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 23QP
Black–Scholes and Dividends [LO2] In addition to the five factors discussed in the chapter, dividends also affect the price of an option. The Black–Scholes option pricing model with dividends is:
All of the variables are the same as the Black–Scholes model without dividends except for the variable d, which is the continuously compounded dividend yield on the stock.
a. What effect do you think the dividend yield will have on the price of a call option? Explain.
b. A stock is currently priced at $94 per share, the standard deviation of its return is 50 percent per year, and the risk-free rate is 4 percent per year, compounded continuously. What is the price of a call option with a strike price of $90 and a maturity of six months if the stock has a dividend yield of 2 percent per year?
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Students have asked these similar questions
KF1.
Which statement is false?
a All else being equal, options of the same strike will increase in price depending on the volatility of the underlying.
b According to put-call parity, if a stock is trading for a price that is at-the-money, the put and the call should be trading at the same, or very close to, the same price.
c A short put option is functionally the same as a long call option (it results in the same thing).
d All statements are true
e All statements are false
Tick all those statements on options that are correct (and don't tick those statements that are incorrect).
O a. The Black-Scholes formula is based on the assumption that the share price follows a geometric Brownian motion.
Ob. The put-call parity formula necessarily requires the assumption that the share price follows a geometric Brownain motion.
0 C. If interest is compounded continuously then the put-call parity formula is P+ S(0) = C + Ke where I is the expiry time.
Od. In general the equation S(T) + (K − S(T))+ (S(T) — K)† + K is valid.
An American put option should never be exercised before the expiry time.
e.
=
Tick all those statements on options that are correct (and don't tick those statements that are incorrect).
a. In general the equation S(T) + (K − S(T))† = (S(T) – K)† + K is valid.
-
b. The Black-Scholes formula is based on the assumption that the share price follows a geometric Brownian motion.
The put-call parity formula necessarily requires the assumption that the share price follows a geometric Brownain motion.
d. An American put option should never be exercised before the expiry time.
e.
If interest is compounded continuously then the put-call parity formula is P + S(0) = C + Ke¯r where T is the expiry
time.
C.
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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- D3) Finance Consider an option with α being a non-negative parameter and the option pays ((S(T))α − K)+ at maturity date T. Let Cα(S(0), σ, r) be the risk neutral price of the option (with interest rate r and volatility σ) when the initial price is S(0). Obviously, C1(S(0), σ, r) = C(S(0), σ, r) is the price of an ordinary call option. Show that, Cα(S(0), σ, r) = e(α−1)(r+ασ2/2)TC((S(0))α, ασ, rα), where rα = α(r − σ2/2) + α2σ2/2.arrow_forwardIT IS NOT DELTA Option _______ is a percentage change in the value of the option per 1% change in the value of the underlying security. b. Rho c. Elasticity d. Thetaarrow_forward6. Factors that affect the value of options Aa Aa Understanding how different factors affect the value of options is the first step to understanding option pricing models. The following table shows how increases in the given factors on the left affect the value of a put option. For each factor, indicate whether an increase in its value causes the value of the put option to increase or to decrease. Causes the Value of the Put Option To Increases in this factor: Increase Decrease Underlying stock price Exercise price Time to expiration Volatility Which of the following best describes a naked option? When an investor sells call options without the stock to back them up When an investor writes call options against stock held in his or her portfolioarrow_forward
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- The hedge ratio of an at-the-money call option on IBM is .4. The hedge ratio of an at-the-money put option is −.6. What is the hedge ratio of an at-the-money straddle position on IBM?arrow_forward6. Equilibrium pricing: Let the subscripts: j = 0 denote the risk-free asset, j = 1,...,n the set of available risky securities, and M the market portfolio. For the questions that follow, assume that CAPM provides an accurate description of reality. a. b. C. d. State the CAPM equation. (1) Use the CAPM equation to show that the following condition is true s; ≤ SM for any j. What is the significance of this condition when interpreted in the context of the capital market line? (5) Assume that B = 0.8, μM = 0.1 and r = 0.05. Using the CAPM, determine the expected return from holding one unit of asset j for one period. (2) Given your answer to c.), what could you conclude (from the perspective of the security market line) if a market survey indicated that the forecasted one- period return on asset j was 8 percent? Describe and motivate the rational trading response that is consistent with your conclusion. (4)arrow_forward1. Consider a family of European call options on a non - dividend - paying stock, with maturity T, each option being identical except for its strike price. The current value of the call with strike price K is denoted by C(K) . There is a risk - free asset with interest rate r >= 0 (b) If you observe that the prices of the two options C( K 1) and C( K 2) satisfy K2 K 1<C(K1)-C(K2), construct a zero - cost strategy that corresponds to an arbitrage opportunity, and explain why this strategy leads to arbitrage.arrow_forward
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