Fundamentals of Corporate Finance
11th Edition
ISBN: 9780077861704
Author: Stephen A. Ross Franco Modigliani Professor of Financial Economics Professor, Randolph W Westerfield Robert R. Dockson Deans Chair in Bus. Admin., Bradford D Jordan Professor
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 25, Problem 13QP
Black–Scholes [LO2] A call option matures in six months. The underlying stock price is $75, and the stock’s return has a standard deviation of 20 percent per year. The risk-free rate is 4 percent per year, compounded continuously. If the exercise price is $0, what is the price of the call option?
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H2.
Suppose that a stock price is currently 70 dollars, and it is known that at the end of each of the next two six-month periods, the price will be either 17 percent higher or 17 percent lower than at the beginning of the period. Find the value of an American put option on the stock that expires a year from now, and has a strike price of 76 dollars. Assume that no arbitrage opportunities exist, and a risk-free interest rate of 11 percent.
Answer =
dollars.
Please show proper step by step calculation
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?
23.10 What are the prices of a call option and a put option with the following characteristics?
Stock price = $46
Exercise price = $50
Risk-free rate = 6% per year, compounded continuously
Maturity = 3 months
Standard deviation = 54% per year
Chapter 25 Solutions
Fundamentals of Corporate Finance
Ch. 25.1 - Prob. 25.1ACQCh. 25.1 - Prob. 25.1BCQCh. 25.2 - Prob. 25.2ACQCh. 25.2 - Prob. 25.2BCQCh. 25.3 - Prob. 25.3ACQCh. 25.3 - Prob. 25.3BCQCh. 25.4 - Why do we say that the equity in a leveraged firm...Ch. 25.4 - Prob. 25.4BCQCh. 25.5 - Prob. 25.5ACQCh. 25.5 - Prob. 25.5BCQ
Ch. 25 - Prob. 25.1CTFCh. 25 - Prob. 25.3CTFCh. 25 - Prob. 1CRCTCh. 25 - Prob. 2CRCTCh. 25 - Prob. 3CRCTCh. 25 - Prob. 4CRCTCh. 25 - Prob. 5CRCTCh. 25 - Prob. 6CRCTCh. 25 - Prob. 7CRCTCh. 25 - Prob. 8CRCTCh. 25 - Prob. 9CRCTCh. 25 - Prob. 10CRCTCh. 25 - Prob. 1QPCh. 25 - Prob. 2QPCh. 25 - PutCall Parity [LO1] A stock is currently selling...Ch. 25 - PutCall Parity [LO1] A put option that expires in...Ch. 25 - PutCall Parity [LO1] A put option and a call...Ch. 25 - PutCall Parity [LO1] A put option and call option...Ch. 25 - BlackScholes [LO2] What are the prices of a call...Ch. 25 - Delta [LO2] What are the deltas of a call option...Ch. 25 - BlackScholes and Asset Value [LO4] You own a lot...Ch. 25 - BlackScholes and Asset Value [L04] In the previous...Ch. 25 - Time Value of Options [LO2] You are given the...Ch. 25 - PutCall Parity [LO1] A call option with an...Ch. 25 - BlackScholes [LO2] A call option matures in six...Ch. 25 - BlackScholes [LO2] A call option has an exercise...Ch. 25 - BlackScholes [LO2] A stock is currently priced at...Ch. 25 - Prob. 16QPCh. 25 - Equity as an Option and NPV [LO4] Suppose the firm...Ch. 25 - Equity as an Option [LO4] Frostbite Thermalwear...Ch. 25 - Prob. 19QPCh. 25 - Prob. 20QPCh. 25 - Prob. 21QPCh. 25 - Prob. 22QPCh. 25 - BlackScholes and Dividends [LO2] In addition to...Ch. 25 - PutCall Parity and Dividends [LO1] The putcall...Ch. 25 - Put Delta [LO2] In the chapter, we noted that the...Ch. 25 - BlackScholes Put Pricing Model [LO2] Use the...Ch. 25 - BlackScholes [LO2] A stock is currently priced at...Ch. 25 - Delta [LO2] You purchase one call and sell one put...Ch. 25 - Prob. 1MCh. 25 - Prob. 2MCh. 25 - Prob. 3MCh. 25 - Prob. 4MCh. 25 - Prob. 5MCh. 25 - Prob. 6M
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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
