Elementary Statistics: Picturing the World (7th Edition)
7th Edition
ISBN: 9780134683416
Author: Ron Larson, Betsy Farber
Publisher: PEARSON
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Chapter 10.2, Problem 32E
To determine
To explain: The chi-square independence test is different from the chi-square homogeneity of proportions test.
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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 10 Solutions
Elementary Statistics: Picturing the World (7th Edition)
Ch. 10.1 - The tax preparation company in Example 1 decides...Ch. 10.1 - Prob. 2TYCh. 10.1 - Prob. 3TYCh. 10.1 - What is a multinomial experiment?Ch. 10.1 - What conditions are necessary to use the...Ch. 10.1 - Finding Expected Frequencies In Exercises 36, find...Ch. 10.1 - Finding Expected Frequencies In Exercises 36, find...Ch. 10.1 - Finding Expected Frequencies In Exercises 36, find...Ch. 10.1 - Finding Expected Frequencies In Exercises 36, find...Ch. 10.1 - Using and Interpreting Concepts Performing a...
Ch. 10.1 - Coffee A researcher claims that the numbers of...Ch. 10.1 - Performing a Chi-Square Goodness-of-Fit Test In...Ch. 10.1 - Performing a Chi-Square Goodness-of-Fit Test In...Ch. 10.1 - Performing a Chi-Square Goodness-of-Fit Test In...Ch. 10.1 - Performing a Chi-Square Goodness-of-Fit Test In...Ch. 10.1 - Performing a Chi-Square Goodness-of-Fit Test In...Ch. 10.1 - Performing a Chi-Square Goodness-of-Fit Test In...Ch. 10.1 - Performing a Chi-Square Goodness-of-Fit Test In...Ch. 10.1 - Performing a Chi-Square Goodness-of-Fit Test In...Ch. 10.1 - In Exercises 17 and 18, (a) find the expected...Ch. 10.1 - In Exercises 17 and 18, (a) find the expected...Ch. 10.2 - The marketing consultant for a travel agency wants...Ch. 10.2 - Prob. 2TYCh. 10.2 - Prob. 3TYCh. 10.2 - Prob. 1ECh. 10.2 - Explain the difference between marginal...Ch. 10.2 - Prob. 3ECh. 10.2 - Prob. 4ECh. 10.2 - Prob. 5ECh. 10.2 - True or False? In Exercises 5 and 6, determine...Ch. 10.2 - Finding Expected Frequencies In Exercises 712, (a)...Ch. 10.2 - Finding Expected Frequencies In Exercises 712, (a)...Ch. 10.2 - Prob. 9ECh. 10.2 - Prob. 10ECh. 10.2 - Prob. 11ECh. 10.2 - Prob. 12ECh. 10.2 - Performing a Chi-Square Independence Test In...Ch. 10.2 - Prob. 14ECh. 10.2 - Performing a Chi-Square Independence Test In...Ch. 10.2 - Performing a Chi-Square Independence Test In...Ch. 10.2 - Performing a Chi-Square Independence Test In...Ch. 10.2 - Performing a Chi-Square Independence Test In...Ch. 10.2 - Prob. 19ECh. 10.2 - Performing a Chi-Square Independence Test In...Ch. 10.2 - Prob. 21ECh. 10.2 - Performing a Chi-Square Independence Test In...Ch. 10.2 - Performing a Chi-Square Independence Test In...Ch. 10.2 - Prob. 24ECh. 10.2 - Prob. 25ECh. 10.2 - Prob. 26ECh. 10.2 - Prob. 27ECh. 10.2 - Prob. 28ECh. 10.2 - Motor Vehicle Crash Deaths The contingency table...Ch. 10.2 - Prob. 30ECh. 10.2 - Prob. 31ECh. 10.2 - Prob. 32ECh. 10.2 - Prob. 33ECh. 10.2 - Prob. 34ECh. 10.2 - Prob. 35ECh. 10.2 - Contingency Tables and Relative Frequencies In...Ch. 10.2 - Prob. 37ECh. 10.2 - Prob. 38ECh. 10.2 - Prob. 39ECh. 10.2 - Conditional Relative Frequencies In Exercises...Ch. 10.2 - Conditional Relative Frequencies In Exercises...Ch. 10.2 - Prob. 42ECh. 10.2 - In your opinion, how safe is the food you buy? CBS...Ch. 10.2 - In your opinion, how safe is the food you buy? CBS...Ch. 10.2 - In your opinion, how safe is the food you buy? CBS...Ch. 10.2 - In your opinion, how safe is the food you buy? CBS...Ch. 10.2 - In your opinion, how safe is the food you buy? CBS...Ch. 10.2 - In your opinion, how safe is the food you buy? CBS...Ch. 10.3 - Find the critical F-value for a right-tailed test...Ch. 10.3 - Prob. 2TYCh. 10.3 - Prob. 3TYCh. 10.3 - Prob. 4TYCh. 10.3 - Explain how to find the critical value for an...Ch. 10.3 - List five properties of the F-distribution.Ch. 10.3 - List the