Statistics for Business and Economics (13th Edition)
13th Edition
ISBN: 9780134506593
Author: James T. McClave, P. George Benson, Terry Sincich
Publisher: PEARSON
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Chapter 2.1, Problem 2.1LM
Complete the following table.
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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 2 Solutions
Statistics for Business and Economics (13th Edition)
Ch. 2.1 - Complete the following table.Ch. 2.1 - A qualitative variable with three classes (X, Y,...Ch. 2.1 - STEM experiences for girls. The National Science...Ch. 2.1 - Cable TV subscriptions and cord cutters. Has the...Ch. 2.1 - Do social robots walk or roll? A social (or...Ch. 2.1 - Top credit card issuers, by region. The Nilson...Ch. 2.1 - Microsoft program security issues. To help its...Ch. 2.1 - Jamming attacks on wireless networks. Refer to the...Ch. 2.1 - The Apprentice contestants performance ratings....Ch. 2.1 - The economic return to earning an MBA. Refer to...
Ch. 2.1 - Profiling UK rental malls. An analysis of the...Ch. 2.1 - History of corporate acquisitions. A corporate...Ch. 2.1 - Twitter opinions of iPhone 6 features. What are...Ch. 2.1 - Museum management. What criteria do museums use to...Ch. 2.1 - Advertising with reader-response cards....Ch. 2.1 - Motivation and right-oriented bias. Evolutionary...Ch. 2.1 - Groundwater contamination in wells. In New...Ch. 2.2 - Graph the relative frequency histogram for the 500...Ch. 2.2 - Refer to Exercise 2.18. Calculate the number of...Ch. 2.2 - Consider the stem-and-leaf display shown here. a....Ch. 2.2 - Minitab was used to generate the following...Ch. 2.2 - Stability of compounds in new drugs. Testing the...Ch. 2.2 - Corporate sustainability of CPA firms. Refer to...Ch. 2.2 - Sanitation inspection of cruise ships. To minimize...Ch. 2.2 - History of corporate acquisitions. Refer to the...Ch. 2.2 - Most valuable NFL teams. Each year Forbes reports...Ch. 2.2 - State SAT scores. Educators are constantly...Ch. 2.2 - Items arriving and departing a work center. In a...Ch. 2.2 - Crude oil biodegradation. In order to protect...Ch. 2.2 - Volkswagen emissions scandal. Recently, the...Ch. 2.2 - Is honey a cough remedy? Does a teaspoon of honey...Ch. 2.2 - Time in bankruptcy. Financially distressed firms...Ch. 2.2 - Prob. 2.33ACACh. 2.2 - Prob. 2.34ACACh. 2.3 - Calculate the mean and median of the following...Ch. 2.3 - Calculate the mean for samples where a. n = 10, x...Ch. 2.3 - Explain how the relationship between the mean and...Ch. 2.3 - Explain the difference between the calculation of...Ch. 2.3 - Calculate the mode, mean, and median of the...Ch. 2.3 - Calculate the mean, median, and mode for each of...Ch. 2.3 - Describe how the mean compares to the median for a...Ch. 2.3 - Use the applet entitled Mean versus Median to find...Ch. 2.3 - Prob. 2.2AECh. 2.3 - Use the applet Mean versus Median to study the...Ch. 2.3 - Hotels use of ecolabels. Ecolabels such as Energy...Ch. 2.3 - Rankings of research universities. Based on...Ch. 2.3 - Performance of stock screeners. Investment...Ch. 2.3 - Performance-based logistics. Refer to the Journal...Ch. 2.3 - Surface roughness of oil field pipe. Oil field...Ch. 2.3 - Prob. 2.47ACICh. 2.3 - Corporate sustainability of CPA firms. Refer to...Ch. 2.3 - Is honey a cough remedy? Refer to the Archives of...Ch. 2.3 - Crude oil biodegradation. Refer to the Journal of...Ch. 2.3 - Symmetric or skewed? Would you expect the data...Ch. 2.3 - Prob. 2.52ACICh. 2.3 - Prob. 2.53ACACh. 2.3 - Prob. 2.54ACACh. 2.3 - Prob. 2.55ACACh. 2.4 - Answer the following questions about variability...Ch. 2.4 - Calculate the range, variance, and standard...Ch. 2.4 - Calculate the variance and standard deviation for...Ch. 2.4 - Compute x,s2, and s for each of the following data...Ch. 2.4 - Calculate the range, variance, and standard...Ch. 2.4 - Using only integers between 0 and 10, construct...Ch. 2.4 - Using only integers between 0 and 10, construct...Ch. 2.4 - Consider the following sample of five...Ch. 2.4 - Use the applet entitled Standard Deviation to find...Ch. 2.4 - Use the applet Standard Deviation to study the...Ch. 2.4 - Use the applet Standard Deviation to study the...Ch. 2.4 - Hotels use of ecolabels. Refer to the Journal of...Ch. 2.4 - Permeability of sandstone during weathering. Refer...Ch. 2.4 - Performance of stock screeners. Refer to the...Ch. 2.4 - Corporate sustainability of CPA firms. Refer to...Ch. 2.4 - Is honey a cough remedy? Refer to the Archives of...Ch. 2.4 - Active nuclear power plants. Refer to Exercise...Ch. 2.4 - Estimating production time. A widely used...Ch. 2.5 - The output from a statistical software package...Ch. 2.5 - Prob. 2.72LMCh. 2.5 - For a set of data with a mound-shaped relative...Ch. 2.5 - The following is a sample of 25 