27. Bonus Question: A one-year European call option on XYZ with a strike price of $220 is trading at $6.58. The current stock price for Microsoft is $218. Suppose that the risk-free rate is 1%, whereas the dividend yield on Microsoft is 0. According to the Black-Scholes model (BSM), what is the implied annual volatility? Choose the best answer. (a) 0.075 (b) 0.167 (c) 0.114 (d) 0.305 28. Bonus Question Use risk-neutral valuation to value a derivative at time t that pays off $1 at time T if the price at maturity, ST goes below K, i.e., ST < K. Let St denote the price of a non-dividend paying stock at time t. Express the risk-neutral price of the derivative using the spot price (St), the strike price (K), the risk-free rate (r), the stock volatility (o), and time to maturity (7 = T - t). Hint: recall that under risk-neutral valuation and GBM, the stock price is given by Ste(r-)T+0√TXE where ~ N(0, 1) (a) Φ ( ) log()-(-)r αντ log()+(r-)r O√T (b) > ) (c) Φ (d) Þ log($)+(r−²²)r O√T log()-(r-)r O√T ST=

27. Bonus Question: A one-year European call option on XYZ with a strike price of $220 is trading at $6.58. The current stock price for Microsoft is $218. Suppose that the risk-free rate is 1%, whereas the dividend yield on Microsoft is 0. According to the Black-Scholes model (BSM), what is the implied annual volatility? Choose the best answer. (a) 0.075 (b) 0.167 (c) 0.114 (d) 0.305 28. Bonus Question Use risk-neutral valuation to value a derivative at time t that pays off $1 at time T if the price at maturity, ST goes below K, i.e., ST < K. Let St denote the price of a non-dividend paying stock at time t. Express the risk-neutral price of the derivative using the spot price (St), the strike price (K), the risk-free rate (r), the stock volatility (o), and time to maturity (7 = T - t). Hint: recall that under risk-neutral valuation and GBM, the stock price is given by Ste(r-)T+0√TXE where ~ N(0, 1) (a) Φ ( ) log()-(-)r αντ log()+(r-)r O√T (b) > ) (c) Φ (d) Þ log($)+(r−²²)r O√T log()-(r-)r O√T ST=

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

See similar textbooks

Similar questions

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 the price of a stock today is at $25. For a strike price of K = $24 a 3-month European call option on that stock is quoted with a price of $2, and a 3-month European put option on the same stock is quoted at $1.5 Assume that the risk-free rate is 10% 3. per annum. (a) Does the put-call parity hold?
Consider a 3-month European call option on a non-dividend-paying stock. The current stock price is $20, the risk-free rate is 6% per annum, and the strike price is $20. Assume a risk-neutral world. You calculate the following values using the Black-Scholes-Merton model: d1 = 0.2000 N(d1) = 0.5793 d2 = 0.1000 N(d2) = 0.5398 a) What is the probability that the call option will be exercised? b) What is the expected stock price at the option’s expiration in 3 months? Assume that all values of the stock price less than $20 are counted as zero. c) What is the expected payoff on the option at expiration (in 3 months)? d) Calculate the PV of the expected payoff from part c).
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 o = 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.
6. Let us consider a European option on a stock that does not yield any dividend. Assume that that the price of this option is described by the Black-Scholes model with a drift of 10% per year, volatility of 40% per year. The current price of the stock is S, = £16. The risk-free interest rate on the market is 4% per year. 1) a) Calculate the price of a call option with strike price of £18 and a maturity T of one year. b) Using the put-call parity calculate the price of the corresponding put op- tion. 2) Imagine that in 6 months from now, the stock costs £16.4. Is it worth to wait 6 months before buying the call option above and investing in a saving account what we would have paid for buying the call at the initial time? Would this still apply if the stock costed £19.2 in 6 months from now?
The current price of a non-dividend-paying stock is $100. The risk free interest rate is 1% per year with continuous compounding. The implied volatility of a one-year at-the-money European vanilla call option is 0.2. (1). What should be the implied volatility of a one-year at-the-money European vanilla put? (2). Compute the price of the put. Express your result in terms of the standard normal cdf (e.g., if you get N(0.01), just keep N(0.01) in your answer.)
Modigliani-Miller Theorem I. 7. Options A. How does the price of a call option respond to the following changes, other things equal? Does the price go up or down? Explain briefly the intuition for your answer. (i). Exercise price rises. (ii). Volatility of stock price rises. 3
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%.
What is the price of a one-month European call option given the following information: the exercise price is $19, the current share price is $19, and the risk-free interest rate is 1% per month. Furthermore, the share price is expected to be either $25 or $15 at the end of the month. The company does not pay dividends. Assume a risk-neutral world. Group of answer choices $3.11 $1.91 $2.49 $3.32 None of the above answers is correct.
Consider a European call option and a European put option that have the same underlying stock, the same strike price K = 40, and the same expiration date 6 months from now. The current stock price is $45. a) Suppose the annualized risk-free rate r = 2%, what is the difference between the call premium and the put premium implied by no-arbitrage? b) Suppose the annualized risk-free borrowing rate = 4%, and the annualized risk-free lending rate = 2%. Find the maximum and minimum difference between the call premium and the put premium, i.e., C − P such that there is no arbitrage opportunities.
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.
Suppose a stock is currently trading for $35, and in one period it will either increase to $38 or decrease to $33. If the one-period risk-free rate is 6%, what is the price of a European put option that expires in one period and has an exercise price of $35? $0.51 $2.32 $1.55 $3.00 $0.76

