Elementary Statistics Plus MyLab Statistics with Pearson eText -- Title-Specific Access Card Package (13th Edition)
13th Edition
ISBN: 9780134763705
Author: Mario F. Triola
Publisher: PEARSON
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Chapter 12.2, Problem 5BSC
Pulse Rates If we use the data given in Exercise 1 with two-way analysis of variance, we get the accompanying display. What do you conclude?
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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 12 Solutions
Elementary Statistics Plus MyLab Statistics with Pearson eText -- Title-Specific Access Card Package (13th Edition)
Ch. 12.1 - In Exercises 1-4, use the following listed arrival...Ch. 12.1 - In Exercises 1-4, use the following listed arrival...Ch. 12.1 - In Exercises 1-4, use the following listed arrival...Ch. 12.1 - In Exercises 1-4, use the following listed arrival...Ch. 12.1 - In Exercises 5-16, use analysis of variance for...Ch. 12.1 - In Exercises 5-16, use analysis of variance for...Ch. 12.1 - In Exercises 5-16, use analysis of variance for...Ch. 12.1 - In Exercises 5-16, use analysis of variance for...Ch. 12.1 - In Exercises 5-16, use analysis of variance for...Ch. 12.1 - Prob. 10BSC
Ch. 12.1 - Triathlon Times Jeff Parent is a statistics...Ch. 12.1 - Arsenic in Rice Listed below are amounts of...Ch. 12.1 - Prob. 13BSCCh. 12.1 - Speed Dating Listed below are attribute ratings of...Ch. 12.1 - In Exercises 15 and 16, use the data set in...Ch. 12.1 - In Exercises 15 and 16, use the data set in...Ch. 12.1 - Tukey Test A display of the Bonferroni test...Ch. 12.2 - Two-Way ANOVA The pulse rates in Table 12-3 from...Ch. 12.2 - Two-Way ANOVA If we have a goal of using the data...Ch. 12.2 - Interaction a. What is an interaction between two...Ch. 12.2 - Balanced Design Does the table given in Exercise 1...Ch. 12.2 - Pulse Rates If we use the data given in Exercise 1...Ch. 12.2 - Weights The weights (kg) in the following table...Ch. 12.2 - Heights The heights (cm) in the following table...Ch. 12.2 - Pancake Experiment Listed below are ratings of...Ch. 12.2 - Marathon Times Listed below are New York City...Ch. 12.2 - Smoking, Gender, and Body Temperature The table...Ch. 12.2 - Transformations of Data Example 1 illustrated the...Ch. 12 - Cola Weights Data Set 26 Cola Weights and Volumes...Ch. 12 - Cola Weights For the four samples described in...Ch. 12 - Cola Weights For the analysis of variance test...Ch. 12 - Cola Weights Identify the value of the test...Ch. 12 - Cola Weights The displayed results from Exercise 1...Ch. 12 - One-Way ANOVA In general, what is one-way analysis...Ch. 12 - One vs. Two What is the fundamental difference...Ch. 12 - Estimating Length Given below is a Minitab display...Ch. 12 - Estimating Length Using the same results displayed...Ch. 12 - Estimating Length Using the same results displayed...Ch. 12 - Speed Dating Data Set 18 Speed Dating in Appendix...Ch. 12 - Author Readability Pages were randomly selected by...Ch. 12 - Prob. 3RECh. 12 - Speed Dating Listed below are attribute ratings of...Ch. 12 - In Exercises 1-5, refer to the following list of...Ch. 12 - In Exercises 1-5, refer to the following list of...Ch. 12 - In Exercises 1-5, refer to the following list of...Ch. 12 - In Exercises 15, refer to the following list of...Ch. 12 - In Exercises 15, refer to the following list of...Ch. 12 - Quarters Assume that weights of quarters minted...Ch. 12 - Job Priority Survey USA Today reported on an...Ch. 12 - Win 4 Lottery Shown below is a histogram of digits...Ch. 12 - Does Weight Change with Age? Refer to Data Set 1...
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