# Option and Risk-free Interest Rate

Topics: Option, Put option, Call option Pages: 2 (395 words) Published: April 26, 2012
Question 1
Consider an option on a non-dividend-paying stock when the stock price is \$30, the exercise price is \$29, the risk-free interest rate is 5% per annum, the volatility is 25% per annum, and the time to maturity is four months. a. What is the price of the option if it is a European call? b. What is the price of the option if it is an American call? c. What is the price of the option if it is a European put? d. Verify that put–call parity holds.

Question 2
Assume that the stock in Question 1is due to go ex-dividend in 1.5 months. The expected dividend is 50 cents. a. What is the price of the option if it is a European call? b. What is the price of the option if it is a European put? c. Use the results in the Appendix to this chapter to determine whether there are any circumstances under which the option is exercised early.

Question 3
What is the price of a European put option on a non-dividend-paying stock when the stock price is \$69, the strike price is \$70, the risk-free interest rate is 5% per annum, the volatility is 35% per annum, and the time to maturity is six months?

Question 4
A foreign currency is currently worth \$1.50. The domestic and foreign risk-free interest rates are 5% and 9%, respectively. Calculate a lower bound for the value of a six-month call option on the currency with a strike price of \$1.40 if it is (a) European and (b) American.

Question 5
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?

Question 6
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...