Assume a stock price of $31.18, risk-free rate of 3.6 percent, standard deviation of 44 percent, N(d) value of .62789, and an N(d₂) value of .54232. What is the value of a three-month call option with a strike price of $30 given the Black-Scholes option pricing model?

Assume a stock price of $31.18, risk-free rate of 3.6 percent, standard deviation of 44 percent, N(d) value of .62789, and an N(d₂) value of .54232. What is the value of a three-month call option with a strike price of $30 given the Black-Scholes option pricing model?

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

Related questions

Q: Assume that the risk-free rate is 2.5% and the required return on the market is 8%. What is the…

A: According to capital assets pricing model, The expected return on equity stock is calculated as…

Q: We will derive a two-state call option value in this problem. Data: S0 = $190; X = $200; 1 + r =…

A: In the given question , we have a two state call option value in this problem, ; X = $200 ; 1+r =…

Q: A call option with an exercise price of $10 and 3 months to maturity has a price offer of $0.75. The…

A: Exercise price is $10 Maturity is 3 months Call premium is $0.75 Current Stock price is $10.90 Risk…

Q: (Option Payoff Diagram) You hold a long position in an option portfolio. It contains an European…

A: An option is a security that allows the holder the choice to purchase or sell the underlying asset…

Q: A stock price is $30. An investor buys one call option contract on the stock with a strike price of…

A: The possible profit or loss that an investor may experience after purchasing a call option at $28…

Q: ou are interested to value a put option with an exercise price of $100 and one year to expiration.…

A: According to put call parity theory there is certain relation ship between the Put , call and stock…

Q: Construct a hedge portfolio and by using the binomial option pricing model and find the values of Pu…

A: An option is a contract that provides the buyer a right to acquire or transfer the underlying asset…

Q: Consider the following data for a certain share. Current Price So = Rs. 80 Exercise Price = E = Rs.…

A: a) Value of a call or put option using normal distribution table is calculated using Blackscholes…

Q: Followings are the strike prices and the relevant options prices for both put and call options. All…

A: Call options are financial contracts that give the option buyer the right but not the obligation to…

Q: n with a strike p

A: and is perfect speculation. So Payment for call X=110 = 20, And receipt on selling the put= 10 So…

Q: Y has a beta of 1.50 and an expected return of 17 percent. Stock Z has a beta of 0.80 and an…

A: CAPM gives the required rate of return based beta of the stock and risk free rate and market average…

Q: Consider the following portfolio: Long 0 puts with strike price 98.0 Short 1 puts with strike price…

A: If the buyer exercises the option, the underlying asset must be sold when the call option is sold.…

Q: Consider the following data for a certain share. Current Price = S0…

A: The value of a call or put option using a normal distribution table can be determined by using the…

Q: Use the following data to estimate the value of a European put option with X = $120. The current…

A: Option Market is a Stock Market Startegy. Under which investor will not purchase the share of the…

Q: b. A financial institution has the following portfolio of over-the-counter options. Option Position…

A: To solve the system of equations, we'll start by rearranging the equations to isolate x, y, and…

Q: Suppose you are attempting to value a 1-year expiration option on a stock with volatility (i.e.,…

A: a. 1 period of 1 year:In this case, the option will expire in exactly 1 year, so there is only 1…

Q: First calculate the delta of the following option. Then use this delta to ESTIMATE the new price of…

A: New Option Price ≈ Current Price + (Delta * Price Increase)Note: We don't have the current option…

Q: A futures price is currently 41 and has a volatility of 30%. The risk-free rate is 5%. The strike…

A: Given: Spot price = 41 Volatility = 30% Risk free rate = 5% Period = 9 months Strike price = 40

Q: Given the following portfolio: Buy one call option on the stock XYZ with a strike price of $52.8 at…

A: Call option strike price = $52.8 Call option premium = $2 Put option strike price = $57.9 Put option…

Q: Suppose that a call option with a strike price of $48 expires in one year and has a current market…

A: According to put call parity theory there is certain relationship between the Put , call and stock…

Q: Consider a market where the assumptions behind the Black-Scholes model hold. A non-dividend paying…

A: The Black-Scholes Model is a model that was developed for the pricing of European options based on…

Q: The risk-free rate of return is 4.24 percent and the market risk premium is 9.5 percent. What is the…

A: To calculate the expected return we will use the below formula Expected return = Risk free rate +…

Q: Consider a call option with an exercise of $20 and which sells for $1.25. Draw the profit diagram…

A: Using excel

Q: The value of an option is $3.16, its vega is 0.7. What will be the expected price of the option if…

A: Vega of an option will measure the impact of changes in volatility on the price of an option.

