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Unformatted text preview: STOR 890, Spring 2011, Homework 3 Note: Try these problems yourselves, and we will organize a meeting before the final exam to discuss them. Assume the BS market in problems (1) — (4). (1) Suppose a stock price is currently $50, the stock return has mean 18% and volatility 30%. What is the probability distribution for the stock price in two years? Specify the mean and standard deviation of the distribution. (2) With the assumptions in (1), specify the strike price K for a European call that becomes mature in two years, such that with probability 0.7 (under the physical measure P ) the option is exercised. (3) A financial institution plans to offer a security, written on a stock S , with pay-off S 2 T at time T . Find the expression of time t price of the security. (4) Suppose a call option on a stock has a market price $2.50, and the stock price is $15, the exercise price is $13, the time to maturity is 3 months, and the annual interest rate is 5%. Find the implied volatility. Hint: Use any software convenient to you to conduct the numerical search....
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- Spring '08
- Options, Mathematical finance, independent Brownian motions