Basic Business Statistics, Student Value Edition
14th Edition
ISBN: 9780134685113
Author: Mark L. Berenson, David M. Levine, David F. Stephan, Kathryn Szabat
Publisher: PEARSON
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Chapter 13, Problem 40PS
a.
To determine
Find the value of the
b.
To determine
Find the critical values at the
c.
To determine
Find the statistical decision that should be made on the basis of above results.
d.
To determine
Construct a
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Problem 3. Pricing a multi-stock option the Margrabe formula
The purpose of this problem is to price a swap option in a 2-stock model, similarly as
what we did in the example in the lectures. We consider a two-dimensional Brownian
motion given by W₁ = (W(¹), W(2)) on a probability space (Q, F,P). Two stock prices
are modeled by the following equations:
dX
=
dY₁ =
X₁ (rdt+
rdt+0₁dW!)
(²)),
Y₁ (rdt+dW+0zdW!"),
with Xo
xo and Yo =yo. This corresponds to the multi-stock model studied in class,
but with notation (X+, Y₁) instead of (S(1), S(2)). Given the model above, the measure
P is already the risk-neutral measure (Both stocks have rate of return r). We write
σ = 0₁+0%. We consider a swap option, which gives you the right, at time T, to
exchange one share of X for one share of Y. That is, the option has payoff
F=(Yr-XT).
(a) We first assume that r = 0 (for questions (a)-(f)). Write an explicit expression for
the process Xt.
Reminder before proceeding to question (b): Girsanov's theorem…
Problem 1. Multi-stock model
We consider a 2-stock model similar to the one studied in class. Namely, we consider
=
S(1)
S(2)
=
S(¹) exp (σ1B(1) + (M1 - 0/1 )
S(²) exp (02B(2) + (H₂-
M2
where (B(¹) ) +20 and (B(2) ) +≥o are two Brownian motions, with
t≥0
Cov (B(¹), B(2)) = p min{t, s}.
"
The purpose of this problem is to prove that there indeed exists a 2-dimensional Brownian
motion (W+)+20 (W(1), W(2))+20 such that
=
S(1)
S(2)
=
=
S(¹) exp (011W(¹) + (μ₁ - 01/1) t)
롱)
S(²) exp (021W (1) + 022W(2) + (112 - 03/01/12) t).
where σ11, 21, 22 are constants to be determined (as functions of σ1, σ2, p).
Hint: The constants will follow the formulas developed in the lectures.
(a) To show existence of (Ŵ+), first write the expression for both W. (¹) and W (2)
functions of (B(1), B(²)).
as
(b) Using the formulas obtained in (a), show that the process (WA) is actually a 2-
dimensional standard Brownian motion (i.e. show that each component is normal,
with mean 0, variance t, and that their…
The scores of 8 students on the midterm exam and final exam were as follows.
Student
Midterm
Final
Anderson
98
89
Bailey
88
74
Cruz
87
97
DeSana
85
79
Erickson
85
94
Francis
83
71
Gray
74
98
Harris
70
91
Find the value of the (Spearman's) rank correlation coefficient test statistic that would be used to test the claim of no correlation between midterm score and final exam score. Round your answer to 3 places after the decimal point, if necessary.
Test statistic: rs =
Chapter 13 Solutions
Basic Business Statistics, Student Value Edition
Ch. 13 - Prob. 1PSCh. 13 - If the values of X in Problem 13.1 from 2 to 25,...Ch. 13 - Fitting a straight line to a set data yields the...Ch. 13 - The production of wine is a multibillion-dollar...Ch. 13 - Zagat’s publisher restaurant rating for various...Ch. 13 - Is an MBA a golden ticket? Pursuing an MBA is a...Ch. 13 - Starbucks Coffee Co. uses a data-based approach to...Ch. 13 - The value of a sports franchise is directly...Ch. 13 - An agent for a residential real estate company in...Ch. 13 - A box office analyst seeks to predict opening...