SEE MORE QUESTIONS

Recommended textbooks for you

Essentials Of Investments

Finance

ISBN:

9781260013924

Author:

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

Publisher:

Mcgraw-hill Education,

FUNDAMENTALS OF CORPORATE FINANCE

Finance

ISBN:

9781260013962

Author:

BREALEY

Publisher:

RENT MCG

Financial Management: Theory & Practice

Finance

ISBN:

9781337909730

Author:

Brigham

Publisher:

Cengage

Foundations Of Finance

Finance

ISBN:

9780134897264

Author:

KEOWN, Arthur J., Martin, John D., PETTY, J. William

Publisher:

Pearson,

Fundamentals of Financial Management (MindTap Cou…

Finance

ISBN:

9781337395250

Author:

Eugene F. Brigham, Joel F. Houston

Publisher:

Cengage Learning

Corporate Finance (The Mcgraw-hill/Irwin Series i…

Finance

ISBN:

9780077861759

Author:

Stephen A. Ross Franco Modigliani Professor of Financial Economics Professor, Randolph W Westerfield Robert R. Dockson Deans Chair in Bus. Admin., Jeffrey Jaffe, Bradford D Jordan Professor

Publisher:

McGraw-Hill Education

Essentials Of Investments

Finance

ISBN:

9781260013924

Author:

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

Publisher:

Mcgraw-hill Education,

FUNDAMENTALS OF CORPORATE FINANCE

Finance

ISBN:

9781260013962

Author:

BREALEY

Publisher:

RENT MCG

Financial Management: Theory & Practice

Finance

ISBN:

9781337909730

Author:

Brigham

Publisher:

Cengage

Foundations Of Finance

Finance

ISBN:

9780134897264

Author:

KEOWN, Arthur J., Martin, John D., PETTY, J. William

Publisher:

Pearson,

Fundamentals of Financial Management (MindTap Cou…

Finance

ISBN:

9781337395250

Author:

Eugene F. Brigham, Joel F. Houston

Publisher:

Cengage Learning

Corporate Finance (The Mcgraw-hill/Irwin Series i…

Finance

ISBN:

9780077861759

Author:

Stephen A. Ross Franco Modigliani Professor of Financial Economics Professor, Randolph W Westerfield Robert R. Dockson Deans Chair in Bus. Admin., Jeffrey Jaffe, Bradford D Jordan Professor

Publisher:

McGraw-Hill Education

SEE MORE TEXTBOOKS