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1. Consider a stock with a price of $120 and a standard deviation of 20 percent. The stock will pay a dividend of $5 in 40 days and a second dividend of $5 and 130 days. The current risk-free rate is 5 percent per annum. An American call on this stock has an exercise price of $150 and expires in 100 days.
Price the American call option using the Black-Scholes Model. Show all calculations.
2. Consider the binomial model for an American call and put on a stock whose price is $60. The exercise price for both the put and the call is $45. The standard deviation of the stock returns is 30 percent per annum, and the risk-free rate is 5 percent per annum. The options expire in 90 days. The stock will pay a dividend equal to 3 percent of its value in 50 days.
(a) Draw the three-period stock tree and the corresponding trees for the call and the put.
(b) Compute the price of these options using the three-period trees.
(c) Explain when, if ever, each option should be exercised.
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