# Math - 1 A stock price is currently \$35 During each 2-month...

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1. A stock price is currently \$35. During each 2-month period for the next four months it will either increase by 8% or decrease by 10%. The risk-free interest rate is 5%. Use a two-step tree to calculate the value of a a derivative that pays off [ max (35– S T , 0)] 2 , where S T is the stock price in 4 months. If the derivative is American-style, should it be exercised early? 2. A stock price is currently \$50. Over each of the next three 2-month periods it will either go up by 10% or down by 10%. The risk-free interest rate is 12%. Using binomial trees: (a) What is the value of a 6-month European put option with a strike price of \$52? (b) What is the value of a 6-month American put option with a strike price of \$52? 3. Consider a European call option on a non-dividend-paying stock where the stock price is \$45, the strike price is \$45, the risk-free rate is 5% per annum, the volatility is 25% per annum, and the time to maturity is 6 months.

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## This note was uploaded on 05/01/2010 for the course MATH 109880 taught by Professor Jacki during the Spring '10 term at Roma Tre.

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Math - 1 A stock price is currently \$35 During each 2-month...

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