FINANCIAL MANAGEMENT: THEORY AND PRACT
15th Edition
ISBN: 9781305632455
Author: BRIGHAM E. F.
Publisher: CENGAGE L
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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?
In 1973, Fischer Black and Myron Scholes developed the Black-Scholes option pricing model(OPM).(1) What assumptions underlie the OPM?
Chapter 8 Solutions
FINANCIAL MANAGEMENT: THEORY AND PRACT
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
- Describe the five variables like Stock Price, Exercise Price, Risk-Free Rate, Volatility or Standard Deviation, and Time to Expiration that the Black-Scholes-Merton Formula uses to calculate the price of call and put options. Explain with some examples for having detail justifications. (Note: Your explanations should be at least 500 words)arrow_forwardA 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.arrow_forwardIn the Black-Scholes option pricing model, the value of a call is inversely related to: a. the risk-free interest stock b. the volatility of the stock c. its time to expiration date d. its stock price e. its strike pricearrow_forward
- 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_forwardBoth call and put options are affected by the following five factors: the exercise price, the underlying stock price, the time to expiration, the stock’s standard deviation, and the risk-free rate. However, the direction of the effects on call and put options could be different. Use the following table to identify whether each statement describes put options or call options. Statement Put Option Call Option 1. An option is more valuable the longer the maturity. 2. A longer maturity in-the-money option on a risky stock is more valuable than the same shorter maturity option. 3. When the exercise price increases, option prices increase. 4. As the risk-free rate increases, the value of the option increases.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_forward
- Use 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_forwardAssume that the value of a call option using the Black-Scholes model is $8.94. The interest rate is 8 percent, and the time to maturity is 90 days. The price of the underlying stock is $47.38, and the exercise price is $45. Calculate the price of a put using the put-call parity relationship.arrow_forwardDraw the profit diagram (profit not payoff) of a portfolio consisting of a long position in two call options with exercise price ?, a short position in five call options with exercise price 2? and a long position in four call options with exercise price 3?. All options have the same maturity date and the same underlying stock. Clearly state any assumptions made. Is the cost of the portfolio positive?arrow_forward
- Assume the following inputs for a call option: (1) current stock price is $25, (2) strike price is $28, (3) time to expiration is 4 months, (4) annualized risk-free rate is 5%, and (5) variance of stock return is 0.33. Use the Black-Scholes model to find the price for the call option. Do not round intermediate calculations. Round your answer to the nearest cent.arrow_forwardThe Black–Scholes option pricing model (OPM) was developed in 1973. The creation of the Black–Scholes OPM played a significant role in the rapid growth of options trading. The derivation of the Black–Scholes Option Pricing Model rests on the concept of a riskless hedge or leveraged buyout According to the Black–Scholes Option Pricing Model, as the variance, σ2σ2, increases, the value of the call option increase or decrease Happy Orange Storage Company has a current stock price of $28.00. A call option on this stock has an exercise price of $28.00 and 0.25 year to maturity. The variance of the stock price is 0.09, and the risk-free rate is 6%. You calculate d₁ to be 0.18 and N(0.18) to be 0.5714. Therefore, d₂ will be 0.03 and N(0.03) will be 0.5120. Using the Black–Scholes Option Pricing Model, what is the value of the option? (Note: Use 2.7183 as the approximate value of e.) $1.877 $1.408 $1.971 $1.689arrow_forwardA call option with X = $55 on a stock priced at S = $60 is sells for $12. Using a volatility estimate of σ = 0.35, you find that N(d1) = 0.7163 and N(d2) = 0.6543. The risk-free interest rate is zero. Is the implied volatility based on the option price more or less than 0.35?arrow_forward
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