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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Chapter 25, Problem 15QP
Black–Scholes [LO2] A stock is currently priced at $47. A call option with an expiration of one year has an exercise price of $50. The risk-free rate is 12 percent per year, compounded continuously, and the standard deviation of the stock’s return is infinitely large. What is the price of the call option?
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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.
HELP WITH 2 PLEASE!!!!
Consider a two period economy. You can buy stocks in period 0, and then sell them in period 1. You can also enter into futures contracts in period 0, which expire in period 1.
Suppose a stock has a β of 0.5. The stock pays no dividends, and is trading at $100. The market has an expected return of 10%. The interest rate is 2%. Suppose the CAPM holds. What is the stock’s expected return? What is the expected price of the stock in period 1?
Consider a futures contract on the stock, expiring at t = 1. What is the fair price of the futures contract, in t = 1 dollars?
Suppose you take a long position in the futures contract in period 0 (so, you promise to pay money, in exchange for getting the stock in period 1). When the futures contract expires in period 1, you receive the stock and immediately sell it. What is the expected amount you will pay in money for the stock? What is the expected amount you get from selling the stock?
Since buying single-stock futures…
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?
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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- 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 calculationarrow_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_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_forward
- 6. Using the Pricing Equation [LO2] A one-year call option contract on Cheesy Poofs Co. stock sells for $725. In one year, the stock will be worth $64 or $81 per share. The exercise price on the call option is $70. What is the current value of the stock if the risk- free rate is 3 percent?arrow_forwardA call option has X=$52 and expire in 360 days (suppose we have 360 days in one year). The risk-free rate is 4%. The call is priced at $11. A put option has X-$52 and is priced at $1. The underlying asset is priced at S0=$43. Suppose in our investments, we could involve one call, one put, one bond, and on stock. How much arbitrage profit could we possibly obtain?arrow_forward4. (15 pts) The current price of a stock is $50 and we assume it can be modeled by geometric Brownian motion with o = .15. If the interest rate is 5% and we want to sell an option to buy the stock for $55 in 2 years, what should be the initial price of the option for there not to be an arbitrage opportunity?arrow_forward
- ?Q.19 Consider a European call option with the following parameters: Assuming a risk-free annual rate of 8%, what is the probability that the option will be exercised in a risk- neutral world? (If required, use the table at the beginning of the document for statistical calculations.) Strike price USD 48 Expiration 6 months Underlying's Price USD 50 Annual volatility 25% A B C 0.70 0.5761 0.6443 D 0.3668arrow_forwardSuppose that a stock price is currently 35 dollars, and it is known that four months from now, the price will be either 51 dollars or 29 dollars. Find the value of a European call option on the stock that expires four months from now, and has a strike price of 39 dollars. Assume that no arbitrage opportunities exist and a risk-free interest rate of 10 percent.Answer =dollars.arrow_forward27. Bonus Question: A one-year European call option on XYZ with a strike price of $220 is trading at $6.58. The current stock price for Microsoft is $218. Suppose that the risk-free rate is 1%, whereas the dividend yield on Microsoft is 0. According to the Black-Scholes model (BSM), what is the implied annual volatility? Choose the best answer. (a) 0.075 (b) 0.167 (c) 0.114 (d) 0.305 28. Bonus Question Use risk-neutral valuation to value a derivative at time t that pays off $1 at time T if the price at maturity, ST goes below K, i.e., ST < K. Let St denote the price of a non-dividend paying stock at time t. Express the risk-neutral price of the derivative using the spot price (St), the strike price (K), the risk-free rate (r), the stock volatility (o), and time to maturity (7 = T - t). Hint: recall that under risk-neutral valuation and GBM, the stock price is given by ST = Ste(r)T+0√TXE where ~ (a) Φ (b) (c) Φ N(0, 1) log()+(r-)T O√T (d) Φ log(5)-(r_²²2)r αντ log()+(r-2²)r O√T…arrow_forward
- Q4 (Exercise 12.3) Let S = $100, K = $120, σ = 30%, r = 0.08, and 8 = 0. a. Compute the Black-Scholes call price for 1 year to maturity and for a variety of very long times to maturity (use T=1, 2, 5, 10, 50, 100, 500). What happens to the option price as T → ∞o? b. Set 8 = 0.001. Repeat (a). Now what happens to the option price? What accounts for the difference?arrow_forwardConsider a stock with a current price of $15 that will be worth either $10 or $25 1 year from now. Assume rf = 0% (annual compounding). You have invented a new derivative security called an "inverse", whose payoff in 1 year is 100 divided by the stock price, i.e., payoff =100/S1 . If the beta of the stock is 1.2, what is the beta of this new derivative?arrow_forwardSuppose 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_forward
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