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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 BackScholes 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 dividendpaying stock. Use the BlackScholes formula and show that these two prices satisfy the PutCall Parity. b) Consider a European call option and a nondividendpaying stock that is very deep in the money (the current stock price is much larger than the strike price K). Using the BlackScholes 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 riskfree 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 $1, would the pseudoAmerican (Black approximation) call price obtained (please estimate) be as accurate? Explain. 3. The DMDollar exchange rate is 1.30 DM/$ today. Assume that the volatility of the exchange rate is = 0.15....
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 Spring '11
 mazaheri
 Management

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