three conditions that must be met in...Ch. 10.3 - Explain how to determine the values of d.f.N and...Ch. 10.3 - Prob. 5ECh. 10.3 - Prob. 6ECh. 10.3 - Prob. 7ECh. 10.3 - Finding a Critical F-Value for a Right-Tailed Test...Ch. 10.3 - Prob. 9ECh. 10.3 - Finding a Critical F-Value for a Right-Tailed Test...Ch. 10.3 - Finding a Critical F-Value for a Right-Tailed Test...Ch. 10.3 - Finding a Critical F-Value for a Right-Tailed Test...Ch. 10.3 - In Exercises 1318, test the claim about the...Ch. 10.3 - In Exercises 1318, test the claim about the...Ch. 10.3 - Prob. 15ECh. 10.3 - Prob. 16ECh. 10.3 - Prob. 17ECh. 10.3 - In Exercises 1318, test the claim about the...Ch. 10.3 - Performing a Two-Sample F-Test In Exercises 1926,...Ch. 10.3 - Prob. 20ECh. 10.3 - Performing a Two-Sample F-Test In Exercises 1926,...Ch. 10.3 - Performing a Two-Sample F-Test In Exercises 1926,...Ch. 10.3 - Performing a Two-Sample F-Test In Exercises 1926,...Ch. 10.3 - Prob. 24ECh. 10.3 - Prob. 25ECh. 10.3 - Performing a Two-Sample F-Test In Exercises 1926,...Ch. 10.3 - Prob. 27ECh. 10.3 - In Exercises 27 and 28, find the right- and...Ch. 10.3 - In Exercises 29 and 30, construct the confidence...Ch. 10.3 - In Exercises 29 and 30, construct the confidence...Ch. 10.4 - A sales analyst wants to determine whether there...Ch. 10.4 - Prob. 2TYCh. 10.4 - Slate the null and alternative hypotheses for a...Ch. 10.4 - What conditions are necessary in order to use a...Ch. 10.4 - Describe the difference between the variance...Ch. 10.4 - Prob. 4ECh. 10.4 - Performing a One-Way ANOVA Test In Exercises 514,...Ch. 10.4 - Performing a One-Way ANOVA Test In Exercises 514,...Ch. 10.4 - Performing a One-Way ANOVA Test In Exercises 514,...Ch. 10.4 - Prob. 8ECh. 10.4 - Prob. 9ECh. 10.4 - Performing a One-Way ANOVA Test In Exercises 514,...Ch. 10.4 - Performing a One-Way ANOVA Test In Exercises 514,...Ch. 10.4 - Prob. 12ECh. 10.4 - Performing a One-Way ANOVA Test In Exercises 514,...Ch. 10.4 - Performing a One-Way ANOVA Test In Exercises 514,...Ch. 10.4 - Prob. 15ECh. 10.4 - Prob. 16ECh. 10.4 - Prob. 17ECh. 10.4 - Prob. 18ECh. 10.4 - The Scheff Test If the null hypothesis is rejected...Ch. 10.4 - Prob. 20ECh. 10.4 - Prob. 21ECh. 10.4 - Prob. 22ECh. 10 - In Exercises 14. (a) identify the claim and state...Ch. 10 - In Exercises 14. (a) identify the claim and state...Ch. 10 - In Exercises 14, (a) identify the claim and state...Ch. 10 - Prob. 10.1.4RECh. 10 - Prob. 10.2.5RECh. 10 - In Exercises 58, (a) find the expected frequency...Ch. 10 - In Exercises 58, (a) find the expected frequency...Ch. 10 - In Exercises 58, (a) find the expected frequency...Ch. 10 - Prob. 10.3.9RECh. 10 - Prob. 10.3.10RECh. 10 - Prob. 10.3.11RECh. 10 - Prob. 10.3.12RECh. 10 - Prob. 10.3.13RECh. 10 - Prob. 10.3.14RECh. 10 - Prob. 10.3.15RECh. 10 - Prob. 10.3.16RECh. 10 - Prob. 10.3.17RECh. 10 - Prob. 10.3.18RECh. 10 - Prob. 10.3.19RECh. 10 - Prob. 10.3.20RECh. 10 - Prob. 10.4.21RECh. 10 - In Exercises 21 and 22, (a) identify the claim and...Ch. 10 - Prob. 1CQCh. 10 - Prob. 2CQCh. 10 - Take this quiz as you would take a quiz in class....Ch. 10 - Prob. 4CQCh. 10 - In each exercise, (a) identify the claim and state...Ch. 10 - Prob. 2CTCh. 10 - In each exercise, (a) identify the claim and state...Ch. 10 - Prob. 4CTCh. 10 - Prob. 5CTCh. 10 - Prob. 6CTCh. 10 - Goodness-of-Fit The table at the right shows an...Ch. 10 - Independence The contingency table below shows the...Ch. 10 - Prob. 1TCh. 10 - Prob. 2TCh. 10 - Prob. 3TCh. 10 - Teacher Salaries The Illinois State Board of...Ch. 10 - Repeat Exercises 14 using the data in the table...Ch. 10 - The table below shows the winning times (in...Ch. 10 - Prob. 2CRCh. 10 - The equation used to predict the annual sweet...Ch. 10 - Prob. 4CRCh. 10 - Prob. 5CRCh. 10 - Reviewing a Movie The contingency table shows how...Ch. 10 - Prob. 7CR
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