INVESTMENTS-CONNECT PLUS ACCESS
11th Edition
ISBN: 2810022611546
Author: Bodie
Publisher: MCG
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Chapter 21, Problem 37PS
Summary Introduction
To evaluate: The fact that a higher volatility in prices results in increase of value of call option supposing that the increase in a stock price will be more than a fall in price.
Introduction:
Volatility: When the prices involved in trade activity are observed, we find that there is a change in the price from time to time-based on the market scenario. This is quite obvious. The degree of range of the changing prices can be measured with the help of a standard deviation of logarithmic returns. The value obtained can be defined as ‘volatility’.
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Students have asked these similar questions
What will happen to a stock’s risk premium if its beta doubles and the market risk premium doubles?
A. The risk premium will be unchanged.
B. The risk premium will decrease by a factor of 2.
C. The risk premium will increase by a factor of 4.
D. The risk premium will increase by a factor of 2.
1.Which of the following is assumed by the Black-Scholes-Merton model?
A.The return from the stock in a short period of time is lognormal
B.The stock price at a future time is lognormal
C.The stock price at a future time is normal
D.None of the above
A call option with X = $50 on a stock currently priced at S = $55 is selling for $10. Using a volatility estimate of σ = .30, you find that N(d1 ) = .6 and N(d2 ) = .5. The risk-free interest rate is zero. Is the implied volatility based on the option price more or less than .30? Explain.
Chapter 21 Solutions
INVESTMENTS-CONNECT PLUS ACCESS
Ch. 21 - Prob. 1PSCh. 21 - Prob. 2PSCh. 21 - Prob. 3PSCh. 21 - Prob. 4PSCh. 21 - Prob. 5PSCh. 21 - Prob. 6PSCh. 21 - Prob. 7PSCh. 21 - Prob. 8PSCh. 21 - Prob. 9PSCh. 21 - Prob. 10PS
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- We showed in the text that the value of a call option increases with the volatility of the stock. Is this also true of put option values? Use the put-call parity theorem as well as a numerical example to prove your answer.arrow_forwardYou write a put option with X = 100 and buy a put with X = 110. The puts are on the same stock and have the same expiration date.a. Draw the payoff graph for this strategy.b. Draw the profit graph for this strategy.c. If the underlying stock has positive beta, does this portfolio have positive or negative beta?arrow_forwardIn this problem we assume the stock price S(t) follows Geometric Brownian Motion described by the following stochastic differential equation: dS = µSdt + o Sdw, where dw is the standard Wiener process and u = 0.13 and o = current stock price is $100 and the stock pays no dividends. 0.20 are constants. The Consider an at-the-money European call option on this stock with 1 year to expiration. What is the most likely value of the option at expiration? Please round your numerical answer to 2 decimal places.arrow_forward
- 2. Derive the single - period binomial model for a put option. Include a single - period example where: u = 1.10, d = 0.95, Rf = 0.05, SO = $100, X = $100. 3. Assume ABC stock's price follows a binomial process, is trading at SO = $100, has u 1.10, d = 0.95, and probability of its price increasing in one period is 0.5 (q = 0.5). a. Show with a binomial tree ABC's possible stock prices, logarithmic returns, and probabilities after one period and two periods. . b. What are the stock's expected logarithmic return and variance for 2 periods and 3 periods? c. Define the properties of a binomial distribution.arrow_forwardSuppose Stock A has B = 1 and an expected return of 11%. Stock B has a B = 1.5. The risk- free rate is 5%. Also consider that the covariance between B and the market is 0.135. Assume the CAPM is true. Answer the following questions: a) Calculate the expected return on share B. b) Find the equation of the Capital Market Line (CML). c) Build a portfolio Q with B = 0 using actions A and B. Indicate weights (interpret your result) and expected return of portfolio Q.arrow_forwardAssume that using the Security Market Line (SML) the required rate of return (RA) on stock A is foundto be half of the required return (RB) on stock B. The risk-free rate (Rf) is one-fourth of the requiredreturn on A. Return on market portfolio is denoted by RM. Find the ratio of beta of A (A) to beta of B(B). d) Assume that the short-term risk-free rate is 3%, the market index S&P500 is expected to payreturns of 15% with the standard deviation equal to 20%. Asset A pays on average 5%, has standarddeviation equal to 20% and is NOT correlated with the S&P500. Asset B pays on average 8%, also hasstandard deviation equal to 20% and has correlation of 0.5 with the S&P500. Determine whetherasset A and B are overvalued or undervalued, and explain why. (Hint: Beta of asset i (??) =???????, where ??,?? are standard deviations of asset i and marketportfolio, ??? is the correlation between asset i and the market portfolio)Question 2. Foreign exchange marketsStatoil, the national…arrow_forward
- Consider a call option on stock XYZ with six months remaining to maturity. In a crisis, the volatility of the share increases and the share price drops. We should expect that: Multiple Choice О the value of the call option increases the value of the call option decreases it is uncertain if the value of the call option increases or decreasesarrow_forwardA call option with X = $55 on a stock priced at S = $60 is sells for $12. Using a volatility estimate of σ = 0.35, you find that N(d1) = 0.7163 and N(d2) = 0.6543. The risk-free interest rate is zero. Is the implied volatility based on the option price more or less than 0.35?arrow_forwardAssume the expected return on the market is 7 percent and the risk-free rate is 4 percent. a. What is the expected return for a stock with a beta equal to 1.10? (Enter your answers in decimals. Do not enter percent values.) b. What is the market risk premium? (Enter your answers in decimals. Do not enter percent values.)arrow_forward
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