Question

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3. (Futures vs options) Consider the market for wheat. The current price of a ton of wheat is 250 USD. In the next year, the price will be 310 with probability 1/3 and 220 with probability 2/3. The interest rate between the two years is 5%

Answer 1

S0 = 250; Su = 310; Sd = 220; r = 5%

u = Su / S0 = 310 / 250 = 1.24; d = Sd / S0 = 220 / 250 = 0.88

Risk neutral probability of up state, p = (1 + r - d) / (u - d) = (1 + 5% - 0.88) / (1.24 - 0.88) = 0.4722

K = 305

Pu = max (K - Su, 0) = max (305 - 310, 0) = 0

Pd = max (K - Sd, 0) = max (305 - 220, 0) = 85

Hence, price of the put option = [p x Pu + (1 - p) x Pd] / (1 + r) = [0.4722 x 0 + (1 - 0.4722) x 85] / (1 + 5%) = $ 42.72