Introduction to Business Statistics
7th Edition
ISBN: 9781111792374
Author: WEIERS
Publisher: Cengage Learning
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Chapter 7.3, Problem 7.18E
A Continuous random variable, x, is
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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 7 Solutions
Introduction to Business Statistics
Ch. 7.1 - What is the difference between a continuous...Ch. 7.1 - What is a probability density function and how is...Ch. 7.1 - Why is the total area beneath a probability...Ch. 7.1 - Prob. 7.4ECh. 7.2 - It has been stated that the nomal distribution is...Ch. 7.2 - Prob. 7.6ECh. 7.2 - Prob. 7.7ECh. 7.2 - Prob. 7.8ECh. 7.2 - Prob. 7.9ECh. 7.2 - The Canada Urban Transit Association has reported...
Ch. 7.2 - Prob. 7.11ECh. 7.2 - In 2009, the average charge for tax preparation by...Ch. 7.2 - It has been reported that the average hotel...Ch. 7.2 - The average American family of four spends $5000...Ch. 7.2 - Prob. 7.15ECh. 7.3 - The normal distribution is really a family of...Ch. 7.3 - In the standard normal distribution, approximately...Ch. 7.3 - A Continuous random variable, x, is normally...Ch. 7.3 - Prob. 7.19ECh. 7.3 - Prob. 7.20ECh. 7.3 - Prob. 7.21ECh. 7.3 - Prob. 7.22ECh. 7.3 - Prob. 7.23ECh. 7.3 - Prob. 7.24ECh. 7.3 - Prob. 7.25ECh. 7.3 - Prob. 7.26ECh. 7.3 - For the normal distribution described in Exercise...Ch. 7.3 - Prob. 7.28ECh. 7.3 - For the normal distribution described in Exercise...Ch. 7.3 - For the normal distribution described in Exercise...Ch. 7.3 - For the normal distribution described in Exercise...Ch. 7.3 - Prob. 7.32ECh. 7.3 - It has been reported that households in the West...Ch. 7.3 - Andre is a fearless circus performer who gets shot...Ch. 7.3 - Drying times for newly painted microwave oven...Ch. 7.3 - KleerCo supplies an under-hood, emissionscontrol...Ch. 7.3 - Prob. 7.37ECh. 7.3 - Prob. 7.38ECh. 7.4 - What is the correction for continuity and why is...Ch. 7.4 - Under what circumstances is it permissible to use...Ch. 7.4 - In a certain binomial distribution, =0.25 and n=40...Ch. 7.4 - In a certain binomial distribution, =0.30 and n=20...Ch. 7.4 - Prob. 7.43ECh. 7.4 - Prob. 7.44ECh. 7.4 - Prob. 7.45ECh. 7.4 - Prob. 7.46ECh. 7.4 - Prob. 7.47ECh. 7.4 - Repeat Exercise 7.46, but without using the...Ch. 7.5 - What is the relationship between the Poisson...Ch. 7.5 - Every day, drivers arrive at a tollbooth. If the...Ch. 7.5 - The main switchboard at the Home Shopping Network...Ch. 7.5 - A random variable is Poision distributed with =1.5...Ch. 7.5 - A random variable is Poision distributed with...Ch. 7.5 - A random variable is Poision distributed with...Ch. 7.5 - The owner of a self-service carwash has found that...Ch. 7.5 - A taxi dispatcher has found that successive calls...Ch. 7.5 - During 2008, U.S. general aviation pilots had 1.20...Ch. 7.5 - The Bureau of Labor Statistics reports the...Ch. 7.6 - A computer statistical package has simulated 1000...Ch. 7.6 - Prob. 7.60ECh. 7.6 - Prob. 7.61ECh. 7.6 - Prob. 7.62ECh. 7 - According to a recent survey, 35% of the adult...Ch. 7 - Prob. 7.64CECh. 7 - Prob. 7.65CECh. 7 - During an annual heating season, the average gas...Ch. 7 - It has been reported that the average monthly cell...Ch. 7 - During 2004, the average number of flying hours...Ch. 7 - During fiscal 2008, the average daily volume for...Ch. 7 - For itemized tax returns in the $60,000—$75,000...Ch. 7 - Of the 1.0 million persons of voting age in Maine,...Ch. 7 - A public relations agency tells its client that...Ch. 7 - Given the results of Exercise 7.72, evaluate the...Ch. 7 - A researcher is studying a particular process and...Ch. 7 - A safety researcher has found that fourth to sixth...Ch. 7 - The number of defects in rolls of aluminum sheet...Ch. 7 - The mileage death rate for motorcycle riders has...Ch. 7 - The “20-ounce” package of mozzarella cheese...Ch. 7 - State Police Academy graduates from a large gradua...Ch. 7 - The trainer for a professional football team has...Ch. 7 - The precooked weight of hamburgers at a gourmet...Ch. 7 - Boxes are filled with sugar by a machine that is...Ch. 7 - In Exercise 7.82, the company would like to put in...Ch. 7 - Discount Micros, a computer mail-order company,...Ch. 7 - The U-Drive car rental corporation has found that...Ch. 7 - Ronnie Rogers, the customer relations manager for...Ch. 7 - A storage warehouse in a relatively remote part of...
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