3330 PS10 - Cornell University Fall 2010 Economics 3330:...

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Cornell University Fall 2010 Economics 3330: Problem Set 10 Due 12/2/2010 1. Consider the following parameters: current stock price $50, standard deviation 50%, exercise price $50, interest rate 4%. a. Use the Black-Scholes formula to find the value of a call option with an exercise price of $50 and expiration of 1 year. b. Use the Black-Scholes formula to find the value of a put option with an exercise price of $50 and expiration of 6 months. c. Verify put-call parity. 2. Find how the value of the call option from problem one changes when each of the following changes in parameters is made individually . In other words, for each of the following, you are only changing one parameter relative to problem one . a. Time to expiration 3 months. C falls to 5.20 b. Standard deviation 25%. C falls to 5.92 c. Exercise price $55. C falls to 8.79 d. Interest rate 10%. C rises to 9.96 3. Option deltas a.What is the delta of a call option? How is it approximated in the Black-Scholes model? b.Fill in the following table for a call option with exercise stock price 50, standard deviation 50%, and interest rate 4% for each of the following current stock prices. Sketch the resulting graph. 10 20 30 40 45 50 55 60 70 80 90 100 140 P r i c e D e l t a c. Now do the same for a put option, including sketching the resulting graph. 10 20 30 40 45 50 55 60 70 80 90 100 140 P r i c e D e l t a 4. A hedge fund has a net asset value of $100 per share and a high water mark of $110. The standard deviation of the fund’s annual returns is 40% and the risk-free rate is 2%. The incentive fee is 20%. All answers should be given in terms of one year. a. According to Black-Scholes, what is the value of the incentive fee?
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This note was uploaded on 04/06/2011 for the course ECON 3330 taught by Professor Mbiekop during the Fall '08 term at Cornell.

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3330 PS10 - Cornell University Fall 2010 Economics 3330:...

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