Question

Given the maturity of an American put option 2 years, riskfree rate 10%, volatility of the stock 40%, current spot price of stock $50, strike price $50, what is the one-step risk neutral probability that stock price goes down considering a three-step binomial tree?

	A.	0.201
	B.	0.452
	C.	0.910
	D.	0.523

Answer 1

Time step = Time to maturity / No of steps

Time step = 2 / 3

Time step = 0.67

Up move factor(U) = e^{Time step}

Up move factor(U) = e^{40% * 0.67}

Up move factor(U) = 1.3874

Down move factor(D) = 1 / Up move factor(U)

Down move factor(D) = 1 / 13874

Down move factor(D) = 0.7208

Risk reutral probability = (e^{risk free rate * Time step} - Down move factor(U) / (Up move factor(U) = Down move factor(U))

Risk reutral probability = (e^{10% * 0.67} - 0.7208) / (1.3874 - 0.7208)

Risk reutral probability = 0.523