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 Price Delta 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 Price Delta 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.
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