Q: a. Long put option with a strike price of €30 and short put option with a strike price of €50 O…

A: Derivative Market -Option Instrument Needs to judge which strategies is been implement which show…

Q: Suppose you bought a put option with a strike price of $21 for $3. What would be your profit from…

A: A put option gives the owner the right, but not the obligation, to sell the underlying asset at the…

Q: Consider a 4-month European put option on a non-dividend-paying share. The share price is $61, the…

A: The binomial model is a mathematical approach used in finance to value options and other derivative…

Q: Question, A trader buys (long) a call option with a strike price of $120 and sells (short) a put…

Q: The value of an option is $6.24, its delta is 0.5, and the price for the underlying stock is $82.…

A: Delta of an Option helps in determining the change in value of an option due to change in price of…

Q: An option is trading at $3.45. If it has a delta of .78, what would the price of the option be if…

A: Options are derivative contract that provides holder a right not obligation to trade certain assets…

Q: An investor buys a 6-month European put option with K, = $75 for $10, buys a 6- month European put…

A: The total cost of the strategy can be defined as below: Total Cost = Buy 75 Strike's PUT Option +…

Q: Suppose that put options on a stock with strike prices $18 and $20 cost $2 and $3.50, respectively.…

A: Bull spread is a strategy created by buying an European put option with lower strike price and…

Q: Given the following portfolio: Buy one call option on the stock XYZ with a strike price of $51.1 at…

A: In case of buying call option, the profit arises when the market price of stock before expiry rises…

Q: RAK Corp. is evaluating a project with the following cash flows: Cash Flow 28,700 10,900 13,600…

A: One of the limitations of traditional IRR is that it is assumed that cash flows from a project are…

Q: ● Information about the underlying asset: spot price 100, expected return 15%, volatility 20%. ●…

A: To calculate the up-factor (u), down-factor (d), and probability of price moving up (p) in the…

Q: An option trader has built a portfolio of three different call options on the same underlying with…

A: Call option give the buyer the right but not the obligation to buy at strike price. This option is…

Q: You are evaluating a put option based on the following information: P = Ke-#.N(-d,) – S-N(-d,) Stock…

A: The Value of PE should be computed using BSM by using the formula stated below:

Q: You have six investment options based on the following three given stocks (X, Y, and Z): State of…

A: Based on the data provided in the question, X and Y have the lowest risk or standard deviation…

Q: With all other variables being equal (the same excerise price, underlying asset, implied volatility,…

A: We need to comment on the given statement and find out if it's true. The statement examines the…

Q: Consider the following portfolio. You write a put option with exercise price $90 and buy a put with…

A: Call options are the financial derivatives that provide the option holder a right to buy some…

Q: Consider a two-step binomial tree. What is the delta of the put option if: the futures price is S =…

A: The delta of a put option is a measure of how the price of the put option is expected to change in…

Q: A trader buys (long) a call option with a strike price of $120 and sells (short) a put option with a…

A: The call Cost is $20Put Cost is $10The strike price for the call option is $120The strike price for…

Q: A stock model has the parameters u = 1.6, d = 0.4, So = 18. A European call option, expiring at t =…

A: All calculations are done in excel, So, there is no intermediate rounding. Workings: If upward…

Question

Assume a stock price of $31.18, risk-free rate of 3.6 percent, standard deviation of 44
percent, N(₁) value of .62789, and an N(d₂) value of .54232. What is the value of a
three-month call option with a strike price of $30 given the Black-Scholes option
pricing model?
Question 9 options:
$3.38
$3.99
$3.68
$1.76
$3.45

