EBK MATLAB: AN INTRODUCTION WITH APPLIC
6th Edition
ISBN: 8220103113663
Author: GILAT
Publisher: YUZU
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Chapter 8, Problem 23P
The number of bacteria NBmeasured at different times t is given in the following table. Determine an exponential
| t(h) | 0 | 1 | 3 | 4 | 6 | 7 | 9 |
| NB | 500 | 600 | 1,000 | 1,400 | 2,300 | 2,700 | 4,100 |
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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 8 Solutions
EBK MATLAB: AN INTRODUCTION WITH APPLIC
Ch. 8 - Prob. 1PCh. 8 - Plot the polynomial y=0.7x413.5x2+6x37 in the...Ch. 8 - Determine the polynomial y(x) that has roots at x...Ch. 8 - Use MATLAB to carry out the following...Ch. 8 - Use MATLAB to carry out the following...Ch. 8 - Use MATLAB to divide the polynomial...Ch. 8 - Use MATLAB to divide the ploynomial...Ch. 8 - The product of four consecutive even integers is...Ch. 8 - The product of three integers with spacing of 3...Ch. 8 - The product of three distinct integers is 6240....
Ch. 8 - A rectangular steel container (no top) has the...Ch. 8 - An aluminum container has the geometry shown in...Ch. 8 - A rectangular box (no top) is welded together...Ch. 8 - The probability P of selecting three distinct...Ch. 8 - Write a user-defined function that adds or...Ch. 8 - Write a user-defined function that multiplies two...Ch. 8 - Write a user-defined function that calculates the...Ch. 8 - A cylinder with base radius rand height h is...Ch. 8 - Consider the parabola: x = 2(y-2)2 +3,and the...Ch. 8 - The following data is given: x -5 -4 -1 1 4 6 9 10...Ch. 8 - 21. The boiling temperature of water TB at various...Ch. 8 - The U.S. population in selected years between 1815...Ch. 8 - The number of bacteria NBmeasured at different...Ch. 8 - Growth data of a sunflower plant is given tn the...Ch. 8 - Use the growth data from Problem 24 for the...Ch. 8 - 26. The following points are given: x 1 2.2 3.7...Ch. 8 - The standard air density. D (average of...Ch. 8 - Write a user-defined function that determines the...Ch. 8 - Estimated values of thermal conductivity of...Ch. 8 - Measurements of the concentration, C, of a...Ch. 8 - Use the data from Problem 30 for the following:...Ch. 8 - The relationship between two variables y and x is...Ch. 8 - Curve-lit the data from the previous problem with...Ch. 8 - When rubber is stretched, its elongation is...Ch. 8 - The transmission of light through a transparent...
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