Loose Leaf for Elementary Statistics: A Step By Step Approach
10th Edition
ISBN: 9781260152821
Author: Bluman, Allan G.
Publisher: McGraw-Hill Education
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Chapter 1.4, Problem 22E
To determine
The independent and dependent variable in the given study.
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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
Loose Leaf for Elementary Statistics: A Step By Step Approach
Ch. 1.1 - Read the following on attendance and grades, and...Ch. 1.1 - Define statistics.Ch. 1.1 - What is a variable?Ch. 1.1 - What is meant by a census?Ch. 1.1 - How does a population differ from a sample?Ch. 1.1 - Explain the difference between descriptive and...Ch. 1.1 - Name three areas where probability is used.Ch. 1.1 - Why is information obtained from samples used more...Ch. 1.1 - What is meant by a biased sample?Ch. 1.1 - determine whether descriptive or inferential...
Ch. 1.1 - determine whether descriptive or inferential...Ch. 1.1 - determine whether descriptive or inferential...Ch. 1.1 - determine whether descriptive or inferential...Ch. 1.1 - determine whether descriptive or inferential...Ch. 1.1 - determine whether descriptive or inferential...Ch. 1.1 - determine whether descriptive or inferential...Ch. 1.1 - determine whether descriptive or inferential...Ch. 1.1 - determine whether descriptive or inferential...Ch. 1.2 - Applying the Concepts 1-2 Fatal Transportation...Ch. 1.2 - Explain the difference between qualitative...Ch. 1.2 - Prob. 2ECh. 1.2 - Why are continuous variables rounded when they are...Ch. 1.2 - Name and define the four types of measurement...Ch. 1.2 - determine whether the data are qualitative or...Ch. 1.2 - determine whether the data are qualitative or...Ch. 1.2 - determine whether the data are qualitative or...Ch. 1.2 - determine whether the data are qualitative or...Ch. 1.2 - determine whether the data are qualitative or...Ch. 1.2 - determine whether the data are qualitative or...Ch. 1.2 - determine whether the data are discrete or...Ch. 1.2 - determine whether the data are discrete or...Ch. 1.2 - determine whether the data are discrete or...Ch. 1.2 - determine whether the data are discrete or...Ch. 1.2 - determine whether the data are discrete or...Ch. 1.2 - determine whether the data are discrete or...Ch. 1.2 - give the boundaries of each value. 17. 24 feelCh. 1.2 - give the boundaries of each value. 18. 6.3...Ch. 1.2 - give the boundaries of each value. 19. 143 milesCh. 1.2 - give the boundaries of each value. 20. 19.63 tonsCh. 1.2 - give the boundaries of each value. 21. 200.7 milesCh. 1.2 - give the boundaries of each value. 22. 19 quartsCh. 1.2 - classify each as nominal-level, ordinal-level,...Ch. 1.2 - classify each as nominal-level, ordinal-level,...Ch. 1.2 - classify each as nominal-level, ordinal-level,...Ch. 1.2 - classify each as nominal-level, ordinal-level,...Ch. 1.2 - classify each as nominal-level, ordinal-level,...Ch. 1.2 - classify each as nominal-level, ordinal-level,...Ch. 1.2 - classify each as nominal-level, ordinal-level,...Ch. 1.2 - classify each as nominal-level, ordinal-level,...Ch. 1.3 - Applying the Concepts 13 American Culture and Drug...Ch. 1.3 - Name five ways that data can be collected.Ch. 1.3 - What is meant by sampling error and nonsampling...Ch. 1.3 - Why are random numbers used in sampling, and how...Ch. 1.3 - Name and define the four basic sampling methods.Ch. 1.3 - For Exercises 510, define a population that may...Ch. 1.3 - For Exercises 510, define a population that may...Ch. 1.3 - For Exercises 510, define a population that may...Ch. 1.3 - For Exercises 510, define a population that may...Ch. 1.3 - For Exercises 510, define a population that may...Ch. 1.3 - For Exercises 5-10, define a population that may...Ch. 1.3 - indentify the sampling method that was used. 11....Ch. 1.3 - indentify the sampling method that was used. 12....Ch. 1.3 - indentify the sampling method that was used. 13....Ch. 1.3 - indentify the sampling method that was used. 14....Ch. 1.3 - indentify the sampling method that was used. 15....Ch. 1.3 - indentify the sampling method that was used. 16....Ch. 1.4 - Todays Cigarettes Vapor or electronic cigarettes...Ch. 1.4 - Explain the difference between an observational...Ch. 1.4 - Prob. 2ECh. 1.4 - List some advantages and disadvantages of an...Ch. 1.4 - List some advantages and disadvantages of an...Ch. 1.4 - What is the difference between an experimental...Ch. 1.4 - What is the difference between independent...Ch. 1.4 - Why are a treatment group and a control group used...Ch. 1.4 - Explain the Hawthorne effect.Ch. 1.4 - What is a confounding variable?Ch. 1.4 - Define the placebo effect in a statistical study.Ch. 1.4 - Prob. 11ECh. 1.4 - Why do researchers use randomization in...Ch. 1.4 - Prob. 13ECh. 1.4 - Prob. 14ECh. 1.4 - determine whether an observational study or an...Ch. 1.4 - determine whether an observational study or an...Ch. 1.4 - determine whether an observational study or an...Ch. 1.4 - determine whether an observational study or an...Ch. 1.4 - identify the independent variable and the...Ch. 1.4 - identify the independent variable and the...Ch. 1.4 - Prob. 21ECh. 