Elementary Statistics: A Step By Step Approach
9th Edition
ISBN: 9780073534985
Author: Allan Bluman
Publisher: McGraw-Hill Science/Engineering/Math
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Chapter 8, Problem 8.4.12RE
a.
To determine
To state: The null and alternative hypotheses and identify the claim.
b.
To determine
To find: The test value.
c.
To determine
To find: The P-value.
d.
To determine
To make: The decision.
e.
To determine
To summarize: The result.
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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 8 Solutions
Elementary Statistics: A Step By Step Approach
Ch. 8.1 - Applying the Concepts 81 Eggs and Your Health The...Ch. 8.1 - Define null and alternative hypotheses, and give...Ch. 8.1 - What is meant by a type I error? A type II error?...Ch. 8.1 - What is meant by a statistical test?Ch. 8.1 - Explain the difference between a one-tailed and a...Ch. 8.1 - What is meant by the critical region? The...Ch. 8.1 - What symbols are used to represent the null...Ch. 8.1 - What symbols are used to represent the...Ch. 8.1 - Explain what is meant by a significant difference.Ch. 8.1 - When should a one-tailed test be used? A...
Ch. 8.1 - In hypothesis testing, why cant the hypothesis be...Ch. 8.1 - Prob. 11ECh. 8.1 - Using the z table (Table E), find the critical...Ch. 8.1 - Prob. 13ECh. 8.1 - For each conjecture, state the null and...Ch. 8.2 - Car Thefts You recently received a job with a...Ch. 8.2 - For Exercises 1 through 25, perform each of the...Ch. 8.2 - Prob. 2ECh. 8.2 - For Exercises 1 through 25, perform each of the...Ch. 8.2 - For Exercises 1 through 25, perform each of the...Ch. 8.2 - Prob. 5ECh. 8.2 - For Exercises 1 through 25, perform each of the...Ch. 8.2 - For Exercises 1 through 25, perform each of the...Ch. 8.2 - For Exercises 1 through 25, perform each of the...Ch. 8.2 - Prob. 9ECh. 8.2 - Prob. 10ECh. 8.2 - Prob. 11ECh. 8.2 - For Exercises 1 through 25, perform each of the...Ch. 8.2 - Prob. 13ECh. 8.2 - For Exercises 1 through 25, perform each of the...Ch. 8.2 - Reject or Not State whether the null hypothesis...Ch. 8.2 - For Exercises 1 through 25, perform each of the...Ch. 8.2 - For Exercises 1 through 25, perform each of the...Ch. 8.2 - For Exercises 1 through 25, perform each of the...Ch. 8.2 - Prob. 19ECh. 8.2 - For Exercises 1 through 25, perform each of the...Ch. 8.2 - For Exercises 1 through 25, perform each of the...Ch. 8.2 - For Exercises 1 through 25, perform each of the...Ch. 8.2 - Transmission Service A car dealer recommends that...Ch. 8.2 - Speeding Tickets A motorist claims that the South...Ch. 8.2 - Sick Days A manager states that in his factory,...Ch. 8.2 - Significance Levels Suppose a statistician chose...Ch. 8.2 - Hourly Wage The president of a company states that...Ch. 8.3 - How Much Nicotine Is in Those Cigarettes? A...Ch. 8.3 - In what ways is the t distribution similar to the...Ch. 8.3 - What are the degrees of freedom for the t test?Ch. 8.3 - Prob. 3ECh. 8.3 - Find the critical value (or values) for the t test...Ch. 8.3 - Using Table F, find the P-value interval for each...Ch. 8.3 - Using Table F, find the P-value interval for each...Ch. 8.3 - Prob. 7ECh. 8.3 - For Exercises 7 through 23, perform each of the...Ch. 8.3 - For Exercises 7 through 23, perform each of the...Ch. 8.3 - For Exercises 7 through 23, perform each of the...Ch. 8.3 - For Exercises 7 through 23, perform each of the...Ch. 8.3 - For Exercises 7 through 23, perform each of the...Ch. 8.3 - Prob. 13ECh. 8.3 - For Exercises 7 through 23, perform each of the...Ch. 8.3 - For Exercises 7 through 23, perform each of the...Ch. 8.3 - For Exercises 7 through 23, perform each of the...Ch. 8.3 - Prob. 17ECh. 8.3 - For Exercises 7 through 23, perform each of the...Ch. 8.3 - For Exercises 7 through 23, perform each of the...Ch. 8.3 - For Exercises 7 through 23, perform each of the...Ch. 8.3 - For Exercises 7 through 23, perform each of the...Ch. 8.3 - For Exercises 7 through 23, perform each of the...Ch. 8.3 - For Exercises 7 through 23, perform each of the...Ch. 8.4 - What were the statistical hypotheses? 