Basic Business Statistics, Student Value Edition
14th Edition
ISBN: 9780134685113
Author: Mark L. Berenson, David M. Levine, David F. Stephan, Kathryn Szabat
Publisher: PEARSON
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Chapter 6, Problem 26PS
a.
To determine
Determine the
b.
To determine
Determine the probability that the downloading time will be more than 36 minutes.
c.
To determine
Determine the probability that the downloading time will be between 30 minutes and 40 minutes.
d.
To determine
Determine the
To determine
Determine the standard deviation of downloading time.
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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
Basic Business Statistics, Student Value Edition
Ch. 6 - Given a standardized normal distribution (with a...Ch. 6 - Given a standard normal distribution (with a mean...Ch. 6 - Given a standardized normal distribution (with a...Ch. 6 - Given a standardized normal distribution (with a...Ch. 6 - Given a normal distribution with =100 and =10,...Ch. 6 - Given a normal distribution with =50 and =4, what...Ch. 6 - In 2015, the per capita consumption of bottled...Ch. 6 - Toby’s Trucking Company determined that the...Ch. 6 - Millennials spent an average of $103 on monthly...Ch. 6 - A Set of final examination grades in an...
Ch. 6 - A Nielsen study indicates that 18-to 34-year olds...Ch. 6 - In 2015, the per capita consumption of soft drinks...Ch. 6 - Many manufacturing problems involve the matching...Ch. 6 - Show that for a sample of n=39, the smallest and...Ch. 6 - For a sample of n=6, list the six Z values.Ch. 6 - The annual NFL Super Bowl is the most widely...Ch. 6 - As player salaries have increased, the cost of...Ch. 6 - The file Property Taxes contains the property...Ch. 6 - Prob. 19PSCh. 6 - One operation of a mill is to cut pieces of steel...Ch. 6 - The file CD Rate contains the yields for a...Ch. 6 - The file Utility contains the electricity costs,...Ch. 6 - Suppose you select one value from a uniform...Ch. 6 - The time between arrivals of customer at a bank...Ch. 6 - A study of the time spent shopping in a...Ch. 6 - Prob. 26PSCh. 6 - The Scheduled commuting time on the Long Island...Ch. 6 - Prob. 28PSCh. 6 - Prob. 29PSCh. 6 - Prob. 30PSCh. 6 - Prob. 31PSCh. 6 - Prob. 32PSCh. 6 - An industrial sewing machine uses ball bearing...Ch. 6 - The fill amount in 2-liter soft drink bottles is...Ch. 6 - In an effort to reduce the number of bottles that...Ch. 6 - Prob. 36PSCh. 6 - The file DomesticBeer Contains the percentage...Ch. 6 - Prob. 38PSCh. 6 - The major stock market indexes had strong results...Ch. 6 - Interns report that when deciding on where to...Ch. 6 - According to the same Glassdoor source mentioned...
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