MyLab Statistics with Pearson eText -- Standalone Access Card -- for Essentials of Statistics
6th Edition
ISBN: 9780134870113
Author: Mario F. Triola
Publisher: PEARSON
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Chapter 1, Problem 6CRE
Standard Deviation One way to get a very rough approximation of the value of a standard deviation of sample data is to find the
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Students have asked these similar questions
In this problem, we consider a Brownian motion (W+) t≥0. We consider a stock model (St)t>0
given (under the measure P) by
d.St 0.03 St dt + 0.2 St dwt,
with So 2. We assume that the interest rate is r = 0.06. The purpose of this problem is to
price an option on this stock (which we name cubic put). This option is European-type, with
maturity 3 months (i.e. T = 0.25 years), and payoff given by
F = (8-5)+
(a) Write the Stochastic Differential Equation satisfied by (St) under the risk-neutral measure
Q. (You don't need to prove it, simply give the answer.)
(b) Give the price of a regular European put on (St) with maturity 3 months and strike K = 2.
(c) Let X =
S. Find the Stochastic Differential Equation satisfied by the process (Xt)
under the measure Q.
(d) Find an explicit expression for X₁ = S3 under measure Q.
(e) Using the results above, find the price of the cubic put option mentioned above.
(f) Is the price in (e) the same as in question (b)? (Explain why.)
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
Chapter 1 Solutions
MyLab Statistics with Pearson eText -- Standalone Access Card -- for Essentials of Statistics
Ch. 1.1 - Online Medical Info USA Today posted this question...Ch. 1.1 - Reported Versus Measured In a survey of 1046...Ch. 1.1 - Statistical Significance Versus Practical...Ch. 1.1 - Correlation One study showed that for a recent...Ch. 1.1 - Consider the Source. In Exercises 58, determine...Ch. 1.1 - Consider the Source. In Exercises 58, determine...Ch. 1.1 - Consider the Source. In Exercises 58, determine...Ch. 1.1 - Consider the Source. In Exercises 58, determine...Ch. 1.1 - Sampling Method. In Exercises 912, determine...Ch. 1.1 - Sampling Method. In Exercises 912, determine...
Ch. 1.1 - Sampling Method. In Exercises 9-12, determine...Ch. 1.1 - Sampling Method. In Exercises 912, determine...Ch. 1.1 - Statistical Significance and Practical...Ch. 1.1 - Statistical Significance and Practical...Ch. 1.1 - Statistical Significance and Practical...Ch. 1.1 - Statistical Significance and Practical...Ch. 1.1 - In Exercises 1720, refer to the sample of body...Ch. 1.1 - In Exercises 1720, refer to the sample of body...Ch. 1.1 - In Exercises 1720, refer to the sample of body...Ch. 1.1 - In Exercises 1720, refer to the sample of body...Ch. 1.1 - In Exercises 2124, refer to the data in the table...Ch. 1.1 - In Exercises 2124, refer to the data in the table...Ch. 1.1 - In Exercises 2124, refer to the data in the table...Ch. 1.1 - In Exercises 2124, refer to the data in the table...Ch. 1.1 - Whats Wrong? In Exercises 2528, identify what is...Ch. 1.1 - Whats Wrong? In Exercises 2528, identify what is...Ch. 1.1 - Whats Wrong? In Exercises 2528, identify what is...Ch. 1.1 - Whats Wrong? In Exercises 25-28, identify what is...Ch. 1.1 - Workplace Attire In a survey conducted by Opinion...Ch. 1.1 - Checking Job Applicants In a study conducted by...Ch. 1.1 - Marriage Proposals In a survey conducted by...Ch. 1.1 - Chillax USA Today reported results from a Research...Ch. 1.1 - Percentages in Advertising An ad for Big Skinny...Ch. 1.1 - Percentages in Advertising Continental Airlines...Ch. 1.1 - Percentages In Advertising A New York Times...Ch. 1.1 - Percentages in Negotiations When the author was...Ch. 1.1 - Whats Wrong with This Picture? The Newport...Ch. 1.1 - Falsifying Data A researcher at the...Ch. 1.2 - Parameter and Statistic In a Harris Interactive...Ch. 1.2 - Quantitative/Categorical Data Identify each of the...Ch. 1.2 - Discrete/Continuous Data Which of the following...Ch. 1.2 - Health Survey In a survey of 1020 adults in the...Ch. 1.2 - In Exercises 512, identify whether the given value...Ch. 1.2 - In Exercises 512, identify whether the given value...Ch. 1.2 - In Exercises 512, identify whether the given value...Ch. 1.2 - In Exercises 512, identify whether the given value...Ch. 1.2 - In Exercises 512, identify whether the given value...Ch. 1.2 - In Exercises 512, identify whether the given value...Ch. 1.2 - In Exercises 512, identify whether the given value...Ch. 1.2 - In Exercises 512, identify whether the given value...Ch. 1.2 - In Exercises 1320, determine whether the data are...Ch. 1.2 - In Exercises 1320, determine whether the data are...Ch. 1.2 - In Exercises 13-20, determine whether the data are...Ch. 1.2 - In Exercises 13-20, determine whether the data are...Ch. 1.2 - In Exercises 1320, determine whether the data are...Ch. 1.2 - In Exercises 1320, determine whether the data are...Ch. 1.2 - In Exercises 1320, determine whether the data are...Ch. 1.2 - In Exercises 1320, determine