An Introduction to Statistical Methods and Data Analysis
7th Edition
ISBN: 9781305269477
Author: R. Lyman Ott, Micheal T. Longnecker
Publisher: Cengage Learning
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Textbook Question
Chapter 9.10, Problem 3E
In an experiment with t = 4 populations means, consider the four linear combinations of those means.
- a. Which of the four linear combinations are contrasts?
- b. Which pairs of contrasts are orthogonal?
- c. Suppose we have two contrasts:
Is testing H0 : l1 = 0 equivalent to testing H0 : l2 = 0? Justify your answer.
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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.)
Chapter 9 Solutions
An Introduction to Statistical Methods and Data Analysis
Ch. 9.10 - In an experiment with t = 4 populations means,...Ch. 9.10 - Refer to Example 8.6. The political action group...Ch. 9.10 - In a study of 10 new producers of iron...Ch. 9.10 - Researchers conducted an experiment to compare the...Ch. 9.10 - Prob. 20SECh. 9.10 - Prob. 22SECh. 9.10 - Prob. 23SE
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