Financial Management: Theory & Practice
16th Edition
ISBN: 9781337909730
Author: Brigham
Publisher: Cengage
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Textbook Question
Chapter 8, Problem 5MC
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
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Which of the following is not a determinant of the value of a call option in the Black-Scholes model?
A. The interest rate.
B. The exercise price of the stock.
C. The price of the underlying stock.
D. The beta of the underlying stock.
Need typed answer only.Please give answer within 45 minutes
II. Suppose you have the following information concerning a particular options.Stock price, S = RM 21Exercise price, K = RM 20Interest rate, r = 0.08Maturity, T = 180 days = 0.5Standard deviation, = 0.5
a. What is correct of the call options using Black-Scholes model? b. Compute the put options price using Black-Scholes model?
c. Outline the appropriate arbitrage strategy and graphically prove that the arbitrage is riskless.Note: Use the call and put options prices you have computed in the previous question (a) and (b) above.b. Name the options/stock strategy used to proof the put-call parity. c. What would be the extent of your profit in (a) depend on?
A call option with X = $50 on a stock currently priced at S = $55 is selling for $10. Using a volatility estimate of σ = .30, you find that N(d1 ) = .6 and N(d2 ) = .5. The risk-free interest rate is zero. Is the implied volatility based on the option price more or less than .30? Explain.
Chapter 8 Solutions
Financial Management: Theory & Practice
Ch. 8 - Define each of the following terms:
Option; call...Ch. 8 - Why do options sell at prices higher than their...Ch. 8 - Describe the effect on a call option’s price that...Ch. 8 - A call option on the stock of Bedrock Boulders has...Ch. 8 - The exercise price on one of Flanagan Company’s...Ch. 8 - Assume that you have been given the following...Ch. 8 - The current price of a stock is $33, and the...Ch. 8 - Use the Black-Scholes model to find the price for...Ch. 8 - The current price of a stock is 20. In 1 year, the...Ch. 8 - The current price of a stock is $15. In 6 months,...
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, finance and related others by exploring similar questions and additional content below.Similar questions
- You are evaluating a put option based on the following information: P = Ke-H•N(-d,) – S-N(-d,) Stock price, So Exercise price, k = RM 11 = RM 10 = 0.10 Maturity, T= 90 days = 0.25 Standard deviation, o = 0.5 Interest rate, r Calculate the fair value of the put based on Black-Scholes pricing model. Cumulative normal distribution table is provided at the back.arrow_forwardAn option is trading at $3.45. If it has a delta of .78, what would the price of the option be if the underlying increases by $.75? A. What would the price of the option be if the underlying decreases by $.55? B. What makes this a call option? C. With a delta of .78, is this option ITM, ATM or OTM and how?arrow_forwardUse the Black-Scholes formula to find the value of a call option based on the following inputs. Note: Do not round intermediate calculations. Round your final answer to 2 decimal places. Stock price Exercise price Interest rate Dividend yield Time to expiration Standard deviation of stock's returns Call value $ 51 $ 64 0.068 0.04 0.50 0.265arrow_forward
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- You are pricing options with the following characteristics: •Current stock price (St): $35.60 •Exercise price (X): $50 •Time to expiration (T-t): 9 months •Risk-free rate (rf): 3.25% •Volatility (0): 45% (a): What is the Black-Scholes value of call option? In your hand-written solution, provide the calculations of d1,d2, and the final call price. Use Excel or another spreadsheet program to compute the values of N(d1) and N(d2). See the notes for details. (b): Using put-call parity, what is the value of a put option? For this case, assume continuous compounding, which implies that PVt(X)=e-r(T-t).X.arrow_forwardYou are given the following information on some company's stock, as well as the risk- free asset. Use it to calculate the price of the call option written on that stock, as well as the price of the put option. (HINT: You should use the Black-Scholes formula!) (Do not round intermediate calculations and round your final answers to 2 decimal places, e.g., 32.16.) Today's stock = $74 price Exercise price = $70 Risk-free rate = Option maturity = 4 months Standard deviation of annual stock returns 4.4% per year, compounded continuously Call price Put price = 62% per yeararrow_forwardUse the Black-Scholes formula to find the value of a call option based on the following inputs. (Round your final answer to 2 decimal places. Do not round intermediate calculations.) Stock price Exercise price Interest rate Dividend yield Time to expiration Standard deviation of stock's returns Call value GA $ $ $ 48 60 0.07 0.04 0.50 0.26arrow_forward
- You use the Black-Scholes-Merton model for a put option on a stock. You calculate N(d1) = 0.60 and N(d2) = 0.56. a) What is the delta of the put option? Solution for A = -0.40 b) You short 100 put options. How would you hedge your delta exposure using the underlying stock? How many shares would you need to buy or sell?arrow_forwardYou are given the following information on some company's stock, as well as the risk- free asset. Use it to calculate the price of the call option written on that stock, as well as the price of the put option. (HINT: You should use the Black-Scholes formula!) (Do not round intermediate calculations and round your final answers to 2 decimal places, e.g., 32.16.) Today's stock $72 price Exercise price = $70 Risk-free rate = deviation of Option maturity = 4 months Standard annual stock returns = Call price Put price 4.3% per year, compounded continuously = 61% per yeararrow_forwardUse the Black-Scholes model to find the price for a call option with the following inputs: (1) current stock price is $32, (2) strike price is $37, (3) time to expiration is 3 months, (4) annualized risk-free rate is 6%, and (5) variance of stock return is 0.25. Do not round intermediate calculations. Round your answer to the nearest cent.arrow_forward
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