Essentials of Statistics, Books a la Carte Edition (5th Edition)
5th Edition
ISBN: 9780321926739
Author: Mario F. Triola
Publisher: PEARSON
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Chapter 1.2, Problem 28BSC
To determine
To identify: The wrong in the situation.
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Problem 4. Margrabe formula and the Greeks (20 pts)
In the homework, we determined the Margrabe formula for the price of an option allowing you to
swap an x-stock for a y-stock at time T. For stocks with initial values xo, yo, common volatility
σ and correlation p, the formula was given by
Fo=yo (d+)-x0Þ(d_),
where
In (±²
Ꭲ
d+
õ√T
and
σ = σ√√√2(1 - p).
дго
(a) We want to determine a "Greek" for ỡ on the option: find a formula for
θα
(b) Is
дго
θα
positive or negative?
(c) We consider a situation in which the correlation p between the two stocks increases: what
can you say about the price Fo?
(d) Assume that yo< xo and p = 1. What is the price of the option?
We consider a 4-dimensional stock price model given (under P) by
dẴ₁ = µ· Xt dt + йt · ΣdŴt
where (W) is an n-dimensional Brownian motion,
π = (0.02, 0.01, -0.02, 0.05),
0.2
0
0
0
0.3
0.4
0
0
Σ=
-0.1
-4a За
0
0.2
0.4 -0.1 0.2)
and a E R. We assume that ☑0 = (1, 1, 1, 1) and that the interest rate on the market is r = 0.02.
(a) Give a condition on a that would make stock #3 be the one with largest volatility.
(b) Find the diversification coefficient for this portfolio as a function of a.
(c) Determine the maximum diversification coefficient d that you could reach by varying the
value of a?
2
Question 1. Your manager asks you to explain why the Black-Scholes model may be inappro-
priate for pricing options in practice. Give one reason that would substantiate this claim?
Question 2. We consider stock #1 and stock #2 in the model of Problem 2. Your manager
asks you to pick only one of them to invest in based on the model provided. Which one do you
choose and why ?
Question 3. Let (St) to be an asset modeled by the Black-Scholes SDE. Let Ft be the price
at time t of a European put with maturity T and strike price K. Then, the discounted option
price process (ert Ft) t20 is a martingale. True or False? (Explain your answer.)
Question 4. You are considering pricing an American put option using a Black-Scholes model
for the underlying stock. An explicit formula for the price doesn't exist. In just a few words (no
more than 2 sentences), explain how you would proceed to price it.
Question 5. We model a short rate with a Ho-Lee model drt = ln(1+t) dt +2dWt. Then the
interest rate…
Chapter 1 Solutions
Essentials of Statistics, Books a la Carte Edition (5th Edition)
Ch. 1.2 - Statistical Significance versus Practical...Ch. 1.2 - Source of Data In conducting a statistical study,...Ch. 1.2 - Voluntary Response Sample What is a voluntary...Ch. 1.2 - Correlation and Causation What is meant by the...Ch. 1.2 - Consider the Source. In Exercises 5-8, determine...Ch. 1.2 - Consider the Source. In Exercises 5-8, determine...Ch. 1.2 - Consider the Source. In Exercises 5-8, determine...Ch. 1.2 - Consider the Source. In Exercises 5-8, determine...Ch. 1.2 - Sampling Method. In Exercises 9-12, determine...Ch. 1.2 - Sampling Method. In Exercises 9-12, determine...
