Question 1: Shares in XYZ Corporation sell today for $20. The risk-free rate is 3% (continuously compounded). In the next six months, XYZ shares will either increase in price by 30%, or decrease by 40%. In the following six months, XYZ shares will again either increase in price by 30%, or decrease in price by 40%. XYZ pays no dividends. (1) What is the price of a European call with strike $19 and expiration in one year? Use a binomial tree. (2) What is the price of a European put with strike $19 and expiration in one year? Use a binomial tree, and then verify your answer with put-call parity. (3) Now obtain the prices of these call and put options using risk-neutral probabilities. Verify that you get the same answers as in (1) and (2). Question 2: 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
Question 1: Shares in XYZ Corporation sell today for $20. The risk-free rate is 3% (continuously compounded). In the next six months, XYZ shares will either increase in price by 30%, or decrease by 40%. In the following six months, XYZ shares will again either increase in price by 30%, or decrease in price by 40%. XYZ pays no dividends. (1) What is the price of a European call with strike $19 and expiration in one year? Use a binomial tree. (2) What is the price of a European put with strike $19 and expiration in one year? Use a binomial tree, and then verify your answer with put-call parity. (3) Now obtain the prices of these call and put options using risk-neutral probabilities. Verify that you get the same answers as in (1) and (2). Question 2: 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
Chapter7: Common Stock: Characteristics, Valuation, And Issuance
Section: Chapter Questions
Problem 6P
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Don't use gpt for answers pls. Thanks!
Transcribed Image Text:Question 1:
Shares in XYZ Corporation sell today for $20. The risk-free rate is 3% (continuously compounded). In
the next six months, XYZ shares will either increase in price by 30%, or decrease by 40%. In the following
six months, XYZ shares will again either increase in price by 30%, or decrease in price by 40%. XYZ pays
no dividends.
(1) What is the price of a European call with strike $19 and expiration in one year? Use a binomial tree.
(2) What is the price of a European put with strike $19 and expiration in one year? Use a binomial tree,
and then verify your answer with put-call parity.
(3) Now obtain the prices of these call and put options using risk-neutral probabilities. Verify that you
get the same answers as in (1) and (2).
Transcribed Image Text:Question 2:
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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