PRIN.OF CORPORATE FINANCE
13th Edition
ISBN: 9781260013900
Author: BREALEY
Publisher: RENT MCG
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Textbook Question
Chapter 21, Problem 12PS
Black–Scholes model Use the Black–Scholes formula to value the following options:
- a. A call option written on a stock selling for $60 per share with a $60 exercise price. The stock’s standard deviation is 6% per month. The option matures in three months. The risk-free interest rate is 1% per month.
- b. A put option written on the same stock at the same time, with the same exercise price and expiration date.
Now for each of these options, find the combination of stock and risk-free asset that would replicate the option.
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Students have asked these similar questions
Use the Black-Scholes formula to value the following options
a. A call option written on a stock selling for $78 per share with a $78 exercise price. The stock's standard deviation is 8% per month
The option matures in three months. The risk-free interest rate is 1.75% per month. (Do not round intermediate calculations. Round
your answer to 2 decimal places.)
Call value
ces
b. A put option written on the same stock at the same time, with the same exercise price and expiration date. (Do not round
Intermediate calculations. Round your answer to 2 decimal places.)
Put value
Suppose that a call option with a strike price of $48 expires in one year and has a current market price of $5.17. The market price of the
underlying stock is $46.25, and the risk-free rate is 1%. Use put-call parity to calculate the price of a put option on the same underlying stock
with a strike of $48 and an expiration of one year.
The price of a put option on the same underlying stock with a strike of $48 and an expiration of one year is $. (Round to the nearest cent.)
You are given the following information concerning options on a particular stock:
Stock price=
Exercise price=
Risk-free rate=
Maturity=
Standard deviation=
$83
Intrinsic value=$
$80
6% per year, compounded continuously
6 months
47% per year
(a)What is the intrinsic value of the call option? (Please keep two digits after the decimal point.)
(b)What is the time premium of the call option? (Please keep two digits after the decimal point.)
Time premium of the call option=$
Chapter 21 Solutions
PRIN.OF CORPORATE FINANCE
Ch. 21 - Binomial model Over the coming year, Ragworts...Ch. 21 - Binomial model Imagine that Amazons stock price...Ch. 21 - Prob. 3PSCh. 21 - Binomial model Suppose a stock price can go up by...Ch. 21 - Prob. 6PSCh. 21 - Two-step binomial model Suppose that you have an...Ch. 21 - Prob. 8PSCh. 21 - Option delta a. Can the delta of a call option be...Ch. 21 - Option delta Suppose you construct an option hedge...Ch. 21 - BlackScholes model Use the BlackScholes formula to...
Ch. 21 - Option risk A call option is always riskier than...Ch. 21 - Option risk a. In Section 21-3, we calculated the...Ch. 21 - Prob. 16PSCh. 21 - Prob. 18PSCh. 21 - American options The price of Moria Mining stock...Ch. 21 - American options Suppose that you own an American...Ch. 21 - American options Recalculate the value of the...Ch. 21 - American options The current price of the stock of...Ch. 21 - American options Other things equal, which of...Ch. 21 - Option exercise Is it better to exercise a call...Ch. 21 - Option delta Use the put-call parity formula (see...Ch. 21 - Option delta Show how the option delta changes as...Ch. 21 - Dividends Your company has just awarded you a...Ch. 21 - Option risk Calculate and compare the risk (betas)...Ch. 21 - Option risk In Section 21-1, we used a simple...Ch. 21 - Prob. 30PS
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- 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 = 0.49arrow_forwardWhat is the value of the following call option according to the Black Scholes Option Pricing Model? What is the value of the put options? Stock Price = $62.50 Strike Price = $60.00 Time to Expiration = 9 Months = 0.75 years. Risk-Free Rate = 2.0%. Stock Return Standard Deviation = 0.45. Draw the payoff picture at expiration for a long position in a call option that has a premium of $1.75 and a strike price of $40. Draw the payoff picture for a short position in the call option given in Problem 2. Draw the payoff picture at expiration for a long position in a put option that has a premium of $3.50 and a strike price of $35. Draw the payoff picture for a short position in the put option given in Problem 4.arrow_forward2. Use the Black-Scholes formula to find the value of a call option on the following stock: Time to expiration = 6 months; Standard deviation = 50% per year Exercise price = $50 Stock price = $ 50 Interest rate = 3% Find the value of a put option on the stock in the above problem with the same exercise price and expiration as the call option.arrow_forward
- Consider a European call option on a non-dividend-paying stock where the stock price is $40, the strike price is $40, the risk-free rate is 4% per annum, the volatility is 30% per annum, and the time to maturity is 6 months. (a) Calculate u, d, and p for a two-step tree. (b) Value the option using a two-step tree.arrow_forwardConsider the following information on a particular stock: Stock price = $89 Exercise price = $85 Risk-free rate = 3% per year, compounded continuously Maturity = 8 months Standard deviation = 59% per year 1. What is the delta of a call option? 2. What is the delta of a put option?arrow_forwardThe Black-Scholes model is used to value call options on the stock of National Co. The following information was identified:· The share price is P43.· The option matures in 6 months· The risk-free rate is 2%.· Price of the option is at P43.What is the exponent of “e” for in computing the value of the call option using the Black-Scholes model?arrow_forward
- Give typing answer with explanation and conclusion A call option has a strike price of $11, and a time to expiration of 0.8 in years. If the stock is trading for $20, N(d1) = 0.5, N(d2) = 0.12, and the risk free rate is 5.40%, what is the value of the call option?arrow_forwardConsider a put option whose underlying asset is a stock index with 6 months to expiration and a strike price of $1000. Suppose the risk-free interest rate for the six months is 2% and that the option’s premium is $74.20. (a) Find the future premium value in six months. (b) What is the buyer’s profit is the index spot price is $1100? (c) What is the buyer’s profit is the index spot price is $900 Only typed answerarrow_forwardYou 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_forward
- A European put option on a non-dividend paying stock has strike price of $40 and time to maturity 9 months. Assume the risk-free interest rate is 5% per annum, the volatility is 20% per annum and the current stock price is $38. Using the Black-Scholes model, calculate the price of the European put option.arrow_forwardAn investor decides to implement a STRADDLE using put options using the following data . The price of stock today is $ 59 , time frame is 6months , the staddle is constructed using a put and a call option with a strike price of $ 61 . The call cost $ 4 and put costs $ 3 . a ) What is the profit ( % ) if in 6 months , if the stock price is at $ 70 b ) What is the profit ( % ) if in 6 months , if the stock price is at $ 60 c ) At what stock price in the future , the investor will make the least / min profit ? d ) Why do investors implement / use this strategy ? For what reason ?arrow_forwardConsider an American Put option with time to expiry of 5 months and a strike price of 82. The current price of the underlying stock is 80. Divide the time to expiry into five 1-month intervals. In each interval, the stock price can either rise by 6, or fall by 6, with unknown probability. The risk-free rate is 4.2% per annum, continuously compounded. Use Binomial Model. What is the value of the option. Provide all necessary calculations.arrow_forward
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