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Unformatted text preview: 1 UNIVERSITY OF TORONTO AT SCARBOROUGH DEPARTMENT OF MANAGEMENT MGTC71: Introduction to Derivatives Markets Problem Set 5 _______________________________________________________________________________ 1. Use the Back-Scholes formula to prove the followings: a) Consider a European call option and a European put option with the same strike price K on the same non- dividend-paying stock. Use the Black-Scholes formula and show that these two prices satisfy the Put-Call Parity. b) Consider a European call option and a non-dividend-paying stock that is very deep in the money (the current stock price is much larger than the strike price K). Using the Black-Scholes formula show that the value of such a call option is approximately equal to the value of a forward contract with delivery price K and maturity T. 2. A Firm has a stock price of 95 and an annual standard deviation of 35%. The risk-free rate is 10% (c.c.). This firm will pay a dividend of $1 in exactly 6 months and no other dividends over the next year. a) Price a European call written on this stock with an exercise price of $100 and a time to maturity of one year. b) Price an American call with an exercise price of $100 and a time to maturity of one year using the pseudo- American call pricing method. c) How accurate is the price you calculated in (b)? Explain. d) If the dividend were $8 instead of $1, would the pseudo-American (Black approximation) call price obtained (please estimate) be as accurate? Explain. 3. The DM-Dollar exchange rate is 1.30 DM/$ today. Assume that the volatility of the exchange rate is = 0.15....
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- Spring '11