Problem
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
i. 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.
ii. What value of N is needed to get the price from the tree within a cent to the true Black Scholes-Merton price?
iii. Find the Black-Scholes Delta's and Gamma's of these two options.