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Unformatted text preview: MIT Sloan School of Management J. Wang 15.407 E52-456 Fall 2003 Problem Set 5: Options Not due 1. You are given the following prices: Security Maturity (years) Strike Price ($) JK stock-- 94 Put on JK stock 1 80 5 Call on JK 1 80 ? Tbill (FV=100) 1- 91 (a) What is the price of the call option? (b) Now suppose that the market price of a JK call option with strike 80 was 30. When you tell your boss that the price you found in part (1) is different, he tells you that you must be wrong, since the market is efficient and thus always right. In other words, the formula you have used to price the call option is just a theory, but in practice it must be that the market knows something that you don’t, perhaps that the stock price is expected to go really high. Do you agree or disagree with him? i. if yes, can you strengthen his argument? ii. if no, can you prove him wrong? 2. In the industry, trader often decomposes the value of an option into ”time value” and ”intrinsic value”. The intrinsic value of an option is the value of the option if you exercise it now, whereas the time value of the option is the difference between the price and the intrinsic value of the option. (a) Given a call option on a stock trading at price S, and strike of K, what is the intrinsic value of the stock? (b) For call options of the same strike, how does the time value changes with maturity? Explain (intuition suffices) (c) For call options of the same maturity, how does the time value changes with the strike? Explain (intuition suffices) (d) Stocks of company A and B are trading at the same price. There are two call options of exact same strike and maturity. Is it necessary that the two options trade at the same price? How about the time value of the two options?...
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This note was uploaded on 01/19/2011 for the course 15 15.407 taught by Professor Wang during the Fall '03 term at MIT.
- Fall '03