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