Intro Stats
4th Edition
ISBN: 9780321826275
Author: Richard D. De Veaux
Publisher: PEARSON
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Chapter 7, Problem 52E
Online clothes II For the online clothing retailer discussed in the previous problem, the
The
| SD | ||
| Income | $50,343.40 | $16,952.50 |
| Total Yearly Purchase | $572.52 | $253.62 |
a) What is the linear regression equation for predicting Total Yearly Purchase from Income?
b) Do the assumptions and conditions for regression appear to be met?
c) What is the predicted Total Yearly Purchase for someone with a yearly Income of $20,000? For someone with an annual Income of $80,000?
d) What percent of the variability in Total Yearly Purchases is accounted for by this model?
e) Do you think the regression might be a useful one for the company? Comment.
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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 7 Solutions
Intro Stats
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Ch. 7 - True or false II If false, explain briefly. a)...Ch. 7 - Prob. 3ECh. 7 - Prob. 4ECh. 7 - Bookstore sales revisited Recall the data we saw...Ch. 7 - Prob. 6ECh. 7 - Prob. 7ECh. 7 - Prob. 8ECh. 7 - Bookstore sales once more Here are the residuals...Ch. 7 - Prob. 10ECh. 7 - Prob. 11ECh. 7 - Prob. 12ECh. 7 - Prob. 13ECh. 7 - 14. Disk drives last time Here is a scatterplot of...Ch. 7 - Prob. 15ECh. 7 - Prob. 16ECh. 7 - More cereal Exercise 15 describes a regression...Ch. 7 - Prob. 18ECh. 7 - Another bowl In Exercise 15, the regression model...Ch. 7 - Prob. 20ECh. 7 - Cereal again The correlation between a cereals...Ch. 7 - Prob. 22ECh. 7 - Prob. 23ECh. 7 - Prob. 24ECh. 7 - Prob. 25ECh. 7 - Prob. 26ECh. 7 - Prob. 27ECh. 7 - Residuals Tell what each of the residual plots...Ch. 7 - Real estate A random sample of records of home...Ch. 7 - 30. Roller coaster The Mitch Hawker poll ranked...Ch. 7 - Prob. 31ECh. 7 - Prob. 32ECh. 7 - Real estate again The regression of Price on Size...Ch. 7 - Prob. 34ECh. 7 - Prob. 35ECh. 7 - More misinterpretations A Sociology student...Ch. 7 - Real estate redux The regression of Price on Size...Ch. 7 - 38. Another ride The regression of Duration of a...Ch. 7 - Prob. 39ECh. 7 - Prob. 40ECh. 7 - Prob. 41ECh. 7 - Prob. 42ECh. 7 - Prob. 43ECh. 7 - Prob. 44ECh. 7 - Prob. 45ECh. 7 - 46. Second inning 2010 Consider again the...Ch. 7 - Prob. 47ECh. 7 - Prob. 48ECh. 7 - Prob. 49ECh. 7 - Prob. 50ECh. 7 - Online clothes An online clothing retailer keeps...Ch. 7 - Online clothes II For the online clothing retailer...Ch. 7 - Prob. 53ECh. 7 - Success in college Colleges use SAT scores in the...Ch. 7 - SAT, take 2 Suppose we wanted to use SAT math...Ch. 7 - Prob. 56ECh. 7 - Prob. 57ECh. 7 - Prob. 58ECh. 7 - Prob. 59ECh. 7 - Drug abuse revisited Chapter 6, Exercise 42...Ch. 7 - Prob. 61ECh. 7 - Prob. 62ECh. 7 - Prob. 63ECh. 7 - 64. Chicken Chicken sandwiches are often...Ch. 7 - Prob. 65ECh. 7 - Prob. 66ECh. 7 - Prob. 67ECh. 7 - Prob. 68ECh. 7 - Prob. 69ECh. 7 - 70. Birthrates 2009 The table shows the number of...Ch. 7 - Prob. 71ECh. 7 - Prob. 72ECh. 7 - Prob. 73ECh. 7 - Prob. 74ECh. 7 - Hard water In an investigation of environmental...Ch. 7 - 76. Gators Wildlife researchers monitor many...Ch. 7 - Prob. 77ECh. 7 - Least squares Consider the four points (200,1950),...
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