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1: Introduction

VIEW

Step 2: Computation

VIEW

Solution

VIEW

Step by step

Solved in 3 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

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

Assume that an investor holds the following portfolio: short stock bought at a price 90$, long one 3- month maturity call option on the same stock with an exercise price of $88. a) Show the payoff structure of this portfolio at option expiration both numerically and graphically. b) Calculate the profit/loss on this position if stocks are selling at $80 on the option maturity date. Calculate the profit/loss on the position if the stocks are selling at $110. Call option premium is $5, while put option premium is $3. Ignore the transaction costs. c) Explain what kind of "bet" the investor is making. What must the investor in such a portfolio believe about the stock price to justify this position?
Put together a Black–Scholes option calculator in Excel to answer the following.(a) What is the call-option value withS0 = $45, K = $48, r = 6%, T = 15 months,and volatility = 40%?(b) What is the put-option value withS0 = $60, K = $65, r = 6%, T = 18 months,and volatility = 20%?(c) What is the put-option value withS0 = $38, K = $40, r = 6%, T = 3 months,and volatility = 60%?(d) What is the call-option value withS0 = $100, K = $95, r = 8%, T = 3 years,and volatility = 40%?
Assume that you have been given the following information on Purcell Corporation's call options: Inputs Intermediate Calculations Current stock price = $12 d1 = 0.32863 Time to maturity of option = 9 months d2 = 0.05477 Variance of stock return = 0.10 N(d1) = 0.62878 Strike price of option = $12 N(d2) = 0.52184 Risk-free rate = 7% According to the Black-Scholes option pricing model, what is the option's value? Do not round intermediate calculations. Round your answer to the nearest cent. Use only the values provided in the problem statement for your calculations. $
what can be best strategy for trailing in Nifty 50 in option trading.
Consider the 1-period binomial model with a bond with A(0) = 60 and A(1) = 70 and a stock with S(0) = 4X and S^u(1) 6Y and S^d(1) = 3Z. = 1. What is the price (payoff) C(1) of a call option with strike price 28? 2. same... with strike price 45? 3. same... with strike price 72? 4. Set up a system of linear equations to determine a replicating portfolio for the call option from part 2 (strike price 45). 5. Solve it and determine the price C(O). 6. Compute, tabulate, and plot the price C(O) as you vary the strike price of the option from 28, 29, ..., 71, 72.
Calculate the implied volatility on a security given the following information: a call option on the security has a premium of 3.5p, the security itself is trading at 50p, the call has an exercise price of 51p and has 120 days to maturity, and the riskless interest rate is 12 per cent. Calculate the implied volatility on a security given the following information: a call option on the security has a premium of 3.5p, the security itself is trading at 50p, the call has an exercise price of 51p and has 120 days to maturity, and the riskless interest rate is 12 per cent.
Assume that K=61, St =65, t = 0.25 (i.e. time to expiry is 3 months), and the risk-free rate is 0.04. The current price of the put option is p = 4. What would the price of the call option ‘c’ need to be for put-call parity to hold?
pls show full working
H2. Using the Black-Scholes model (BSOPM), compute the standard deviation that is implied by the following call option data as: the time to the option's maturity is 0.25 years, the price of the underlying option asset is RM30, the continuously compounded risk-free interest rate is 0.12. the exercise or striking price is RM30, and the cost or premium of the call is RM1.90.
Consider a portfolio that offers an expected rate of return of 11% and a standard deviation of 26%. T-bills offer a risk-free 7% rate of return. What is the maximum level of risk aversion for which the risky portfolio is still preferred to T-bills? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Consider a portfolio consisting of one share and several European call options with the same expiry, but different strike prices. The payoff diagram of the portfolio is given by the following figure. Find the strike prices and the positions of each call option. Portfolio payoff 25 20 15 10 15 20 25 30 Stock price Payoff
Assume an interest rate of zero. A Call option and a Put option with the same exercise price, X = 100p are priced at 9p for the Call and 4p for the Put. What is the price of the synthetic share?

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