Consider a stock with a current price () of $100 and a constant annualized return volatility () of 20%. The stock does not pay dividends. A risk-free zero-coupon bond with $1 par and one year maturity is worth $0.95 today.

a) Using the approach discussed in class, construct a two-step binomial tree to approximate the stock price dynamics, with each step being 1 year. List the stock price at each node at one and two years.

b) Compute the risk-neutral probability of going up and going down at each step.

c) Based on the binomial tree, compute the current value and the delta of a European put option on the stock with a maturity of two years and a strike price of $110.

d) Based on the binomial tree, compute the current value and the delta of an American put option on the stock with a maturity of two years and a strike price of $110.