Zinc Company is currently trading for $30 per share. The stock pays no dividends. You are interested in valuing a one-year at-the-money European put option on Zinc stock. Assume that the volatility of Zinc stock is 40% per year and its beta is 0.95. The risk-free interest rate is 6%. (a) What is the intrinsic value of the put option? What is the time value of the put option? Interpret these two values. (b) You would like to replicate this put option using a portfolio of stocks and bonds. What portfolio would you hold? (c) What is the leverage ratio of the put option? What is the beta of the put option? Based on your answers, discuss why investors may want to include put options in their portfolios. (d) If you hold an American put option, would it ever be optimal to exercise it early? If so, under what circumstance?

Zinc Company is currently trading for $30 per share. The stock pays no dividends. You are interested in valuing a one-year at-the-money European put option on Zinc stock. Assume that the volatility of Zinc stock is 40% per year and its beta is 0.95. The risk-free interest rate is 6%. (a) What is the intrinsic value of the put option? What is the time value of the put option? Interpret these two values. (b) You would like to replicate this put option using a portfolio of stocks and bonds. What portfolio would you hold? (c) What is the leverage ratio of the put option? What is the beta of the put option? Based on your answers, discuss why investors may want to include put options in their portfolios. (d) If you hold an American put option, would it ever be optimal to exercise it early? If so, under what circumstance?

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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You think that there is an arbitrage opportunity on the market. The current stock price of Wesley corp. is $20 per share. A one- year put option on Wesley corp. with a strike price of $18 sells for $3.33, while the identical call sells for $7. The one-year risk- free interest rate is 8%. Assuming that the put option is fairly priced, compute the fair price of the call option and explain what you must do to exploit this arbitrage opportunity and what will be your gain.
A one-month European put option on a non-dividend-paying stock is currently selling for $2.50. The stock price is $47, the strike price is $50, and the risk-free interest rate is 6% per annum. What opportunities, if any, are there for an arbitrageur? no opportunities; the put is fairly priced. an arbitrage strategy exists that could generate profit with a present value of at least $0.25. An arbitrageur should lend $49.50 for one month, buy the stock, and write the put option An arbitrageur should borrow $47.00 for one month, sell the stock, and write the put option
(1 point) Suppose that a stock price is currently 57 dollars, and it is known that five months from now, the price will be either 17 percent higher or 17 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 54 dollars. Assume that no arbitrage opportunities exist, and a risk-free interest rate of 7 percent. Answer = dollars.
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.
only answer b) Question 2. (a) Use the Black-Scholes formula to find the current price of a European call option on a stock paying no income with strike 60 and maturity 18 months from now. Assume the current stock price is 50, the lognormal volatility of the stock is σ = 20%, and the constant continuously compounded interest rate is r = 10%. (b) Repeat part (a) for a European put with strike 60 and maturity 18 months from now
The price of a non-dividend-paying stock is $50 and the price of a 4-month European call option on the stock with a strike price of $50 is $3. The risk-free rate is 4% per annum. The price of the corresponding 4-month European put option with same strike price is $2. Establish which of the following options is true. O I. None of the above. O II. There are arbitrage opportunities because the put-call parity relation does not hold. The arbitrage opportunity is given by selling short the put option and the stock and buying the call option. The proceeds of this strategy are invested at the risk-free rate until the expiration date. O II There are no arbitrage opportunities as the put-call parity relation holds. O IV. There are arbitrage opportunities because the put-call parity relation does not hold. The arbitrage opportunity is given by selling short the call option and borrowing money from the bank at the risk-free rate to buy the stock and put option.
Without using the Black‐Scholes model, compute the price of a European put option on a non‐dividend‐paying stock with the strike price is $70 when the stock price is $73, the risk‐free interest rate is 10% pa, the volatility is 40% pa, and the time to maturity is 6 months?
Consider a European call on Procter and Gamble stock (PG) that expires in one period. The current stock price is $120, the strike price is $130, and the risk-free rate is 5%. Assume that PG stock will either go up to $150 (probability = .4), or go down to $90 (probability = .6). Construct a replicating portfolio based on shares of PG stock and a position in a risk-free asset, and compute the price of the call option.
Consider a European call on Amazon Stock (AMZN) that expires in one period. The current stock price is $100, the strike price is $120, and the risk-free rate is 5%. Assume AMZN stock will either go up to $140 or down to $80. Construct a replicating portfolio using shares of AMZN stock and a position in a risk-free asset … what is the value of the call option?
Find the price of a 1-year European call option with a strike price of $110 if the stock price is $100, the volatility of the stock is 25%, the risk-free rate is 2%, and the stock doesn't pay any dividends.
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.
The DB stock currently sells for 185 kr. A one-year put option with strike price200 kr has a premium of 30 kr, and the risk free rate is 15%. What is the priceof a one-year call option with strike price 200 kr if we assume there are notransaction costs and the market is free of arbitrage? DO IT FAST

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