EBK ELEMENTARY STATISTICS USING EXCEL
7th Edition
ISBN: 9780136937401
Author: Triola
Publisher: VST
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Chapter 6.2, Problem 4BSC
To determine
To find: The shape of the numbers obtained in the lottery.
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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 6 Solutions
EBK ELEMENTARY STATISTICS USING EXCEL
Ch. 6.1 - 1. Normal Distribution What’s wrong with the...Ch. 6.1 - Prob. 2BSCCh. 6.1 - Prob. 3BSCCh. 6.1 - Prob. 4BSCCh. 6.1 - Continuous Uniform Distribution. In Exercises 5–8,...Ch. 6.1 - Continuous Uniform Distribution. In Exercises 5–8,...Ch. 6.1 - Prob. 7BSCCh. 6.1 - Prob. 8BSCCh. 6.1 - Standard Normal Distribution. In Exercises 9–12,...Ch. 6.1 - Standard Normal Distribution. In Exercises 9–12,...
Ch. 6.1 - Standard Normal Distribution. In Exercises 9–12,...Ch. 6.1 - Standard Normal Distribution. In Exercises 9–12,...Ch. 6.1 - Standard Normal Distribution. In Exercises 13–16,...Ch. 6.1 - Standard Normal Distribution. In Exercises 13–16,...Ch. 6.1 - Standard Normal Distribution. In Exercises 13–16,...Ch. 6.1 - Standard Normal Distribution. In Exercises 13–16,...Ch. 6.1 - Prob. 17BSCCh. 6.1 - Prob. 18BSCCh. 6.1 - Prob. 19BSCCh. 6.1 - Prob. 20BSCCh. 6.1 - Prob. 21BSCCh. 6.1 - Prob. 22BSCCh. 6.1 - Prob. 23BSCCh. 6.1 - Prob. 24BSCCh. 6.1 - Prob. 25BSCCh. 6.1 - Prob. 26BSCCh. 6.1 - Prob. 27BSCCh. 6.1 - Prob. 28BSCCh. 6.1 - Prob. 29BSCCh. 6.1 - Prob. 30BSCCh. 6.1 - Prob. 31BSCCh. 6.1 - Prob. 32BSCCh. 6.1 - Prob. 33BSCCh. 6.1 - Prob. 34BSCCh. 6.1 - Prob. 35BSCCh. 6.1 - Prob. 36BSCCh. 6.1 - Finding Bone Density Scores. In Exercises 37–40...Ch. 6.1 - Prob. 38BSCCh. 6.1 - Prob. 39BSCCh. 6.1 - Prob. 40BSCCh. 6.1 - Prob. 41BSCCh. 6.1 - Prob. 42BSCCh. 6.1 - Prob. 43BSCCh. 6.1 - Prob. 44BSCCh. 6.1 - Prob. 45BSCCh. 6.1 - Prob. 46BSCCh. 6.1 - Prob. 47BSCCh. 6.1 - Prob. 48BSCCh. 6.1 - Prob. 49BBCh. 6.1 - Prob. 50BBCh. 6.2 - Prob. 1BSCCh. 6.2 - Prob. 2BSCCh. 6.2 - Prob. 3BSCCh. 6.2 - Prob. 4BSCCh. 6.2 - IQ Scores. In Exercises 5–8, find the area of the...Ch. 6.2 - IQ Scores. In Exercises 5–8, find the area of the...Ch. 6.2 - Prob. 7BSCCh. 6.2 - IQ Scores. In Exercises 5–8, find the area of the...Ch. 6.2 - IQ Scores. In Exercises 9–12, find the indicated...Ch. 6.2 - IQ Scores. In Exercises 9–12, find the indicated...Ch. 6.2 - Prob. 11BSCCh. 6.2 - Prob. 12BSCCh. 6.2 - Prob. 13BSCCh. 