payoff (1). (Hint: serve that arr is normally distributed, since rt is an Ornstein Uhlenbeck process). Problem 3. Weather is very important for farmers. Suppose that you are approached by a farmer who is worried about warm temperatures and wishes to purchase a call option on the average weather temperature over the next year. Specifically, the weather (in Fahrenheit) follows the process and the farmer wants a payoff equal to max (X K, 0) (1) You observe that call options on the weather follow the following process dC a) Use Exercise 15.1 in ATC to prove that A (at) 0 for all weather derivatives. (Hint: Observe that the average return from investing in weather derivatives is just the riskless rate b) Provide an analytical price for the option with payoff (1). (Hint: serve that arr is normally distributed, since rt is an Ornstein Uhlenbeck process)