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hwk2-2011

# 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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