A share in stock ZZ currently trades at $80. The volatility of the stock price is 25% and the

expected return on this stock is 12%. The continuously compounded risk-free rate is 3%.

Assume that the volatility, the expected rate of return, and the risk-free rate are constant, and

that ZZ pays no dividends

(1) Find the prices of an at-the-money European call and an at-the-money European put

with maturity six months for different steps h in the tree (h = T/N). Consider N = 5, N = 10, N

= 50, and N = 100 and use the spreadsheet BinomialTree that is on Canvas.

(2) What value of N is needed to get the price from the tree within a cent to the true Black

Scholes-Merton price?

(3) Find the Black-Scholes Delta's and Gamma's of these two options