1.4 - Prob. 22ECh. 1.4 - Prob. 23ECh. 1.4 - Prob. 24ECh. 1.4 - Prob. 25ECh. 1.4 - suggest some confounding variables that the...Ch. 1.4 - For Exercises 2731, give a reason why the...Ch. 1.4 - Here is the whole truth about back pain.Ch. 1.4 - For Exercises 2731, give a reason why the...Ch. 1.4 - give a reason why the statement made might be...Ch. 1.4 - Prob. 31ECh. 1.4 - List the steps you should perform when conducting...Ch. 1.4 - Prob. 33ECh. 1.4 - Comment on the following statement, taken from a...Ch. 1.4 - In an ad for women, the following statement was...Ch. 1.4 - Prob. 36ECh. 1.4 - Prob. 37ECh. 1.4 - An ad for an exercise product stated: Using this...Ch. 1.4 - Prob. 39ECh. 1.4 - Just l capsule of Brand X can provide 24 hours of...Ch. 1.4 - Male children born to women who smoke during...Ch. 1.4 - Caffeine and Health In the 1980s, a study linked...Ch. 1 - state whether descriptive or inferential...Ch. 1 - state whether descriptive or inferential...Ch. 1 - state whether descriptive or inferential...Ch. 1 - state whether descriptive or inferential...Ch. 1 - state whether descriptive or inferential...Ch. 1 - state whether descriptive or inferential...Ch. 1 - state whether descriptive or inferential...Ch. 1 - state whether descriptive or inferential...Ch. 1 - classify each as nominal-level, ordinal-level,...Ch. 1 - Classify each as nominal-level, ordinal-level,...Ch. 1 - classify each as nominal-level, ordinal-level,...Ch. 1 - classify each as nominal-level, ordinal-level,...Ch. 1 - classify each as nominal-level, ordinal-level,...Ch. 1 - classify each as nominal-level, ordinal-level,...Ch. 1 - classify each as nominal-level, ordinal-level,...Ch. 1 - classify each as nominal-level, ordinal-level,...Ch. 1 - classify each as nominal-level, ordinal-level,...Ch. 1 - classify each as nominal-level, ordinal-level,...Ch. 1 - classify each variable as qualitative or...Ch. 1 - classify each variable as qualitative or...Ch. 1 - classify each variable as qualitative or...Ch. 1 - classify each variable as qualitative or...Ch. 1 - classify each variable as qualitative or...Ch. 1 - classify each variable as qualitative or...Ch. 1 - classify each variable as qualitative or...Ch. 1 - classify each variable as qualitative or...Ch. 1 - classify each variable as discrete or continuous....Ch. 1 - classify each variable as discrete or continuous....Ch. 1 - classify each variable as discrete or continuous....Ch. 1 - classify each variable as discrete or continuous....Ch. 1 - classify each variable as discrete or continuous....Ch. 1 - classify each variable as discrete or continuous....Ch. 1 - classify each variable as discrete or continuous....Ch. 1 - classify each variable as discrete or continuous....Ch. 1 - give the boundaries of each value. 35. 56 yards.Ch. 1 - give the boundaries of each value. 36. 105.4...Ch. 1 - give the boundaries of each value. 37. 72.6 tons.Ch. 1 - give the boundaries of each value. 38. 9.54...Ch. 1 - classify each sample as random, systematic,...Ch. 1 - classify each sample as random, systematic,...Ch. 1 - classify each sample as random, systematic,...Ch. 1 - classify each sample as random, systematic,...Ch. 1 - classify each sample as random, systematic,...Ch. 1 - classify each sample as random, systematic,...Ch. 1 - identify each study as being either observational...Ch. 1 - identify each study as being either observational...Ch. 1 - identify each study as being either observational...Ch. 1 - identify each study as being either observational...Ch. 1 - For Exercises 4952, identify the independent and...Ch. 1 - identify the independent and dependent variables...Ch. 1 - identify the independent and dependent variables...Ch. 1 - identify the independent and dependent variables...Ch. 1 - explain why the claims of these studies might be...Ch. 1 - explain why the claims of these studies might be...Ch. 1 - explain why the claims of these studies might be...Ch. 1 - For Exercises 5358, explain why the claims of...Ch. 1 - explain why the claims of these studies might be...Ch. 1 - explain why the claims of these studies might be...Ch. 1 - Determine whether each statement is true or false....Ch. 1 - Determine whether each statement is true or false....Ch. 1 - Prob. 3CQCh. 1 - Prob. 4CQCh. 1 - Prob. 5CQCh. 1 - The height of basketball players is considered a...Ch. 1 - Prob. 7CQCh. 1 - Prob. 8CQCh. 1 - Select the best answer. 9. What are the boundaries...Ch. 1 - Select the best answer. 10. A researcher divided...Ch. 1 - Prob. 11CQCh. 1 - Select the best answer. 12. A study that involves...Ch. 1 - Prob. 13CQCh. 1 - Two major branches of statistics are _____ and...Ch. 1 - Prob. 15CQCh. 1 - The group of all subjects under study is called...Ch. 1 - A group of subjects selected from the group of all...Ch. 1 - Three reasons why samples are used in statistics:...Ch. 1 - The four basic sampling methods are a. ______ b....Ch. 1 - Prob. 20CQCh. 1 - Prob. 21CQCh. 1 - For each statement, decide whether descriptive or...Ch. 1 - Classify each as nominal-level, ordinal-level,...Ch. 1 - Classify each variable as discrete or continuous....Ch. 1 - Give the boundaries of each. a. 32 minutes b. 0.48...
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