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 12, Problem 12.1.4RE
a.
To determine
To state: The hypothesis
To identify: The claim.
b.
To determine
To find: The critical value.
c.
To determine
To compute: The test value.
d.
To determine
To make: The decision.
e.
To determine
To explain: The results.
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Does there appear to be a positive or negative relationship between price and screen size? Use a scatter plot to examine the relationship. How to take snapshots: if you use a MacBook, press Command+ Shift+4 to take snapshots. If you are using Windows, use the Snipping Tool to take snapshots.
Question 1: Determine and interpret the correlation coefficient between the two variables. In your interpretation, discuss the direction of the relationship (positive, negative, or zero relationship). Also discuss the strength of the relationship.
Value of correlation coefficient:
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Strength of the relationship (strong/moderate/weak):
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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.)
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?
Chapter 12 Solutions
Elementary Statistics: A Step By Step Approach
Ch. 12.1 - Colors That Make You Smarter The following set of...Ch. 12.1 - What test is used to compare three or more means?Ch. 12.1 - State three reasons why multiple t tests cannot be...Ch. 12.1 - What are the assumptions for ANOVA?Ch. 12.1 - Define between-group variance and within-group...Ch. 12.1 - State the hypotheses used in the ANOVA test.Ch. 12.1 - When there is no significant difference among...Ch. 12.1 - Prob. 7ECh. 12.1 - For Exercises 7 through 20, assume that all...Ch. 12.1 - For Exercises 7 through 20, assume that all...
Ch. 12.1 - For Exercises 7 through 20, assume that all...Ch. 12.1 - Prob. 11ECh. 12.1 - For Exercises 7 through 20, assume that all...Ch. 12.1 - For Exercises 7 through 20, assume that all...Ch. 12.1 - For Exercises 7 through 20, assume that all...Ch. 12.1 - Prob. 15ECh. 12.1 - For Exercises 7 through 20, assume that all...Ch. 12.1 - For Exercises 7 through 20, assume that all...Ch. 12.1 - For Exercises 7 through 20, assume that all...Ch. 12.1 - For Exercises 7 through 20, assume that all...Ch. 12.1 - For Exercises 7 through 20, assume that all...Ch. 12.2 - Colors That Make You Smarter The following set of...Ch. 12.2 - What two tests can be used to compare two means...Ch. 12.2 - Explain the difference between the two tests used...Ch. 12.2 - For Exercises 3 through 8, the null hypothesis was...Ch. 12.2 - For Exercises 3 through 8, the null hypothesis was...Ch. 12.2 - For Exercises 3 through 8, the null hypothesis was...Ch. 12.2 - For Exercises 3 through 8, the null hypothesis was...Ch. 12.2 - For Exercises 3 through 8, the null hypothesis was...Ch. 12.2 - For Exercises 3 through 8, the null hypothesis was...Ch. 12.2 - For Exercises 9 through 13, do a complete one-way...Ch. 12.2 - Prob. 10ECh. 12.2 - For Exercises 9 through 13, do a complete one-way...Ch. 12.2 - For Exercises 9 through 13, do a complete one-way...Ch. 12.2 - Prob. 13ECh. 12.3 - Automobile Sales Techniques The following outputs...Ch. 12.3 - Prob. 1ECh. 12.3 - Explain what is meant by main effects and...Ch. 12.3 - Prob. 3ECh. 12.3 - How are the F test values computed?Ch. 12.3 - Prob. 5ECh. 12.3 - In a two-way ANOVA, variable A has six levels and...Ch. 12.3 - Prob. 7ECh. 12.3 - When can the main effects for the two-way ANOVA be...Ch. 12.3 - Prob. 9ECh. 12.3 - For Exercises 9 through 15, perform these steps....Ch. 12.3 - For Exercises 9 through 15, perform these steps....Ch. 12.3 - For Exercises 9 through 15, perform these steps....Ch. 12.3 - Prob. 13ECh. 12.3 - For Exercises 9 through 15, perform these steps....Ch. 12.3 - Prob. 15ECh. 12 - If the null hypothesis is rejected in Exercises 1...Ch. 12 - Prob. 12.1.2RECh. 12 - Prob. 12.1.3RECh. 12 - Prob. 12.1.4RECh. 12 - Prob. 12.1.5RECh. 12 - If the null hypothesis is rejected in Exercises 1...Ch. 12 - Prob. 12.1.7RECh. 12 - Prob. 12.1.8RECh. 12 - Review Preparation for Statistics A statistics...Ch. 12 - Effects of Different Types of Diets A medical...Ch. 12 - Prob. 1DACh. 12 - Prob. 2DACh. 12 - Prob. 3DACh. 12 - Prob. 1CQCh. 12 - Prob. 2CQCh. 12 - Prob. 3CQCh. 12 - Determine whether each statement is true or false....Ch. 12 - Prob. 5CQCh. 12 - Prob. 6CQCh. 12 - Prob. 7CQCh. 12 - Prob. 8CQCh. 12 - Complete the following statements with the best...Ch. 12 - Prob. 10CQCh. 12 - For Exercises 11 through 17, use the traditional...Ch. 12 - Prob. 12CQCh. 12 - Prob. 13CQCh. 12 - Prob. 14CQCh. 12 - Prob. 15CQCh. 12 - Prob. 16CQCh. 12 - For Exercises 11 through 17, use the traditional...Ch. 12 - Shown here are the abstract and two tables from a...Ch. 12 - Shown here are the abstract and two tables from a...Ch. 12 - Prob. 3CTCCh. 12 - Prob. 4CTCCh. 12 - Prob. 5CTCCh. 12 - Prob. 6CTCCh. 12 - Prob. 7CTCCh. 12 - Adult Children of Alcoholics Shown here are the...Ch. 12 - Prob. 9CTCCh. 12 - Prob. 10CTCCh. 12 - Prob. 11CTC
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