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 27QP
Black–Scholes [LO2] A stock is currently priced at $50. The stock will never pay a dividend. The risk-free rate is 12 percent per year, compounded continuously, and the standard deviation of the stock’s return is 60 percent. A European call option on the stock has a strike price of $100 and no expiration date, meaning that it has an infinite life. Based on Black–Scholes, what is the value of the call option? Do you see a paradox here? Do you see a way out of the paradox?
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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?
Question 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%.
(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.
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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- 27. 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_forwardHELP 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…arrow_forwardA power option pays off [max(S₁ - X),01² at time T where ST is the stock price at time T and X is the strike price. Consider the situation where X = 26 and T is one year. The stock price is currently $24 and at the end of one year it will either $30 or $18. The risk-free interest rate is 5% per annum, compounded continuously. What is the risk- neutral probability of the stock rising to $30? 0.500 0.603 0.450 None of the abovearrow_forward
- Question 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 o = 20%, and the constant continuously compounded interest rate is r = 10%. (b) Repeat part (a) for a European put with strike 60 and maturity 18 months from now.arrow_forwardH2. 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_forwardonly answer b) Question 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%. (b) Repeat part (a) for a European put with strike 60 and maturity 18 months from nowarrow_forward
- The DB stock currently sells for 185 kr. A one-year put option with strike price200 kr has a premium of 30 kr, and the risk free rate is 15%. What is the priceof a one-year call option with strike price 200 kr if we assume there are notransaction costs and the market is free of arbitrage? DO IT FASTarrow_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_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
- 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_forwardAn increase in the rate of interest A fall in the level of demand A decrease in the rate of interest A stock sells P110. A call option on the stock with an exercise price of P105 and expires in 43 days. If the interest rate is 0.11 and the standard deviation of the stock's return is 0.25, what is the price of the CALL OPTION according to the Black-Scholes Model? P6.92 P8.05 T P7.68 P6.88 O Focu: States)arrow_forwardThe stock price of Google is $32. The price of an American call option with strike price $32 and a six-month expiration date is $5 and the price of the corresponding Amertican put option (same maturity and expiration date) is $6. The risk-free interest rate is 5%. Are these prices compatible with the absence of arbitrage opportunities? Why? O1. No, because the put-call parity relationship suggests that ct - Pt = St - K exp(-Ro (T-t)) and this is not satisfied in this case. O II. Yes, because the price of the American put option is greater than the price of the American call option violating the inequality conditions defining the put-call parity relationship. O II. No, because the put-call parity relationship for American options suggests that St - Ks t - Pt s St - K exp(-Ro (T-t)). O V.It depends on whether the stock pays dividends or not.arrow_forward
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