Elementary Statistics 2nd Edition
2nd Edition
ISBN: 9781259724275
Author: William Navidi, Barry Monk
Publisher: McGraw-Hill Education
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Chapter 10.1, Problem 29E
a.
To determine
To find: The value of
b.
To determine
To find: The degrees of freedom.
c.
To determine
To find: The appropriate word to complete the statement.
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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 10 Solutions
Elementary Statistics 2nd Edition
Ch. 10.1 - In Exercises 5 and 6, fill in each blank with e...Ch. 10.1 - In Exercises 5 and 6, fill in each blank with e...Ch. 10.1 - Prob. 7ECh. 10.1 - Prob. 8ECh. 10.1 - In Exercises 9-14, construct the confidence...Ch. 10.1 - Prob. 10ECh. 10.1 - In Exercises 9-14, construct the confidence...Ch. 10.1 - Prob. 12ECh. 10.1 - Prob. 13ECh. 10.1 - Prob. 14E
Ch. 10.1 - Does this diet help? A group of 78 people enrolled...Ch. 10.1 - Contaminated water: The concentration of benzene...Ch. 10.1 - Fertilizer: In an agricultural experiment, the...Ch. 10.1 - Computer crashes: A computer system administrator...Ch. 10.1 - Are you smarter than your older brother? In a...Ch. 10.1 - Effectiveness of distance learning: A study was...Ch. 10.1 - Boys and girls: The National Health Statistics...Ch. 10.1 - Body mass index: In a survey of adults with...Ch. 10.1 - Energy drinks: A survey of college students...Ch. 10.1 - Low-fat or low-carb? Are low-fat diets or low-carb...Ch. 10.1 - Online testing: Do you prefer taking tests on...Ch. 10.1 - Drive safely: How often does the average driver...Ch. 10.1 - Interpret calculator display: The following TI-84...Ch. 10.1 - Prob. 28ECh. 10.1 - Prob. 29ECh. 10.1 - Prob. 30ECh. 10.1 - Prob. 31ECh. 10.2 - In Exercises 3 and 4, fill in each blank with the...Ch. 10.2 - Prob. 4ECh. 10.2 - Prob. 5ECh. 10.2 - Prob. 6ECh. 10.2 - In Exercises 7-12, construct the confidence...Ch. 10.2 - In Exercises 7-12, construct the confidence...Ch. 10.2 - In Exercises 7-12, construct the confidence...Ch. 10.2 - In Exercises 7-12, construct the confidence...Ch. 10.2 - In Exercises 7-12, construct the confidence...Ch. 10.2 - Prob. 12ECh. 10.2 - Traffic accidents: Traffic engineers compared...Ch. 10.2 - Computers in the classroom: In a new experimental...Ch. 10.2 - Pain after surgery: In a random sample of 50...Ch. 10.2 - Pretzels: In order to judge the effectiveness of...Ch. 10.2 - Defective electronics: A team of designers was...Ch. 10.2 - Prob. 18ECh. 10.2 - Cancer prevention: Colonoscopy is a medical...Ch. 10.2 - Social media: A Pew poll found that in a sample of...Ch. 10.2 - Interpret calculator display: The following TI-84...Ch. 10.2 - Prob. 22ECh. 10.2 - Prob. 23ECh. 10.2 - Prob. 24ECh. 10.2 - Finding the sample size: Polls are to be conducted...Ch. 10.3 - In Exercises 3 and 4, fill in each blank with the...Ch. 10.3 - Prob. 4ECh. 10.3 - Prob. 5ECh. 10.3 - In Exercises 5 and 6, determine whether the...Ch. 10.3 - Fast computer: microprocessors are compared on a...Ch. 10.3 - Brake wear: For a sample of 9 automobiles, the...Ch. 10.3 - Strength of concrete: The compressive strength, m...Ch. 10.3 - Truck pollution: In an experiment to determine the...Ch. 10.3 - High cholesterol: A group of eight individuals...Ch. 10.3 - Tires and fuel economy: A tire manufacturer is...Ch. 10.3 - Prob. 13ECh. 10.3 - Prob. 14ECh. 10.3 - Interpret calculator display: The following TI-84...Ch. 10.3 - Interpret calculator display: The following TI-84...Ch. 10.3 - Prob. 17ECh. 10.3 - Prob. 18ECh. 10.3 - Advantage of matched pairs: Refer to Exercise 12....Ch. 10.3 - Paired or independent? To construct a confidence...Ch. 10 - In Exercises 1 and 2, determine whether the...Ch. 10 - Prob. 2CQCh. 10 - Prob. 3CQCh. 10 - Prob. 4CQCh. 10 - Prob. 5CQCh. 10 - Prob. 6CQCh. 10 - Prob. 7CQCh. 10 - Prob. 8CQCh. 10 - Prob. 9CQCh. 10 - Prob. 10CQCh. 10 - Prob. 11CQCh. 10 - Refer to Exercise 11. Find the critical value for...Ch. 10 - Prob. 13CQCh. 10 - Prob. 14CQCh. 10 - Prob. 15CQCh. 10 - Prob. 1RECh. 10 - Prob. 2RECh. 10 - Prob. 3RECh. 10 - Prob. 4RECh. 10 - Prob. 5RECh. 10 - Prob. 6RECh. 10 - Prob. 7RECh. 10 - Prob. 8RECh. 10 - Prob. 9RECh. 10 - Prob. 10RECh. 10 - Prob. 11RECh. 10 - Prob. 12RECh. 10 - Prob. 13RECh. 10 - Prob. 14RECh. 10 - Prob. 15RECh. 10 - Prob. 1WAICh. 10 - Prob. 2WAICh. 10 - Prob. 3WAICh. 10 - Prob. 4WAICh. 10 - Prob. 1CSCh. 10 - Prob. 2CSCh. 10 - Prob. 3CS
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