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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