2. What were...Ch. 8.4 - Give three examples of proportions.Ch. 8.4 - Why is a proportion considered a binomial...Ch. 8.4 - When you are testing hypotheses by using...Ch. 8.4 - What are the mean and the standard deviation of a...Ch. 8.4 - Prob. 5ECh. 8.4 - For Exercises 5 through 20, perform each of the...Ch. 8.4 - Prob. 7ECh. 8.4 - For Exercises 5 through 20, perform each of the...Ch. 8.4 - Prob. 9ECh. 8.4 - For Exercises 5 through 20, perform each of the...Ch. 8.4 - Prob. 11ECh. 8.4 - For Exercises 5 through 20, perform each of the...Ch. 8.4 - For Exercises 5 through 20, perform each of the...Ch. 8.4 - For Exercises 5 through 20, perform each of the...Ch. 8.4 - Youth Smoking Researchers suspect that 18% of all...Ch. 8.4 - For Exercises 5 through 20, perform each of the...Ch. 8.4 - For Exercises 5 through 20, perform each of the...Ch. 8.4 - For Exercises 5 through 20, perform each of the...Ch. 8.4 - For Exercises 5 through 20, perform each of the...Ch. 8.4 - For Exercises 5 through 20, perform each of the...Ch. 8.4 - When np or nq is not 5 or more, the binomial table...Ch. 8.4 - First-Class Airline Passengers In the past, 20% of...Ch. 8.4 - Show that Z=pppqn can be derived from z=Xu by...Ch. 8.5 - Testing Gas Mileage Claims Assume that you are...Ch. 8.5 - Prob. 1ECh. 8.5 - Using Table G, find the critical value(s) for...Ch. 8.5 - Using Table G, find the P-value interval for each...Ch. 8.5 - Using Table G, find the P-value interval for each...Ch. 8.5 - Prob. 5ECh. 8.5 - For Exercises 5 through 20, assume that the...Ch. 8.5 - For Exercises 5 through 20, assume that the...Ch. 8.5 - For Exercises 5 through 20, assume that the...Ch. 8.5 - Prob. 9ECh. 8.5 - For Exercises 5 through 20, assume that the...Ch. 8.5 - Tornado Deaths A researcher claims that the...Ch. 8.5 - Interstate Speeds It has been reported that the...Ch. 8.5 - Prob. 13ECh. 8.5 - For Exercises 5 through 20, assume that the...Ch. 8.5 - For Exercises 5 through 20, assume that the...Ch. 8.5 - For Exercises 5 through 20, assume that the...Ch. 8.5 - For Exercises 5 through 20, assume that the...Ch. 8.5 - For Exercises 5 through 20, assume that the...Ch. 8.5 - For Exercises 5 through 20, assume that the...Ch. 8.5 - For Exercises 5 through 20, assume that the...Ch. 8.6 - First-Time Births According to the almanac, the...Ch. 8.6 - One-Way Airfares The average one-way airfare from...Ch. 8.6 - Prob. 3ECh. 8.6 - Prison Time According to a public service website,...Ch. 8.6 - Working at Home Workers with a formal arrangement...Ch. 8.6 - Newspaper Reading Times A survey taken several...Ch. 8.6 - Prob. 7ECh. 8.6 - How is the power of a test related to the type II...Ch. 8.6 - Prob. 9ECh. 8 - Prob. 8.2.1RECh. 8 - For Exercises 1 through 20, perform each of the...Ch. 8 - For Exercises 1 through 20, perform each of the...Ch. 8 - For Exercises 1 through 20, perform each of the...Ch. 8 - Prob. 8.2.5RECh. 8 - For Exercises 1 through 20, perform each of the...Ch. 8 - For Exercises 1 through 20, perform each of the...Ch. 8 - For Exercises 1 through 20, perform each of the...Ch. 8 - Prob. 8.4.9RECh. 8 - For Exercises 1 through 20, perform each of the...Ch. 8 - For Exercises 1 through 20, perform each of the...Ch. 8 - Prob. 8.4.12RECh. 8 - For Exercises 1 through 20, perform each of the...Ch. 8 - For Exercises 1 through 20, perform each of the...Ch. 8 - For Exercises 5 through 20, assume that the...Ch. 8 - For Exercises 5 through 20, assume that the...Ch. 8 - For Exercises 5 through 20, assume that the...Ch. 8 - Prob. 8.5.18RECh. 8 - Plant Leaf Lengths A biologist knows that the...Ch. 8 - Tire Inflation To see whether people are keeping...Ch. 8 - The Data Bank is found in Appendix B, or on the...Ch. 8 - Select a random sample of 15 individuals and test...Ch. 8 - Select a random sample of at least 30 individuals,...Ch. 8 - Select a sample of 20 individuals and test the...Ch. 8 - Using the data from Data Set XIII, select a sample...Ch. 8 - Using the data obtained in Exercise 5, test the...Ch. 8 - Determine whether each statement is true or false....Ch. 8 - Determine whether each statement is true or false....Ch. 8 - Determine whether each statement is true or false....Ch. 8 - Determine whether each statement is true or false....Ch. 8 - Determine whether each statement is true or false....Ch. 8 - When the value of is increased, the probability...Ch. 8 - If you wish to test the claim that the mean of the...Ch. 8 - The degrees of freedom for the chi-square test for...Ch. 8 - For the t test, one uses _______ instead of . a. n...Ch. 8 - Complete the following statements with the best...Ch. 8 - Complete the following statements with the best...Ch. 8 - A conjecture about a population parameter is...Ch. 8 - Complete the following statements with the best...Ch. 8 - Complete the following statements with the best...Ch. 8 - For the following exercises where applicable: a....Ch. 8 - For Exercises 1 through 25, perform each of the...Ch. 8 - For Exercises 1 through 25, perform each of the...Ch. 8 - Prob. 18CQCh. 8 - Prob. 19CQCh. 8 - For Exercises 1 through 25, perform each of the...Ch. 8 - Prob. 21CQCh. 8 - Prob. 22CQCh. 8 - 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