Business Analytics
3rd Edition
ISBN: 9780135231678
Author: Evans, James R. (james Robert)
Publisher: PEARSON EDUCATION (COLLEGE)
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Chapter 4, Problem 1.26PE
Compute the
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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 4 Solutions
Business Analytics
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Ch. 4 - Prob. 3.1CYUCh. 4 - Prob. 3.2CYUCh. 4 - Prob. 3.3CYUCh. 4 - What is a cross-tabulation?Ch. 4 - Prob. 4.2CYUCh. 4 - Explain the difference between a population and a...Ch. 4 - List and explain the common measures of location...Ch. 4 - Prob. 5.3CYUCh. 4 - Prob. 5.4CYUCh. 4 - Prob. 5.5CYUCh. 4 - Prob. 5.6CYUCh. 4 - Prob. 5.7CYUCh. 4 - Prob. 5.8CYUCh. 4 - Prob. 6.1CYUCh. 4 - Use Excel to find the mean and variance for the...Ch. 4 - Prob. 7.1CYUCh. 4 - Prob. 7.2CYUCh. 4 - Prob. 8.1CYUCh. 4 - Prob. 8.2CYUCh. 4 - Prob. 9.1CYUCh. 4 - Prob. 9.2CYUCh. 4 - Prob. 9.3CYUCh. 4 - What rules are typically used to identify...Ch. 4 - Prob. 10.2CYUCh. 4 - Summarize statistical tools that are typically...Ch. 4 - Prob. 11.2CYUCh. 4 - What are the principles of statistical thinking?Ch. 4 - Prob. 12.2CYUCh. 4 - Prob. 12.3CYUCh. 4 - A survey handed out to individuals at a major...Ch. 4 - Prob. 1.2PECh. 4 - Identify each of the variables in the Excel file...Ch. 4 - Prob. 1.4PECh. 4 - Prob. 1.5PECh. 4 - Prob. 1.6PECh. 4 - Prob. 1.7PECh. 4 - Prob. 1.8PECh. 4 - Prob. 1.9PECh. 4 - Prob. 1.10PECh. 4 - Prob. 1.11PECh. 4 - Prob. 1.12PECh. 4 - Use a PivotTable to construct a frequency...Ch. 4 - Prob. 1.14PECh. 4 - Prob. 1.15PECh. 4 - Prob. 1.16PECh. 4 - Prob. 1.17PECh. 4 - Prob. 1.18PECh. 4 - Prob. 1.19PECh. 4 - Prob. 1.20PECh. 4 - Use a PivotTable to construct a cross-tabulation...Ch. 4 - Use PivotTables to construct cross-tabulations for...Ch. 4 - Prob. 1.23PECh. 4 - Prob. 1.24PECh. 4 - Prob. 1.25PECh. 4 - Compute the mean, median, midrange, and mode for...Ch. 4 - Considering the data in the Excel file Home Market...Ch. 4 - Considering the data in the Excel file Home Market...Ch. 4 - In the Excel file Facebook Survey, find the range,...Ch. 4 - Prob. 1.30PECh. 4 - For the Excel file Tablet Computer Sales, find the...Ch. 4 - The Excel file Atlanta Airline Data provides...Ch. 4 - Prob. 1.33PECh. 4 - Prob. 1.34PECh. 4 - Apply the Descriptive Statistics tool for subsets...Ch. 4 - Use the Descriptive Statistics tool to summarize...Ch. 4 - Prob. 1.38PECh. 4 - The Data worksheet in the Excel file Airport...Ch. 4 - Prob. 1.40PECh. 4 - Prob. 1.41PECh. 4 - Prob. 1.42PECh. 4 - Prob. 1.43PECh. 4 - Prob. 1.44PECh. 4 - Prob. 1.45PECh. 4 - Prob. 1.46PECh. 4 - Prob. 1.47PECh. 4 - Prob. 1.48PECh. 4 - Prob. 1.49PECh. 4 - Prob. 1.50PECh. 4 - Prob. 1.51PECh. 4 - Prob. 1.52PECh. 4 - Prob. 1.53PECh. 4 - In the Excel file Debt and Retirement Savings, use...Ch. 4 - Prob. 1.55PECh. 4 - Prob. 1.56PECh. 4 - Prob. 1.57PECh. 4 - Prob. 1.58PECh. 4 - Prob. 1.59PECh. 4 - In the Excel file Weddings, determine the...Ch. 4 - Prob. 1.61PECh. 4 - The Excel file Beverage Sales lists a sample of...Ch. 4 - For the Presidents Inn Guest Database, find the...Ch. 4 - Prob. 1.64PECh. 4 - For the Excel file Credit Risk Data, compute the...Ch. 4 - Compute the z-scores for the data in the Excel...Ch. 4 - Prob. 1.67PECh. 4 - In the Excel file Weddings, find the mean, median,...Ch. 4 - Use the following approaches to analyze the survey...Ch. 4 - Prob. 1.70PECh. 4 - A producer of computer-aided design software for...Ch. 4 - Prob. 1.72PECh. 4 - Prob. 1.73PECh. 4 - A Midwest pharmaceutical company manufactures...Ch. 4 - Find the mean and variance of a deck of 52 cards,...Ch. 4 - Elizabeth Burke has received several questions...
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