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. $11.43 Replicating Portfolio is Buy 0.33 shares and Borrow $28.57 ... Call Price = Replicating Portfolio is Buy 0.33 shares and Buy $28.57 in bonds... Call Price = $68.57 Replicating Portfolio is Buy 0.66 shares and Buy $18.23 in bonds ... Call Price = $68.57 Replicating Portfolio is Buy 0.66 shares and Borrow $13.57 ... Call Price = $11.43

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. $11.43 Replicating Portfolio is Buy 0.33 shares and Borrow $28.57 ... Call Price = Replicating Portfolio is Buy 0.33 shares and Buy $28.57 in bonds... Call Price = $68.57 Replicating Portfolio is Buy 0.66 shares and Buy $18.23 in bonds ... Call Price = $68.57 Replicating Portfolio is Buy 0.66 shares and Borrow $13.57 ... Call Price = $11.43

Intermediate Financial Management (MindTap Course List)

13th Edition

ISBN:9781337395083

Author:Eugene F. Brigham, Phillip R. Daves

Publisher:Eugene F. Brigham, Phillip R. Daves

Chapter5: Financial Options

Section: Chapter Questions

Problem 4MC

See similar textbooks

Similar questions

An analyst has modeled the stock of a company using the Fama-French three-factor model. The market return is 10%, the return on the SMB portfolio (rSMB) is 3.2%, and the return on the HML portfolio (rHML) is 4.8%. If ai = 0, bi = 1.2, ci = 20.4, and di = 1.3, what is the stock’s predicted return?
In 1973, Fischer Black and Myron Scholes developed the Black-Scholes option pricing model (OPM). (1) What assumptions underlie the OPM? (2) Write out the three equations that constitute the model. (3) According to the OPM, what is the value of a call option with the following characteristics? Stock price = 27.00 Strike price = 25.00 Time to expiration = 6 months = 0.5 years Risk-free rate = 6.0% Stock return standard deviation = 0.49
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.
Suppose that a stock price is currently 49 dollars, and it is known that one month from now, the price will be either 8 percent higher or 8 percent lower. Find the value of an American call option on the stock that expires one month from now, and has a strike price of 51 dollars. Assume that no arbitrage opportunities exist, and a risk-free interest rate of 7 percent.
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?
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.
What would be the price of a two-month European put option on a non-dividend-paying stockwhen the stock price is $68.50, the strike price is$70, and the risk-free interest rate is 5% per annum?Assume a volatility of 60% for this stock.
Your broker has recommended that you purchase stock in Alacan, Inc. She estimates that the 1-year target price is $76.00, and Alacan consistently pays an annual dividend of $17.00. Analysts estimate that the stock has a beta of 0.91. The current risk-free rate is 2.70% and the market risk premium (RM - RF) is 9.50%. Assuming that CAPM holds, what is the intrinsic value of this stock?
Suppose the 1-year futures price on a stock-index portfolio is 1,914, the stock index currently is 1,900, the 1-year risk-free interest rate is 3%, and the year-end dividend that will be paid on a $1,900 investment in the market index portfolio is $40.a. By how much is the contract mispriced?b. Formulate a zero-net-investment arbitrage portfolio and show that you can lock in riskless profits equal to the futures mispricing.c. Now assume (as is true for small investors) that if you short sell the stocks in the market index, the proceeds of the short sale are kept with the broker, and you do not receive any interest income on the funds. Is there still an arbitrage opportunity (assuming that you don’t already own the shares in the index)? Explain.d. Given the short-sale rules, what is the no-arbitrage band for the stock-futures price relation-ship? That is, given a stock index of 1,900, how high and how low can the futures price be without giving rise to arbitrage opportunities?
5 ABL shares are currently trading at a price of $30, while HHT shares are trading at a price of $37.98. The risk-free rate is 1.24% per year. Using the information above, perform each of the following tasks: c) Compute the Delta (number of shares) that if you also short a call on HHT will create a risk-free portfolio. Assume the call is European and that the strike-price is $34.7517 d) Using the information above, compute the risk-neutral probability of HHT shares increasing 10% if the time-step to the next node is 1 year. f) Find the Black-Scholes price of the call on ABL with a strike price of $29.19 if there is 6 months until the call expires and the annual standard deviation of the stock price is 20%.