Option and Risk-free Interest Rate

1 January 2017

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.

We will write a custom essay sample on
Option and Risk-free Interest Rate
or any similar topic specifically for you
Do Not Waste
Your Time
HIRE WRITER

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 three-month European put with an exercise price of 700.

A limited
time offer!
Get authentic custom
ESSAY SAMPLEwritten strictly according
to your requirements