6.2 - Prob. 14BSCCh. 6.2 - Prob. 15BSCCh. 6.2 - Prob. 16BSCCh. 6.2 - Prob. 17BSCCh. 6.2 - Prob. 18BSCCh. 6.2 - Prob. 19BSCCh. 6.2 - Prob. 20BSCCh. 6.2 - Prob. 21BSCCh. 6.2 - Prob. 22BSCCh. 6.2 - Prob. 23BSCCh. 6.2 - Prob. 24BSCCh. 6.2 - Prob. 25BSCCh. 6.2 - In Exercises 21–24, use these parameters (based on...Ch. 6.2 - In Exercises 21–24, use these parameters (based on...Ch. 6.2 - Prob. 28BSCCh. 6.2 - Prob. 29BSCCh. 6.2 - Prob. 30BSCCh. 6.2 - Prob. 31BSCCh. 6.2 - Prob. 32BSCCh. 6.2 - Prob. 33BSCCh. 6.2 - Prob. 34BSCCh. 6.2 - Prob. 35BSCCh. 6.2 - Prob. 36BSCCh. 6.2 - Prob. 37BBCh. 6.2 - Prob. 38BBCh. 6.3 - Prob. 1BSCCh. 6.3 - Prob. 2BSCCh. 6.3 - Prob. 3BSCCh. 6.3 - Prob. 4BSCCh. 6.3 - Prob. 5BSCCh. 6.3 - Prob. 6BSCCh. 6.3 - Prob. 7BSCCh. 6.3 - Prob. 8BSCCh. 6.3 - Prob. 9BSCCh. 6.3 - In Exercises 7–10, use the same population of {4,...Ch. 6.3 - Prob. 11BSCCh. 6.3 - Prob. 12BSCCh. 6.3 - Prob. 13BSCCh. 6.3 - Prob. 14BSCCh. 6.3 - Prob. 15BSCCh. 6.3 - Prob. 16BSCCh. 6.3 - Prob. 17BSCCh. 6.3 - Prob. 18BSCCh. 6.3 - Prob. 19BBCh. 6.3 - Prob. 20BBCh. 6.4 - Prob. 1BSCCh. 6.4 - Prob. 2BSCCh. 6.4 - Prob. 3BSCCh. 6.4 - Prob. 4BSCCh. 6.4 - Prob. 5BSCCh. 6.4 - Prob. 6BSCCh. 6.4 - Prob. 7BSCCh. 6.4 - Prob. 8BSCCh. 6.4 - Prob. 9BSCCh. 6.4 - Prob. 10BSCCh. 6.4 - Prob. 11BSCCh. 6.4 - Prob. 12BSCCh. 6.4 - Prob. 13BSCCh. 6.4 - Prob. 14BSCCh. 6.4 - Prob. 15BSCCh. 6.4 - Prob. 16BSCCh. 6.4 - Prob. 17BSCCh. 6.4 - Prob. 18BSCCh. 6.4 - Prob. 19BSCCh. 6.4 - Prob. 20BBCh. 6.5 - Prob. 1BSCCh. 6.5 - Prob. 2BSCCh. 6.5 - Prob. 3BSCCh. 6.5 - Prob. 4BSCCh. 6.5 - Prob. 5BSCCh. 6.5 - Prob. 6BSCCh. 6.5 - Prob. 7BSCCh. 6.5 - Prob. 8BSCCh. 6.5 - Prob. 9BSCCh. 6.5 - Prob. 10BSCCh. 6.5 - Prob. 11BSCCh. 6.5 - Prob. 12BSCCh. 6.5 - Prob. 13BSCCh. 6.5 - Prob. 14BSCCh. 6.5 - Prob. 15BSCCh. 6.5 - Prob. 16BSCCh. 6.5 - Prob. 17BSCCh. 6.5 - Prob. 18BSCCh. 6.5 - Prob. 19BSCCh. 6.5 - Prob. 20BSCCh. 6.5 - Prob. 21BBCh. 6.5 - Prob. 22BBCh. 6 - Prob. 1CQQCh. 6 - Prob. 2CQQCh. 6 - Prob. 3CQQCh. 6 - Prob. 4CQQCh. 6 - Prob. 5CQQCh. 6 - Prob. 6CQQCh. 6 - Prob. 7CQQCh. 6 - Prob. 8CQQCh. 6 - Prob. 9CQQCh. 6 - Prob. 10CQQCh. 6 - Prob. 1RECh. 6 - Prob. 2RECh. 6 - Prob. 3RECh. 6 - Prob. 4RECh. 6 - Prob. 5RECh. 6 - Prob. 6RECh. 6 - Prob. 7RECh. 6 - Prob. 8RECh. 6 - Prob. 9RECh. 6 - Prob. 10RECh. 6 - Prob. 1CRECh. 6 - Prob. 2CRECh. 6 - Prob. 3CRECh. 6 - Prob. 4CRECh. 6 - Prob. 5CRECh. 6 - Prob. 1FDD
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