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hwk2-2011 - STOR 890 Spring 2011 Homework 2 Note Try these...

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STOR 890, Spring 2011, Homework 2 Note: Try these problems yourselves and contribute to the class discussion on Thur. 3/3. (1) Consider a binomial model with T = 2 where the stock has an initial price of $100 and can go up 15% or down 5% in each period. The price of a European call option on this stock with strike price $115 and maturity T = 2 is $5.424. What should be the initial value of a risk-free security that pays $1 at t = 1? We assume a constant interest rate r . (2) A European call option and put option on a stock both have a strike price of $20 and an expiration date in three months. Both sell for $3. The risk-free annual interest rate is 10%, the current stock price is $19, and a $1 dividend is expected in one month. Identify an arbitrage opportunity open to a trader. (3) Consider a two-period binomial tree with S (0) = $50, r = 2%. After one period the price of the stock can go up to $55 or drop to $47, and it will pay (in both cases) a dividend of $3. If it goes up the first period, then it can go up to $58 or down to $48 the second period. If it goes down
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