Ch. 1.2 - Sampling Method. In Exercises 9-12, determine...Ch. 1.2 - Sampling Method. In Exercises 9-12, determine...Ch. 1.2 - Statistical Significance and Practical...Ch. 1.2 - Statistical Significance and Practical...Ch. 1.2 - Statistical Significance and Practical...Ch. 1.2 - Statistical Significance and Practical...Ch. 1.2 - In Exercises 17-20, refer to the data in the table...Ch. 1.2 - In Exercises 17-20, refer to the data in the table...Ch. 1.2 - Prob. 19BSCCh. 1.2 - Conclusion If we use the listed pulse rates with...Ch. 1.2 - In Exercises 21-24, refer to the data in the table...Ch. 1.2 - Prob. 22BSCCh. 1.2 - Prob. 23BSCCh. 1.2 - In Exercises 21-24, refer to the data in the table...Ch. 1.2 - Prob. 25BSCCh. 1.2 - Whats Wrong? In Exercises 25-28, identify what is...Ch. 1.2 - Whats Wrong? In Exercises 25-28, identify what is...Ch. 1.2 - Prob. 28BSCCh. 1.2 - Percentages. In Exercises 29-36, answer the given...Ch. 1.2 - Percentages. In Exercises 29-36, answer the given...Ch. 1.2 - Percentages. In Exercises 29-36, answer the given...Ch. 1.2 - Prob. 32BSCCh. 1.2 - Percentages in Advertising An ad for Big Skinny...Ch. 1.2 - Percentages. In Exercises 29-36, answer the given...Ch. 1.2 - Percentages. In Exercises 29-36, answer the given...Ch. 1.2 - Percentages in Advertising A New York Times...Ch. 1.2 - ATV Accidents The Associated Press provided an...Ch. 1.2 - Falsifying Data A researcher at the...Ch. 1.2 - Whats Wrong with This Picture? The Newport...Ch. 1.3 - Parameter and Statistic What is a parameter, and...Ch. 1.3 - Prob. 2BSCCh. 1.3 - Discrete/Continuous Data Which of the following...Ch. 1.3 - Identifying the Population In a Gallup poll of...Ch. 1.3 - In Exercises 5-12, determine whether the given...Ch. 1.3 - In Exercises 5-12, determine whether the given...Ch. 1.3 - In Exercises 5-12, determine whether the given...Ch. 1.3 - In Exercises 5-12, determine whether the given...Ch. 1.3 - In Exercises 5-12, determine whether the given...Ch. 1.3 - In Exercises 5-12, determine whether the given...Ch. 1.3 - In Exercises 5-12, determine whether the given...Ch. 1.3 - In Exercises 5-12, determine whether the given...Ch. 1.3 - In Exercises 13-20, determine whether the given...Ch. 1.3 - In Exercises 13-20, determine whether the given...Ch. 1.3 - In Exercises 13-20, determine whether the given...Ch. 1.3 - In Exercises 13-20, determine whether the given...Ch. 1.3 - Prob. 17BSCCh. 1.3 - In Exercises 13-20, determine whether the given...Ch. 1.3 - Prob. 19BSCCh. 1.3 - In Exercises 13-20, determine whether the given...Ch. 1.3 - In Exercises 21-28, determine which of the four...Ch. 1.3 - In Exercises 21-28, determine which of the four...Ch. 1.3 - Prob. 23BSCCh. 1.3 - In Exercises 21-28, determine which of the four...Ch. 1.3 - In Exercises 21-28, determine which of the four...Ch. 1.3 - In Exercises 21-28, determine which of the four...Ch. 1.3 - In Exercises 21-28, determine which of the four...Ch. 1.3 - In Exercises 21-28, determine which of the four...Ch. 1.3 - In Exercises 29-32, identify the level of...Ch. 1.3 - In Exercises 29-32, identify the level of...Ch. 1.3 - In Exercises 29-32, identify the level of...Ch. 1.3 - In Exercises 29-32, identify the level of...Ch. 1.3 - Countable For each of the following, categorize...Ch. 1.3 - Scale for Rating Food A group of students develops...Ch. 1.3 - Interpreting Temperature Increase In the Born...Ch. 1.4 - Simple Random Sample At a national conference of...Ch. 1.4 - Observational Study and Experiment You want to...Ch. 1.4 - Simple Random Convenience Sample A student of the...Ch. 1.4 - Convenience Sample The author conducted a survey...Ch. 1.4 - In Exercises 5-8, determine whether the given...Ch. 1.4 - In Exercises 5-8, determine whether the given...Ch. 1.4 - In Exercises 5-8, determine whether the given...Ch. 1.4 - In Exercises 5-8, determine whether the given...Ch. 1.4 - In Exercises 9-20, identify which of these types...Ch. 1.4 - In Exercises 9-20, identify which of these types...Ch. 1.4 - In Exercises 9-20, identify which of these types...Ch. 1.4 - In Exercises 9-20, identify which of these types...Ch. 1.4 - In Exercises 9-20, identify which of these types...Ch. 1.4 - In Exercises 9-20, identify which of these types...Ch. 1.4 - In Exercises 9-20, identify which of these types...Ch. 1.4 - In Exercises 9-20, identify which of these types...Ch. 1.4 - In Exercises 9-20, identify which of these types...Ch. 1.4 - In Exercises 9-20, identify which of these types...Ch. 1.4 - In Exercises 9-20, identify which of these types...Ch. 1.4 - In Exercises 9-20, identify which of these types...Ch. 1.4 - Simple Random Samples. In Exercises 21-26,...Ch. 1.4 - Simple Random Samples. In Exercises 21-26,...Ch. 1.4 - Prob. 23BSCCh. 1.4 - Simple Random Samples. In Exercises 21-26,...Ch. 1.4 - Simple Random Samples. In Exercises 21-26,...Ch. 1.4 - Simple Random Samples. In Exercises 21-26,...Ch. 1.4 - Prob. 27BBCh. 1.4 - In Exercises 27-30, indicate whether the...Ch. 1.4 - In Exercises 27-30, indicate whether the...Ch. 1.4 - In Exercises 27-30, indicate whether the...Ch. 1.4 - In Exercises 31-34, identify which of these...Ch. 1.4 - In Exercises 31-34, identify which of these...Ch. 1.4 - Prob. 33BBCh. 1.4 - In Exercises 33-36, identify which of these...Ch. 1.4 - Blinding For the study described in Exercise 34,...Ch. 1.4 - Sample Design Literacy In Cardiovascular Effects...Ch. 1 - Chicago Bulls The numbers of the current players...Ch. 1 - Chicago Bulls Which of the following best...Ch. 1 - Earthquake Depths Data Set 16 includes depths (km)...Ch. 1 - Earthquake Depths Are the earthquake depths...Ch. 1 - Earthquake Depths Which of the following best...Ch. 1 - Earthquake Depths True or false: If you construct...Ch. 1 - Prob. 7CQQCh. 1 - Parameter and Statistic In a recent Gallup poll,...Ch. 1 - Observational Study or Experiment Are the data...Ch. 1 - 10. Statistical Significance and Practical...Ch. 1 - Walmart Stores Currently, there are 4227 Walmart...Ch. 1 - Whats Wrong? A survey sponsored by the American...Ch. 1 - Whats Wrong? A survey included 4230 responses from...Ch. 1 - Sampling Seventy-two percent of Americans squeeze...Ch. 1 - Percentages a. The labels on U-Turn protein energy...Ch. 1 - Why the Discrepancy? A Gallup poll was taken two...Ch. 1 - Statistical Significance and Practical...Ch. 1 - Marijuana Survey In a recent Pew poll of 1500...Ch. 1 - Marijuana Survey Identify the type of sampling...Ch. 1 - Marijuana Survey Exercise 8 referred to a Pew poll...Ch. 1 - For Chapter 2 through Chapter 14, the Cumulative...Ch. 1 - For Chapter 2 through Chapter 14, the Cumulative...Ch. 1 - For Chapter 2 through Chapter 14, the Cumulative...Ch. 1 - For Chapter 2 through Chapter 14, the Cumulative...Ch. 1 - Prob. 5CRECh. 1 - For Chapter 2 through Chapter 14, the Cumulative...Ch. 1 - For Chapter 2 through Chapter 14, the Cumulative...Ch. 1 - For Chapter 2 through Chapter 14, the Cumulative...Ch. 1 - For Chapter 2 through Chapter 14, the Cumulative...Ch. 1 - For Chapter 2 through Chapter 14, the Cumulative...Ch. 1 - For Chapter 2 through Chapter 14, the Cumulative...Ch. 1 - For Chapter 2 through Chapter 14, the Cumulative...Ch. 1 - Simple Random Sample In this project, we will use...Ch. 1 - Critical Thinking The concept of six degrees of...Ch. 1 - Critical Thinking The concept of six degrees of...
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