Question

Your are in New Zealand. You are planning to price an American put option on Canadian dollar futures, maturing in 4 months. You plan to use a 2 step tree. The New Zealand interest rate is 0.70%, while the Canadian interest rate is 3.50% (both with continuous compounding). The Canadian dollar futures price has volatility 20.00%. What is the risk neutral probability for the up state?

Answer 1

Up Move factor (U) = e ^{* T}

Up Move factor (U) = e^{20% * (4 / 12)}

Up Move factor (U) = 1.1224

Down move factor (D) = 1 / U

Down move factor (D) = 1 / 1.1224

Down move factor (D) = 0.8909

Risk neutral probability of Up move = (e^{(Domestice risk free rate - Foreign risk free rate) * Time to Expiry} - D) / (U - D)

Risk neutral probability of Up move = (e^{(0.7% - 3.5%) * (4/12)} - 0.8909) / (1.1224 - 0.8909)

Risk neutral probability of Up move = 43.1145%