APPLIED STAT.IN BUS.+ECONOMICS
6th Edition
ISBN: 9781259957598
Author: DOANE
Publisher: RENT MCG
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Chapter 12.4, Problem 20SE
Instructions for exercises 12.20–12.22: (a) Use Excel to make a
12.20
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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 12 Solutions
APPLIED STAT.IN BUS.+ECONOMICS
Ch. 12.1 - For each sample, do a test for zero correlation....Ch. 12.1 - Instructions for Exercises 12.2 and 12.3: (a) Make...Ch. 12.1 - Prob. 3SECh. 12.1 - Prob. 4SECh. 12.1 - Instructions for exercises 12.412.6: (a) Make a...Ch. 12.1 - Prob. 6SECh. 12.2 - (a) Interpret the slope of the fitted regression...Ch. 12.2 - (a) Interpret the slope of the fitted regression...Ch. 12.2 - Prob. 9SECh. 12.2 - (a) Interpret the slope of the fitted regression...
Ch. 12.2 - (a) Interpret the slope of the fitted regression...Ch. 12.3 - Prob. 12SECh. 12.3 - Prob. 13SECh. 12.3 - The regression equation Credits = 15.4 .07 Work...Ch. 12.3 - Below are fitted regressions for Y = asking price...Ch. 12.3 - Refer back to the regression equation in exercise...Ch. 12.3 - Refer back to the regression equation in exercise...Ch. 12.4 - Instructions for exercises 12.18 and 12.19: (a)...Ch. 12.4 - Instructions for exercises 12.18 and 12.19: (a)...Ch. 12.4 - Instructions for exercises 12.2012.22: (a) Use...Ch. 12.4 - Instructions for exercises 12.2012.22: (a) Use...Ch. 12.4 - Instructions for exercises 12.2012.22: (a) Use...Ch. 12.5 - Instructions for exercises 12.23 and 12.24: (a)...Ch. 12.5 - Instructions for exercises 12.23 and 12.24: (a)...Ch. 12.5 - A regression was performed using data on 32 NFL...Ch. 12.5 - A regression was performed using data on 16...Ch. 12.6 - Below is a regression using X = home price (000),...Ch. 12.6 - Below is a regression using X = average price, Y =...Ch. 12.6 - Instructions for exercises 12.2912.31: (a) Use...Ch. 12.6 - Instructions for exercises 12.2912.31: (a) Use...Ch. 12.6 - Instructions for exercises 12.2912.31: (a) Use...Ch. 12.7 - Refer to the Weekly Earnings data set below. (a)...Ch. 12.7 - Prob. 33SECh. 12.8 - Prob. 34SECh. 12.8 - Prob. 35SECh. 12.9 - Calculate the standardized residual ei and...Ch. 12.9 - Prob. 37SECh. 12.9 - An estimated regression for a random sample of...Ch. 12.9 - An estimated regression for a random sample of...Ch. 12.9 - Prob. 40SECh. 12.9 - Prob. 41SECh. 12.9 - Prob. 42SECh. 12.9 - Prob. 43SECh. 12.11 - Prob. 44SECh. 12.11 - Prob. 45SECh. 12 - (a) How does correlation analysis differ from...Ch. 12 - (a) What is a simple regression model? (b) State...Ch. 12 - (a) Explain how you fit a regression to an Excel...Ch. 12 - (a) Explain the logic of the ordinary least...Ch. 12 - (a) Why cant we use the sum of the residuals to...Ch. 12 - Prob. 6CRCh. 12 - Prob. 7CRCh. 12 - Prob. 8CRCh. 12 - Prob. 9CRCh. 12 - Prob. 10CRCh. 12 - Prob. 11CRCh. 12 - Prob. 12CRCh. 12 - (a) What is heteroscedasticity? Identify its two...Ch. 12 - (a) What is autocorrelation? Identify two main...Ch. 12 - Prob. 15CRCh. 12 - Prob. 16CRCh. 12 - (a) What is a log transform? (b) What are its...Ch. 12 - (a) When is logistic regression needed? (b) Why...Ch. 12 - Prob. 46CECh. 12 - Prob. 47CECh. 12 - Prob. 48CECh. 12 - Instructions: Choose one or more of the data sets...Ch. 12 - Prob. 50CECh. 12 - Prob. 51CECh. 12 - Prob. 52CECh. 12 - Prob. 53CECh. 12 - Instructions: Choose one or more of the data sets...Ch. 12 - Instructions: Choose one or more of the data sets...Ch. 12 - Instructions: Choose one or more of the data sets...Ch. 12 - Prob. 57CECh. 12 - Prob. 58CECh. 12 - Prob. 59CECh. 12 - Prob. 60CECh. 12 - Prob. 61CECh. 12 - Prob. 62CECh. 12 - Prob. 63CECh. 12 - Prob. 64CECh. 12 - Prob. 65CECh. 12 - In the following regression, X = weekly pay, Y =...Ch. 12 - Prob. 67CECh. 12 - In the following regression, X = total assets (...Ch. 12 - Prob. 69CECh. 12 - Below are percentages for annual sales growth and...Ch. 12 - Prob. 71CECh. 12 - Prob. 72CECh. 12 - Prob. 73CECh. 12 - Simple regression was employed to establish the...Ch. 12 - Prob. 75CECh. 12 - Prob. 76CECh. 12 - Prob. 77CECh. 12 - Below are revenue and profit (both in billions)...Ch. 12 - Below are fitted regressions based on used vehicle...Ch. 12 - Below are results of a regression of Y = average...Ch. 12 - Prob. 81CE
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