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Unformatted text preview: Math 238, Financial Mathematics Problem set 2 January 27, 2009 These problems are due on Friday January 30, 5:00pm. You can give them to me in class, drop them in my office, or put them in my mailbox outside the mathematics department. You will need to use Matlab or some other computational tool in some of these problems. Problem 1 Derive the put-call parity relation using the Black-Scholes partial differential equation and then give a detailed no-arbitrage interpretation of it. Problem 2 (a) Use the formula for the explicit solution of the BS equation to price one call option today, where S (0) = $850, the strike time is three months, the strike price is K = $950, the volatility is 40% and the interest rate is 1%. (b) Plot this price as a function of the volatility from 15% to 60%. (c) Calculate the hedge ratio one month before strike time for (a), for a range of S around the strike price, and plot it. (d) What is the price of a put with the same parameters as (a)? (e) What is the price of a put with parameters as in (a) except that...
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This note was uploaded on 11/08/2009 for the course MATH 238 taught by Professor Papanicolaou during the Winter '08 term at Stanford.
- Winter '08