whether the data are...Ch. 1.2 - In Exercises 2128, determine which of the four...Ch. 1.2 - In Exercises 2128, determine which of the four...Ch. 1.2 - In Exercises 2128, determine which of the four...Ch. 1.2 - In Exercises 2128, determine which of the four...Ch. 1.2 - In Exercises 2128, determine which of the four...Ch. 1.2 - In Exercises 2128, determine which of the four...Ch. 1.2 - In Exercises 2128, determine which of the four...Ch. 1.2 - In Exercises 2128, determine which of the four...Ch. 1.2 - In Exercises 2932, identify the level of...Ch. 1.2 - Social Security Numbers As part of a project in a...Ch. 1.2 - Temperatures As this exercise is being written, it...Ch. 1.2 - College Ranks As of this writing, U.S. News World...Ch. 1.2 - Countable For each of the following, categorize...Ch. 1.3 - Back Pain Treatment In a study designed to test...Ch. 1.3 - Blinding What does it mean when we say that the...Ch. 1.3 - Replication In what specific way was replication...Ch. 1.3 - Sampling Method The patients included in the study...Ch. 1.3 - Exercises 58 refer to the study of an association...Ch. 1.3 - Experiment or Observational Study Is the study an...Ch. 1.3 - Exercises 58 refer to the study of an association...Ch. 1.3 - Sampling Method Assume that the population...Ch. 1.3 - In Exercises 920, identify which of these types of...Ch. 1.3 - In Exercises 920, identify which of these types of...Ch. 1.3 - In Exercises 920, identify which of these types of...Ch. 1.3 - In Exercises 920, identify which of these types of...Ch. 1.3 - In Exercises 920, identify which of these types of...Ch. 1.3 - In Exercises 920, identify which of these types of...Ch. 1.3 - In Exercises 920, identify which of these types of...Ch. 1.3 - In Exercises 920, identify which of these types of...Ch. 1.3 - In Exercises 920, identify which of these types of...Ch. 1.3 - In Exercises 920, identify which of these types of...Ch. 1.3 - In Exercises 920, identify which of these types of...Ch. 1.3 - In Exercises 920, identify which of these types of...Ch. 1.3 - Critical Thinking: Whats Wrong? In Exercises 2128,...Ch. 1.3 - Critical Thinking: Whats Wrong? In Exercises 2128,...Ch. 1.3 - Critical Thinking: Whats Wrong? In Exercises 2128,...Ch. 1.3 - Critical Thinking: Whats Wrong? In Exercises 2128,...Ch. 1.3 - Critical Thinking: Whats Wrong? In Exercises 2128,...Ch. 1.3 - Critical Thinking: Whats Wrong? In Exercises 2128,...Ch. 1.3 - Critical Thinking: Whats Wrong? In Exercises 2128,...Ch. 1.3 - Critical Thinking: Whats Wrong? In Exercises 2128,...Ch. 1.3 - In Exercises 2932, indicate whether the...Ch. 1.3 - Prob. 30BBCh. 1.3 - In Exercises 2932, indicate whether the...Ch. 1.3 - In Exercises 2932, indicate whether the...Ch. 1.3 - In Exercises 3336, identify which of these designs...Ch. 1.3 - In Exercises 3336, identify which of these designs...Ch. 1.3 - In Exercises 3336, identify which of these designs...Ch. 1.3 - In Exercises 3336, identify which of these designs...Ch. 1.3 - Simple Random Sample vs. Random Sample Refer to...Ch. 1 - Hospitals In a study of births in New York State,...Ch. 1 - Hospitals Which of the following best describes...Ch. 1 - Birth Weights In the same study cited in Exercise...Ch. 1 - Birth Weights Are the birth weights described in...Ch. 1 - Birth Weights Which of the following best...Ch. 1 - Statistic /Parameter In an AARP survey of 1019...Ch. 1 - AARP Survey Refer to the survey described in...Ch. 1 - Observational Study or Experiment Are the data...Ch. 1 - Physicians Health Study In the Physicians Health...Ch. 1 - Sampling In a statistical study, which of the...Ch. 1 - Whats Wrong? In an American Optometric Association...Ch. 1 - Paying for First Dates USA Today posted this...Ch. 1 - Sample Design Literacy In Cardiovascular Effects...Ch. 1 - Divorces and Margarine One study showed that there...Ch. 1 - Simple Random Sample Which of the following is/are...Ch. 1 - Defense of Marriage Act Both of the following...Ch. 1 - Colleges in United States Currently, there are...Ch. 1 - Percentages a. The labels on U-Turn protein energy...Ch. 1 - Types of Data In each of the following, identify...Ch. 1 - Statistical Significance and Practical...Ch. 1 - Prob. 1CRECh. 1 - Prob. 2CRECh. 1 - Tallest Person Robert Wadlow (19181940) is the...Ch. 1 - Body Temperature The given expression is used for...Ch. 1 - Determining Sample Size The given expression is...Ch. 1 - Standard Deviation One way to get a very rough...Ch. 1 - Standard Deviation The standard deviation is an...Ch. 1 - Standard Deviation The given expression is used to...Ch. 1 - Scientific Notation. In Exercises 912, the given...Ch. 1 - Scientific Notation. In Exercises 912, the given...Ch. 1 - Scientific Notation. In Exercise 912, the given...Ch. 1 - Prob. 12CRECh. 1 - Prob. 1TPCh. 1 - Critical Thinking: Do Male Symphony Conductors...Ch. 1 - Critical Thinking: Do Male Symphony Conductors...Ch. 1 - Critical Thinking: Do Male Symphony Conductors...Ch. 1 - Critical Thinking: Do Male Symphony Conductors...
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