Statistics
13th Edition
ISBN: 9780135820100
Author: MCCLAVE, James T., Sincich, Terry
Publisher: PEARSON
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Chapter 6.2, Problem 12UP
To determine
Define the MVUE for a parameter.
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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
Statistics
Ch. 6.1 - What is the difference between a population...Ch. 6.1 - What is a sampling distribution of a sample...Ch. 6.1 - 5.1 The probability distribution shown here...Ch. 6.1 - 5.3 Consider the population described by the...Ch. 6.1 - Refer to Exercise 6.5 and find E(x) = μ. Then use...Ch. 6.1 - Refer to Exercise 6.5. Assume that a random sample...Ch. 6.1 - In Example 6.3, we used the computer to generate...Ch. 6.2 - What is a point estimator of a population...Ch. 6.2 - What is the difference between a biased and...Ch. 6.2 - What is the MVUE for a parameter?
Ch. 6.2 - What are the properties of an ideal estimator?
Ch. 6.2 - 5.8 Consider the following probability...Ch. 6.2 - 5.9 Consider the following probability...Ch. 6.2 - 5.10 Consider the following probability...Ch. 6.2 - Refer to Exercise 6.5.
Show that is an unbiased...Ch. 6.2 - Refer to Exercise 6.5.
Find the sampling...Ch. 6.2 - Refer to Exercise 6.7, in which we found the...Ch. 6.3 - Prob. 21UPCh. 6.3 - How does the mean of the sampling distribution of...Ch. 6.3 - How does the standard deviation of the sampling...Ch. 6.3 - Another name given to the standard deviation of x̄...Ch. 6.3 - State the Central Limit Theorem.
Ch. 6.3 - Will the sampling distribution of x̄ always be...Ch. 6.3 - Suppose a random sample of n measurements is...Ch. 6.3 - Suppose a random sample of n = 25 measurements is...Ch. 6.3 - Consider the following probability...Ch. 6.3 - A random sample of n = 64 observations is drawn...Ch. 6.3 - A random sample of n = 100 observations is...Ch. 6.3 - 5.20 A random sample of n = 900 observations is...Ch. 6.3 - Open the applet Sampling Distributions. On the...Ch. 6.3 - Open the applet Sampling Distributions. On the...Ch. 6.3 - Corporate sustainability of CPA firms. Refer to...Ch. 6.3 - Voltage sags and swells. Refer to the Electrical...Ch. 6.3 - Physical activity of obese young adults. In a...Ch. 6.3 - Cost of unleaded fuel. According to the American...Ch. 6.3 - Requests to a Web server. In Exercise 5.10 (p....Ch. 6.3 - Shell lengths of sea turtles. Refer to the Aquatic...Ch. 6.3 - Tomato as a taste modifier. Miraculin is a protein...Ch. 6.3 - Uranium in the Earth’s crust. Refer to the...Ch. 6.3 - Critical part failures in NASCAR vehicles. Refer...Ch. 6.3 - Motivation of drug dealers. Refer to the Applied...Ch. 6.3 - Is exposure to a chemical in Teflon-coated...Ch. 6.3 - Characteristics of antiwar demonstrators. Refer to...Ch. 6.3 - Hand washing versus hand rubbing. Refer to the...Ch. 6.3 - Video game players and divided attention tasks....Ch. 6.4 - Suppose a random sample of n measurements is...Ch. 6.4 - Suppose a random sample of n = 500 measurements is...Ch. 6.4 - 5.38 A random sample of n = 80 measurements is...Ch. 6.4 - 5.39 A random sample of n = 250 measurements is...Ch. 6.4 - A random sample of n = 1,500 measurements is drawn...Ch. 6.4 - 5.41 Consider a population with values of x equal...Ch. 6.4 - Do social robots walk or roll? Refer to the...Ch. 6.4 - Paying for music downloads. According to a recent...Ch. 6.4 - Working on summer vacation. According to an...Ch. 6.4 - Superstitions survey. A Harris (Feb. 2013) poll...Ch. 6.4 - Crop damage by wild boars. Refer to the Current...Ch. 6.4 - Downloading “apps” to your cell phone. Refer to...Ch. 6.4 - Hotel guest satisfaction. Refer to the results of...Ch. 6.4 - Fingerprint expertise. Refer to the Psychological...Ch. 6 - Prob. 63UPCh. 6 - Prob. 64UPCh. 6 - Prob. 65UPCh. 6 - Prob. 66UPCh. 6 - Prob. 67UPCh. 6 - Prob. 68LMCh. 6 - Prob. 69LMCh. 6 - Prob. 70LMCh. 6 - Prob. 71LMCh. 6 - 5.56 A random sample of n = 500 observations is...Ch. 6 - 5.57 A random sample of n = 300 observations is...Ch. 6 - 5.58 Use a statistical software package to...Ch. 6 - 5.59 Use a statistical software package to...Ch. 6 - Suppose x equals the number of heads observed when...Ch. 6 - A random sample of size n is to be drawn from a...Ch. 6 - Salaries of travel managers. According to a 2012...Ch. 6 - Children’s attitudes toward reading. In the...Ch. 6 - Dentists’ use of laughing gas. According to the...Ch. 6 - Marital name changing. Refer to the Advances in...Ch. 6 - Violence and stress. Interpersonal violence (e.g.,...Ch. 6 - Research on eating disorders. Refer to The...Ch. 6 - Prob. 84ACICh. 6 - Prob. 85ACICh. 6 - Prob. 86ACICh. 6 - Prob. 87ACICh. 6 - Prob. 88ACICh. 6 - Prob. 89ACICh. 6 - Prob. 90ACACh. 6 - Prob. 91ACACh. 6 - 5.76 Soft-drink bottles. A soft-drink bottler...
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