measurements: a....Ch. 2.5 - Given a data set with a largest value of 760 and a...Ch. 2.5 - Voltage sags and swells. The power quality of a...Ch. 2.5 - Permeability of sandstone during weathering. Refer...Ch. 2.5 - Do social robots walk or roll? Refer to the...Ch. 2.5 - College dropout study. The American Economic...Ch. 2.5 - Motivation of drug dealers. Consider a study of...Ch. 2.5 - Sanitation inspection of cruise ships. Refer to...Ch. 2.5 - Volkswagen emissions scandal. Refer to the...Ch. 2.5 - Auditing water resources in Australia. Australia...Ch. 2.5 - The Apprentice contestants performance ratings....Ch. 2.5 - Shopping vehicle and judgment. While shopping at...Ch. 2.5 - Buy-side vs. sell-side analysts earnings...Ch. 2.5 - Prob. 2.87ACACh. 2.5 - Improving SAT scores. The National Education...Ch. 2.5 - Prob. 2.89ACACh. 2.6 - Compute the z-score corresponding to each of the...Ch. 2.6 - Give the percentage of measurements in a data set...Ch. 2.6 - In terms of percentiles, define QL, QM and QU.Ch. 2.6 - Compare the z-scores to decide which of the...Ch. 2.6 - Suppose that 40 and 90 are two elements of a...Ch. 2.6 - Mathematics assessment test scores. According to...Ch. 2.6 - Prob. 2.96ACBCh. 2.6 - Prob. 2.97ACBCh. 2.6 - Sanitation inspection of cruise ships Refer to the...Ch. 2.6 - Prob. 2.99ACICh. 2.6 - Prob. 2.100ACICh. 2.6 - Executive networking and firm performance. Do...Ch. 2.6 - Blue- vs. red-colored exam study. In a study of...Ch. 2.6 - Ranking PhD programs in economics. Thousands of...Ch. 2.6 - Using z-scores for grades. At one university, the...Ch. 2.6 - Prob. 2.105ACACh. 2.7 - A sample data set has a mean of 57 and a standard...Ch. 2.7 - Suppose a data set consisting of exam scores has a...Ch. 2.7 - Consider the horizontal box plot shown below. a....Ch. 2.7 - Prob. 2.109LMCh. 2.7 - Prob. 2.7AECh. 2.7 - Rankings of research universities. Refer to the...Ch. 2.7 - Voltage sags and swells. Refer to the Electrical...Ch. 2.7 - Treating psoriasis with the Doctorfish of Kangal....Ch. 2.7 - Budget lapsing at army hospitals. Accountants use...Ch. 2.7 - Salary offers to MBAs. Consider the top salary...Ch. 2.7 - Prob. 2.115ACICh. 2.7 - Prob. 2.116ACICh. 2.7 - Sanitation inspection of cruise ships. Referto...Ch. 2.7 - Network server downtime. A manufacturer of network...Ch. 2.7 - Permeability of sandstone during weathering. Refer...Ch. 2.7 - Prob. 2.120ACACh. 2.7 - Prob. 2.121ACACh. 2.8 - Construct a scatterplot for the data in the...Ch. 2.8 - Construct a scatterplot for the data in the...Ch. 2.8 - Prob. 2.124ACBCh. 2.8 - Prob. 2.125ACBCh. 2.8 - Lobster trap placement. Strategic placement of...Ch. 2.8 - Does elevation impact hitting performance in...Ch. 2.8 - Prob. 2.128ACBCh. 2.8 - Prob. 2.129ACBCh. 2.8 - Spreading rate of spilled liquid A contract...Ch. 2.8 - Performance ratings of government agencies. The...Ch. 2.8 - Most valuable NFL teams. Refer to the Forbes...Ch. 2.8 - Best-paid CEOs. Refer to Glassdoor Economic...Ch. 2.8 - Prob. 2.134ACACh. 2.10 - Museum management. Refer to the Museum Management...Ch. 2.10 - Volkswagen emissions scandal. Refer to the...Ch. 2.10 - BP oil leak. In the summer of 2010, an explosion...Ch. 2 - Construet a relative frequency histogram for the...Ch. 2 - Discuss the conditions under which the median is...Ch. 2 - Consider the following three measurements: 50, 70,...Ch. 2 - Refer to Exercise 2.141c. For parts a-d, determine...Ch. 2 - For each of the following data sets, compute x,...Ch. 2 - For each of the following data sets, compute x,...Ch. 2 - Explain why we generally prefer the standard...Ch. 2 - If the range of a set of data is 20, find a rough...Ch. 2 - Prob. 2.147LMCh. 2 - Motivation of drug dealers. Refer to the Applied...Ch. 2 - Slogs for Fortune 500 firms. Web site...Ch. 2 - Management system failures. The U.S. Chemical...Ch. 2 - Business marketing publications....Ch. 2 - U.S. business bankruptcies. The American...Ch. 2 - Prob. 2.153ACBCh. 2 - Products Made in the USA. Made in the USA is a...Ch. 2 - Prob. 2.155ACBCh. 2 - Drivers stopped by police. According to the Bureau...Ch. 2 - U.S. wine export markets. The Center for...Ch. 2 - Prob. 2.158ACICh. 2 - Hull failures of oil tankers. Owing to several...Ch. 2 - Software defects. The Promise Software Engineering...Ch. 2 - Prob. 2.161ACICh. 2 - Time to develop price quotes. A manufacturer of...Ch. 2 - Trend in Iraq War casualties. While the United...Ch. 2 - Prob. 2.164ACICh. 2 - Radiation levels in homes. In some locations,...Ch. 2 - Doctors and ethics. For physicians confronted with...Ch. 2 - Prob. 2.167ACICh. 2 - Investigating the claims of weight-loss clinics....Ch. 2 - Age discrimination study. The Age Discrimination...Ch. 2 - No Child Left Behind Act. According to the...Ch. 2 - Steel rod quality. In his essay Making Things...
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