Problem 1. This problem concerns the pricing of a European option in a two-period multiplicative binomial...

 

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Problem 1. This problem concerns the pricing of a European option in a two-period multiplicative binomial tree market. Suppose the present stock price is So = 50, the time interval is AT = 0.5 years, and the multiplicative factors are u = 1.2, d=0.8 (so the stock price 0.5 years from now is either uSo or dSo, and the stock price 1 year from now is either u2So, udSo, or d So). Assume the risk-free rate is constant and is 4% per year. a) Find the no arbitrage price of a European put with strike 45 and maturity 1 year. b) Verify that the formula derived in class for the price of a derivative security in a general N-period tree matches the price from part a). c) Describe the trading strategy that replicates this option, using stock and the risk-free bond. Problem 1. This problem concerns the pricing of a European option in a two-period multiplicative binomial tree market. Suppose the present stock price is So = 50, the time interval is AT = 0.5 years, and the multiplicative factors are u = 1.2, d=0.8 (so the stock price 0.5 years from now is either uSo or dSo, and the stock price 1 year from now is either u2So, udSo, or d So). Assume the risk-free rate is constant and is 4% per year. a) Find the no arbitrage price of a European put with strike 45 and maturity 1 year. b) Verify that the formula derived in class for the price of a derivative security in a general N-period tree matches the price from part a). c) Describe the trading strategy that replicates this option, using stock and the risk-free bond.

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Answer a To find the no arbitrage price of a European put with strike 45 and maturity 1 year we can use the multiplicative binomial tree model to calc... View the full answer