Research Methods for the Behavioral Sciences (MindTap Course List)
5th Edition
ISBN: 9781305104136
Author: Frederick J Gravetter, Lori-Ann B. Forzano
Publisher: Wadsworth Publishing
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Textbook Question
Chapter 3, Problem 2E
Some variables, such as height, can be measured directly, and the measurement procedure is usually quite straightforward. Other variables—for example, hunger, motivation, or attitude about the death penalty—are more difficult to measure.
- Describe one procedure that might be used to measure hunger.
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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 3 Solutions
Research Methods for the Behavioral Sciences (MindTap Course List)
Ch. 3.2 - Define a construct and explain the role that...Ch. 3.2 - Define an operational definition and explain the...Ch. 3.3 - Define a positive relationship and a negative...Ch. 3.3 - Define the validity of measurement and explain why...Ch. 3.3 - Define the reliability of measurement and explain...Ch. 3.4 - Compare and contrast the four scales of...Ch. 3.5 - Identify the three modalities of measurement and...Ch. 3.6 - Define a ceiling effect and a floor effect and...Ch. 3.6 - Define an artifact and explain how examples of...Ch. 3 - In addition to the key words, you should also be...
Ch. 3 - Some variables, such as height, can be measured...Ch. 3 - Briefly explain what an operational definition is...Ch. 3 - A researcher evaluates a new cholesterol...Ch. 3 - A clinical researcher has developed a new test for...Ch. 3 - Suppose that a social scientist has developed a...Ch. 3 - Explain how inter-rater reliability is...Ch. 3 - A researcher claims that intelligence can be...Ch. 3 - Identify the scale of measurement that allows each...Ch. 3 - What is the primary advantage of self-report...Ch. 3 - Describe the strengths and weaknesses of...Ch. 3 - What is a ceiling effect, and how can it be a...Ch. 3 - What are demand characteristics, and how do they...Ch. 3 - Describe how the concept of participant reactivity...Ch. 3 - Select a subject and use a full-text database such...Ch. 3 - Select one construct from the following list:...Ch. 3 - For each of the following operational definitions,...
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