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.

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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.

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