Elementary Statistics: Picturing the World (6th Edition)
6th Edition
ISBN: 9780321911216
Author: Ron Larson, Betsy Farber
Publisher: PEARSON
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Question
Chapter 11.1, Problem 14E
a.
To determine
To identify: The claim and state
b.
To determine
To find: The critical value.
c.
To determine
To find: the test statistic.
d.
To determine
To decide: Whether to reject or fail to reject the null hypothesis at a level of significance
e.
To determine
To interpret: The decision in the context of the original claim.
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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 11 Solutions
Elementary Statistics: Picturing the World (6th Edition)
Ch. 11.1 - Prob. 1TYCh. 11.1 - Prob. 2TYCh. 11.1 - Prob. 3TYCh. 11.1 - Prob. 1ECh. 11.1 - When the sign test is used, what population...Ch. 11.1 - Describe the test statistic for the sign test when...Ch. 11.1 - In your own words, explain why the hypothesis test...Ch. 11.1 - Explain how to use the sign test to test a...Ch. 11.1 - List the two conditions that must be met in order...Ch. 11.1 - Prob. 7E
Ch. 11.1 - Temperature A meteorologist claims that the median...Ch. 11.1 - Prob. 9ECh. 11.1 - Temperature During a weather report, a...Ch. 11.1 - Prob. 11ECh. 11.1 - Prob. 12ECh. 11.1 - Prob. 13ECh. 11.1 - Prob. 14ECh. 11.1 - Unit Size A renters organization claims that the...Ch. 11.1 - Prob. 16ECh. 11.1 - Prob. 17ECh. 11.1 - Prob. 18ECh. 11.1 - Prob. 19ECh. 11.1 - Prob. 20ECh. 11.1 - Prob. 21ECh. 11.1 - Prob. 22ECh. 11.1 - Prob. 23ECh. 11.1 - Contacting Parents A research organization...Ch. 11.1 - Prob. 25ECh. 11.1 - Prob. 26ECh. 11.1 - Prob. 27ECh. 11.1 - Ages of Grooms A marriage counselor claims that...Ch. 11.2 - Prob. 1TYCh. 11.2 - Prob. 2TYCh. 11.2 - Prob. 1ECh. 11.2 - Prob. 2ECh. 11.2 - Prob. 3ECh. 11.2 - Prob. 4ECh. 11.2 - Prob. 5ECh. 11.2 - Prob. 6ECh. 11.2 - Prob. 7ECh. 11.2 - Performing a Wilcoxon Test In Exercises 38, (a)...Ch. 11.2 - Wilcoxon Signed-Rank Test for n 30 When you are...Ch. 11.2 - Prob. 10ECh. 11.2 - Prob. 1CSCh. 11.2 - Prob. 2CSCh. 11.2 - Prob. 3CSCh. 11.2 - Prob. 4CSCh. 11.2 - Prob. 5CSCh. 11.2 - Prob. 6CSCh. 11.2 - Prob. 7CSCh. 11.3 - Prob. 1TYCh. 11.3 - Prob. 1ECh. 11.3 - Explain why the Kruskal-Wallis test is always a...Ch. 11.3 - Prob. 3ECh. 11.3 - Prob. 4ECh. 11.3 - Prob. 5ECh. 11.3 - Prob. 6ECh. 11.3 - Comparing Two Tests In Exercises 7 and 8, (a)...Ch. 11.3 - Comparing Two Tests In Exercises 7 and 8, (a)...Ch. 11.4 - Prob. 1TYCh. 11.4 - Prob. 1ECh. 11.4 - Prob. 2ECh. 11.4 - Prob. 3ECh. 11.4 - Prob. 4ECh. 11.4 - Prob. 5ECh. 11.4 - Prob. 6ECh. 11.4 - Prob. 7ECh. 11.4 - Prob. 8ECh. 11.4 - Prob. 9ECh. 11.4 - Prob. 10ECh. 11.4 - Prob. 11ECh. 11.4 - Prob. 12ECh. 11.4 - Prob. 13ECh. 11.4 - Prob. 14ECh. 11.5 - Prob. 1TYCh. 11.5 - Prob. 2TYCh. 11.5 - Prob. 3TYCh. 11.5 - In your own words, explain why the hypothesis test...Ch. 11.5 - Describe the test statistic for the runs test when...Ch. 11.5 - Finding the Number of Runs In Exercises 36,...Ch. 11.5 - Prob. 4ECh. 11.5 - Finding the Number of Runs In Exercises 36,...Ch. 11.5 - Prob. 6ECh. 11.5 - Prob. 7ECh. 11.5 - Prob. 8ECh. 11.5 - Prob. 9ECh. 11.5 - Prob. 10ECh. 11.5 - Finding Critical Values In Exercises 1114, use the...Ch. 11.5 - Prob. 12ECh. 11.5 - Prob. 13ECh. 11.5 - Prob. 14ECh. 11.5 - Prob. 15ECh. 11.5 - Prob. 16ECh. 11.5 - Prob. 17ECh. 11.5 - Prob. 18ECh. 11.5 - Prob. 19ECh. 11.5 - Prob. 20ECh. 11.5 - Prob. 21ECh. 11.5 - Prob. 22ECh. 11.5 - Runs Test with Quantitative Data In Exercises...Ch. 11 - Using an Inappropriate Test Discuss the...Ch. 11 - Prob. 11.1.1RECh. 11 - Prob. 11.1.2RECh. 11 - Prob. 11.1.3RECh. 11 - Prob. 11.1.4RECh. 11 - Prob. 11.1.5RECh. 11 - Prob. 11.1.6RECh. 11 - Prob. 11.2.7RECh. 11 - In Exercises 7 and 8, use a Wilcoxon test to test...Ch. 11 - Prob. 11.3.9RECh. 11 - Prob. 11.3.10RECh. 11 - Prob. 11.4.11RECh. 11 - Prob. 11.4.12RECh. 11 - Prob. 11.5.13RECh. 11 - Prob. 11.5.14RECh. 11 - Prob. 1CQCh. 11 - Prob. 2CQCh. 11 - Prob. 3CQCh. 11 - Prob. 4CQCh. 11 - Prob. 5CQCh. 11 - Prob. 1CTCh. 11 - Prob. 2CTCh. 11 - Prob. 3CTCh. 11 - Prob. 4CTCh. 11 - Prob. 5CTCh. 11 - How Would You Do It? (a) What sampling technique...Ch. 11 - Prob. 2RSRDCh. 11 - Prob. 3RSRDCh. 11 - Prob. 1TCh. 11 - Prob. 2TCh. 11 - Prob. 3TCh. 11 - Prob. 4TCh. 11 - Prob. 5TCh. 11 - Prob. 6T
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