- Need ASAP PLS A stock price is currently $65. After each 6 month, the price is expected to go up by or down with the volatility of 25%. The risk-free rate interest rate is 7% per annum with continuous compounding. Questions What will be the risk-neutral probability of an up move - p? What is the value of a 6-month European Call option with a strike price of $65?arrow_forward1. The stock price of Heavy Metal (HM) changes only once a month: either it goes up by 20% or it falls by 16.7%. Its price now is $40. The interest rate is 12.7% per year, or about 1% per month. a. What is the value of a one-month call option with an exercise price of $40? b. What is the option delta? c. What is the option delta of the two-month call over the first one-month period? d. Show how the payoffs of this call option can be replicated by buying HM’s stock andborrowing. e. What is the value of a two-month call option with an exercise price of $40?arrow_forward6.11 A stock index is currently 990, the risk-free rate is 5%, and the dividend yield on the index is 2%. Use a three-step tree to value an 18-month American put option with a strike price of 1,000 when the volatility is 20% per annum. How much does the option holder gain by being able to exercise early? When is the gain made?arrow_forward
- Suppose that an American put option with a strike price of $155.5 and maturity of 12.0 months costs $11.0. The underlying stock price equals 143. The continuously compounded risk-free rate is 6.5 percent per year. What is the potential arbitrage profit from buying a put option on one share of stock? O 12.401 1.5 no arbitrage profit available 11.943 1.6783arrow_forward6. Consider European call and put options on a stock. The stock price is $50, the time to maturity is ten months, the risk-free rate of interest is 8% per year (with continuous compounding), the exercise price is $45, and the volatility is 40%. A dividend of $0.75 is expected after three months, after six months, and again after nine months. Calculate the price of the call option and put option.arrow_forward12. Delta What are the deltas of a call option and a put option with the following characteristics? What does the delta of the option tell you? Stock price $47 Exercise price = $40 Risk-free rate = 6% per year, compounded continuously Maturity = 9 months Standard deviation = 43% per year =arrow_forward
- 2. The price of a European call that expires in six months and has a strike price of $30 is $2. The underlying stock price is $29, and a dividend of $0.50 is expected in two months and again in five months. The term structure is flat, with all risk-free interest rates being 10%. Calculate the price of a European put option that expires in six months and has a strike price of $30. PY of Dividends Dividend 1* e^(-12) + Dividend 2 * e^(-12)arrow_forwardQuestion 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%.arrow_forward10. Assume the following data: Stock price = $50; Exercise price = $45; Risk-free rate = 6 percent per year; Continuously compounded variance = 0.2; Expiration = three months. Calculate the value of a European call option. (Use the Black-Scholes formula.) Options- $5.92 $7.62 $5 $7.90arrow_forward
- 3 Using Black-Scholes find the price of a European call option on a non-dividend paying stock when the stock price is $69, the strike price is 70, the risk-free interest rate is 12% per annum, the volatility is 30% per annum, and the time to maturity is three months? What is the value of a put using theses parameters (use put-call parity)? What happens to the price of the call if volatility is 10% and 50%? Show the prices at these volatilites.arrow_forward(1 point) Suppose that a stock price is currently 57 dollars, and it is known that five months from now, the price will be either 17 percent higher or 17 percent lower. Find the value of a European put option on the stock that expires five months from now, and has a strike price of 54 dollars. Assume that no arbitrage opportunities exist, and a risk-free interest rate of 7 percent. Answer = dollars.arrow_forwardConsider a 2-year European put with a strike price of $52 on a stock whose current stock price is $50. Suppose that there are two time steps, and in each time step the stock price either moves up by 30% or moves down by 30%. Also suppose that risk-free rate is 7% per annum with continuous compounding. What is the value of the European put option?arrow_forward
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