A European call option and put option on a stock both have a strike price of $20 and an expiration date in 4 months. Both sell for $3. The risk-free interest rate is 8.0% per annum, the current stock price is $19, and a $1 dividend is expected in one month. What is the present value of the arbitrage opportunity open to a trader? Enter your answer rounded to two decimal places, skip the $sign. For example, if your calculation results in $98.1234567, you only need to enter 98.12.

A European call option and put option on a stock both have a strike price of $20 and an expiration date in 4 months. Both sell for $3. The risk-free interest rate is 8.0% per annum, the current stock price is $19, and a $1 dividend is expected in one month. What is the present value of the arbitrage opportunity open to a trader? Enter your answer rounded to two decimal places, skip the $sign. For example, if your calculation results in $98.1234567, you only need to enter 98.12.

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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A European call that will expire in one year is currently trading for $3. Assume the risk-free rate (based on continuous compounding) is 5%, the underlying stock price is $60 and the strike price is $55. a. Is there an arbitrage opportunity? b. Describe exactly what a trader should do to take advantage of the arbitrage opportunity assuming it exists. c. Determine the present value of the profit that the trader can earn assuming you identify an arbitrage opportunity. Use at least four decimal places for those questions that require a numerical answer.
Suppose that a stock price is currently 35 dollars, and it is known that four months from now, the price will be either 51 dollars or 29 dollars. Find the value of a European call option on the stock that expires four months from now, and has a strike price of 39 dollars. Assume that no arbitrage opportunities exist and a risk-free interest rate of 10 percent.Answer =dollars.
Use the Black-Scholes model to find the value for a European put option that has an exercise price of $62.00 and four months to expiration. The underlying stock is selling for $63.00 currently and pays an annual dividend of $1.92. The standard deviation of the stock’s returns is 0.21 and risk-free interest rate is 5.0%. (Round intermediary calculations to 4 decimal places. Round your final answer to 2 decimal
Use the Black-Scholes model to find the value for a European put option that has an exercise price of $62.00 and four months to expiration. The underlying stock is selling for $62.50 currently and pays an annual dividend of $1.47. The standard deviation of the stock's returns is 0.14 and risk-free interest rate is 3.5%. (Round intermediary calculations to 4 decimal places. Round your final answer to 2 decimal places.) $ Put value
Suppose that a stock price is currently 68 dollars, and it is known that at the end of each of the next two six-month periods, the price will be either 19 percent higher or 19 percent lower than at the beginning of the period. Find the value of a European put option on the stock that expires a year from now, and has a strike price of 67 dollars. Assume that no arbitrage opportunities exist, and a risk-free interest rate of 7 percent. Answer = dollars.
Consider a European put and a European call option which are both written on a non-dividend paying stock, have the same strike price K = £80 and expire in T = 2 months. These options are trading for p = £21 and c = £30.80, respectively. The underlying stock price is S0 = £90. The continuously compounded risk-free rate of interest is r = 10% per annum. What is the present value of the arbitrage profit? Please explain your answer and show your workings. In your response, please show all cash flows (both today and at expiration) and explain why this is an arbitrage (i.e. risk-less) profit.
A stock has a current price of $67. An option on this stock that expires in six months has an exercise price of $65. The stock will pay a dividend of $5 in three months. Assume an annualized volatility of 30% and a continuously compounded risk - free rate of 5% per annum. Use the Black - Sholes - Merton model to price this option. 1) Suppose the option is a European put. Calculate the value of the put. 2) Suppose this option is an American call. Use Black's approximation to calculate the value of this call.
Suppose that Stock XYZ is currently trading at $50 and does not pay any dividends. Using a binomial tree with two periods, we would like to price a European call option with a strike of $50 and a maturity of six months. Assume that annual continuously compounded interest rate is 1% and the volatility of the stock is 30% per year. What is the value of q? 0.5565 0.4709 0.5000 0.3401 0.5000. You selected this answer.
Suppose that a stock price is currently 64 dollars, and it is known that at the end of each of the next two six- month periods, the price will be either 18 percent higher or 18 percent lower than at the beginning of the period. Find the value of a European put option on the stock that expires a year from now, and has a strike price of 58 dollars. Assume that no arbitrage opportunities exist, and a risk-free interest rate of 10 percent.
Suppose that a stock price is currently 56 dollars, and it is known that five months from now, the price will be either 22 percent higher or 22 percent lower. Find the value of a European put option on the stock that expires five months from now, and has a strike price of 55 dollars. Assume that no arbitrage opportunities exist, and a risk-free interest rate of 6 percent.
Suppose that a stock price is currently 61 dollars, and it is known that at the end of each of the next two six-month periods, the price will be either 18 percent higher or 18 percent lower than at the beginning of the period. Find the value of a European put option on the stock that expires a year from now, and has a strike price of 64 dollars. Assume that no arbitrage opportunities exist, and a risk-free interest rate of 10 percent.
A European put option on a non-dividend paying stock has strike price of $40 and time to maturity 9 months. Assume the risk-free interest rate is 5% per annum, the volatility is 20% per annum and the current stock price is $38. Using the Black-Scholes model, calculate the price of the European put option.

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