Ch. 13 - How do you interpret a coefficient by of...Ch. 13 - If SSR= 36 and SSE=4, determine SST and then...Ch. 13 - If SSR=66 and SST=88, Compute the coefficient of...Ch. 13 - If SSE= 10 and SSR=30, compute the coefficient of...Ch. 13 - If SSR=120, Why is it impossible for SST to equal...Ch. 13 - In problem 13.4 on page 493, the percentage of...Ch. 13 - In problem 13.5 on page 493, you used the summated...Ch. 13 - In Problem 13.6 on page 494, a prospective MBA...Ch. 13 - In Problem 13.7 on page 494, you used the plate...Ch. 13 - In problem 13.8 on page 494, you used annual...Ch. 13 - In problem 13.9 on page 494, an agent for a real...Ch. 13 - In problem 13.10 on page 494, you used You tube...Ch. 13 - The following results provide the X Values,...Ch. 13 - The following results show the X Values,...Ch. 13 - In problem 13.5 on page 493, you used the summated...Ch. 13 - In problem 13.4 on page 493, you used the...Ch. 13 - In problem 13.7 on page 494, you used the plate...Ch. 13 - In problem 13.6 on page 494, a prospective MBA...Ch. 13 - In problem 13.9 on page 494, an agent for a real...Ch. 13 - Prob. 30PSCh. 13 - Prob. 31PSCh. 13 - The residuals for 10 consecutive time periods are...Ch. 13 - The residuals for 15 consecutive time periods are...Ch. 13 - In Problem 13.7 on page 494 concerning the...Ch. 13 - What is the relationship between the price of...Ch. 13 - Prob. 36PSCh. 13 - A freshly brewed shot of espresso has three...Ch. 13 - The owners of a chain of ice cream stores have the...Ch. 13 - You are testing the null hypothesis that there is...Ch. 13 - Prob. 40PSCh. 13 - Prob. 41PSCh. 13 - In problem 13.4 on page 493, you used the...Ch. 13 - Prob. 43PSCh. 13 - In problem 13.6 on page 494, a prospective MBA...Ch. 13 - In Problem 13.7 on page 494, you used the plate...Ch. 13 - Prob. 46PSCh. 13 - In Problem 13.9 on page 494, an agent for a real...Ch. 13 - In Problem 13.10 on page 494, you used you used...Ch. 13 - The volatility of a stock is often measured by its...Ch. 13 - Prob. 50PSCh. 13 - Prob. 51PSCh. 13 - Movie companies need to predict the gross receipts...Ch. 13 - Prob. 53PSCh. 13 - Prob. 54PSCh. 13 - Prob. 55PSCh. 13 - Based on a sample of n=20, the latest-squares...Ch. 13 - Prob. 57PSCh. 13 - In Problem 13.4 on page 493, you used the...Ch. 13 - In Problem 13.7 on page 494, you used the plate...Ch. 13 - In Problem 13.6 on page 494, a prospective MBA...Ch. 13 - Prob. 61PSCh. 13 - Prob. 62PSCh. 13 - In problem 13.10 on page 494, you used YouTube...Ch. 13 - Prob. 64PSCh. 13 - Prob. 65PSCh. 13 - When is the unexplained variation (i.e., error sum...Ch. 13 - Prob. 67PSCh. 13 - Prob. 68PSCh. 13 - Prob. 69PSCh. 13 - How do you evaluate the assumptions of regression...Ch. 13 - When and how do you use the Durbin-Watson...Ch. 13 - Prob. 72PSCh. 13 - Can you use movie critics’ opinions to forecast...Ch. 13 - Management of a soft-drink botting company has the...Ch. 13 - Measuring the height of a California redwood tree...Ch. 13 - You want to develop a model to predict the asking...Ch. 13 - You want to develop a model to predict the taxes...Ch. 13 - An analyst has the objective of predicting the...Ch. 13 - An accountant for a large department store has the...Ch. 13 - On January 28, 1986, the space shuttle Challenger...Ch. 13 - A baseball analyst would like to study various...Ch. 13 - Can you use the annual revenues generated by...Ch. 13 - In Problem 13.82 you used annual revenue to...Ch. 13 - During the fall harvest season in the United...Ch. 13 - Refer to the discussion of beta values and market...Ch. 13 - The file CEO 2016 includes the total compensation...Ch. 13 - In Problem 13.8, 13.20, 13.30, 13.46, 13.62,...
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- Business discussarrow_forwardBusiness discussarrow_forwardI just need to know why this is wrong below: What is the test statistic W? W=5 (incorrect) and What is the p-value of this test? (p-value < 0.001-- incorrect) Use the Wilcoxon signed rank test to test the hypothesis that the median number of pages in the statistics books in the library from which the sample was taken is 400. A sample of 12 statistics books have the following numbers of pages pages 127 217 486 132 397 297 396 327 292 256 358 272 What is the sum of the negative ranks (W-)? 75 What is the sum of the positive ranks (W+)? 5What type of test is this? two tailedWhat is the test statistic W? 5 These are the critical values for a 1-tailed Wilcoxon Signed Rank test for n=12 Alpha Level 0.001 0.005 0.01 0.025 0.05 0.1 0.2 Critical Value 75 70 68 64 60 56 50 What is the p-value for this test? p-value < 0.001arrow_forward
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