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/n Rutgers Business School Rutgers, The State University of New Jersey Derivatives Spring 2024 HW7 Due date: Due: April 24, 2024 (Wednesday) Required (8 Questions): Chapter 17. Options on Stock Indices and Currencies 17.2, 17.3, 17.7, 17.10, 17.11 Chapter 18. Futures Options 18.1, 18.14, 18.15 1 17.2 "Once we know how to value options on a stock paying a dividend yield, we know how to value options on stock indices and currencies." Explain this statement. 17.3 A stock index is currently 300, the dividend yield on the index is 3% per annum, and the risk-free interest rate is 8% per annum. What is a lower bound for the price of a six- month European call option on the index when the strike price is 290? 17.7 Calculate the value of an eight-month European put option on a currency with a strike price of 0.50. The current exchange rate is 0.52, the volatility of the exchange rate is 12%, the domestic risk-free interest rate is 4% per annum, and the foreign risk-free interest rate is 8% per annum. 17.10 Consider a stock index currently standing at 250. The dividend yield on the index is 4% per annum, and the risk-free rate is 6% per annum. A three-month European call option on the index with a strike price of 245 is currently worth $10. What is the value of a three-month put option on the index with a strike price of 245? 17.11 An index currently stands at 696 and has a volatility of 30% per annum. The risk-free rate of interest is 7% per annum and the index provides a dividend yield of 4% per annum. Calculate the value of a three-month European put with an exercise price of 700. 18.1 Explain the difference between a call option on yen and a call option on yen futures. 18.14 A futures price is currently 25, its volatility is 30% per annum, and the risk-free interest rate is 10% per annum. What is the value of a nine-month European call on the futures with a strike price of 26? 18.15 A futures price is currently 70, its volatility is 20% per annum, and the risk-free interest rate is 6% per annum. What is the value of a five-month European put on the futures with a strike price of 65? 2