After describing the main hypothesis made in the black and Scholes model explain the reasons why the volatility smile (or skew) is showing up in the options markets? Describe three alternative models to the Black and Scholes model (except the sticky delta and the sticky strike methods) and explain/justify how they cope with the phenomenon of volatility skew.

After describing the main hypothesis made in the black and Scholes model explain the reasons why the volatility smile (or skew) is showing up in the options markets? Describe three alternative models to the Black and Scholes model (except the sticky delta and the sticky strike methods) and explain/justify how they cope with the phenomenon of volatility skew.

Intermediate Financial Management (MindTap Course List)

13th Edition

ISBN:9781337395083

Author:Eugene F. Brigham, Phillip R. Daves

Publisher:Eugene F. Brigham, Phillip R. Daves

Chapter5: Financial Options

Section: Chapter Questions

Problem 3P: Black-Scholes Model Assume that you have been given the following information on Purcell Industries...

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Black-Scholes Model Assume that you have been given the following information on Purcell Industries call options: According to the Black-Scholes option pricing model, what is the option’s value?
You have been hired at the investment firm of Bowers & Noon. One of its clients doesn’t understand the value of diversification or why stocks with the biggest standard deviations don’t always have the highest expected returns. Your assignment is to address the client’s concerns by showing the client how to answer the following questions: Write out the equation for the Capital Market Line (CML), and draw it on the graph. Interpret the plotted CML. Now add a set of indifference curves and illustrate how an investor’s optimal portfolio is some combination of the risky portfolio and the risk-free asset. What is the composition of the risky portfolio?
You have been hired at the investment firm of Bowers & Noon. One of its clients doesn’t understand the value of diversification or why stocks with the biggest standard deviations don’t always have the highest expected returns. Your assignment is to address the client’s concerns by showing the client how to answer the following questions: What is the Capital Asset Pricing Model (CAPM)? What are the assumptions that underlie the model? What is the Security Market Line (SML)?
You have been hired at the investment firm of Bowers Noon. One of its clients doesnt understand the value of diversification or why stocks with the biggest standard deviations dont always have the highest expected returns. Your assignment is to address the clients concerns by showing the client how to answer the following questions: d. Construct a plausible graph that shows risk (as measured by portfolio standard deviation) on the x-axis and expected rate of return on the y-axis. Now add an illustrative feasible (or attainable) set of portfolios and show what portion of the feasible set is efficient. What makes a particular portfolio efficient? Dont worry about specific values when constructing the graphmerely illustrate how things look with reasonable data.
You have been hired at the investment firm of Bowers Noon. One of its clients doesnt understand the value of diversification or why stocks with the biggest standard deviations dont always have the highest expected returns. Your assignment is to address the clients concerns by showing the client how to answer the following questions: e. Add a set of indifference curves to the graph created for part b. What do these curves represent? What is the optimal portfolio for this investor? Add a second set of indifference curves that leads to the selection of a different optimal portfolio. Why do the two investors choose different portfolios?
You have been hired at the investment firm of Bowers Noon. One of its clients doesnt understand the value of diversification or why stocks with the biggest standard deviations dont always have the highest expected returns. Your assignment is to address the clients concerns by showing the client how to answer the following questions: Add a set of indifference curves to the graph created for part b. What do these curves represent? What is the optimal portfolio for this investor? Add a second set of indifference curves that leads to the selection of a different optimal portfolio. Why do the two investors choose different portfolios?
Explain in your own words what dynamic hedging is, and how a trader could profit by dynamically hedging an option if they have a forecast of volatility that is different to implied volatility.
After describing the delta hedging and the gamma trading strategies (delta and gamma being based onthe Black and Scholes model) please analyse how they can be altered if you used instead of the Blackand Scholes model, the sticky delta and the sticky strike models. Then describe how the sticky delta andthe sticky strike impact the portfolio theta, vega and P&L when the market decrease or increase?
For each of the statements below, determine if they are TRUE/FALSE and briefly explain why. a) Delta hedging is most difficult for at-the-money options just before their expiration. b) A protective put with a higher strike price provides greater downside protection but lower upside gains. c) A covered call with a lower strike price provides greater downside protection but a lower maximum gain on the upside. d) It is possible to change the Gamma of a portfolio of options by adding the underlying assets to your position. e) You have delta hedged a long call position on a stock. The stock price drops. To maintain your hedge, you need to buy back some shares.
Volatility smile” is referred to as evidence against the Black-Scholes model. Why is that? A) Black-Scholes model assumes that different options on a given stock have different values for implied volatility b.) Volatility of returns on one and the same stock, over one and the same future period of time, can only take one value C) Black-Scholes model generates option premium close to the observed premium if the observed stock volatility is used
Suppose the solid line represents the capital market line that results from a CAPM equilibrium and the dotted curves represent indifference curves for a given individual. Which of the following is correct if point M corresponds to the market portfolio? Group of answer choices The individual optimally holds only the market portfolio, M. The individual optimally holds portfolio B which can be partially characterized by a long position in the riskless asset. The individual optimally holds portfolio B which can be partially characterized by a short position in the riskless security The individual optimally holds portfolio A which can be partially characterized by a long position in the riskless security. None of the above.
Explain why the delta hedging of a negative gamma options position loses money.