EBK MATLAB: AN INTRODUCTION WITH APPLIC
6th Edition
ISBN: 8220103113663
Author: GILAT
Publisher: YUZU
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Chapter 6, Problem 7P
Write a program that generates a
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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
EBK MATLAB: AN INTRODUCTION WITH APPLIC
Ch. 6 - Prob. 1PCh. 6 - Given: d=6e=4f=2 . Evaluate the following...Ch. 6 - Given: v=[-2 4 1 0 2 1 2] and w=[2 50 1 2 1 3]....Ch. 6 - Use the vectors v and w from Problem 3. Use...Ch. 6 - Evaluate the following expressions without using...Ch. 6 - Use loops to create a 46 matrix in which the value...Ch. 6 - Write a program that generates a vector with 30...Ch. 6 - Write a program that asks the user to input a...Ch. 6 - Write a program that asks the user to input a...Ch. 6 - The daily high temperature (°F) in New York City...
Ch. 6 - The Pascal triangle can be displayed as elements...Ch. 6 - Fibonacci numbers are the numbers in a sequence in...Ch. 6 - The reciprocal Fibonacci constant ?is defined by...Ch. 6 - The value of p can be estimated from:...Ch. 6 - The value of p can be estimated from the...Ch. 6 - Write a program that (a) generates a vector with...Ch. 6 - A vector is given by x= [9 -1.5 13.4 13.3 -2.1 4.6...Ch. 6 - The Pythagorean theorem states that a2+ b2= c2....Ch. 6 - Write a MATLAB program in a script file that finds...Ch. 6 - A safe prime is a prime number that can be written...Ch. 6 - Sexy primes are two prime numbers that the...Ch. 6 - A Mersenne prime is a prime number that is equal...Ch. 6 - A perfect number is a positive integer that is...Ch. 6 - A list of exam scores (S) (in percent out of 100%...Ch. 6 - The Taylor series expansion for axis:...Ch. 6 - Write a MATLAB program in a script file that finds...Ch. 6 - The following are formulas for calculating the...Ch. 6 - Body mass index (BMI) is a measure of obesity. In...Ch. 6 - Write a program in a script file that calculates...Ch. 6 - Write a program that determines the change given...Ch. 6 - The concentration of a drug in the body CPcan be...Ch. 6 - One numerical method for calculating the cubic...Ch. 6 - Write a program in a script file that converts a...Ch. 6 - In a one-dimensional random walk, the position x...Ch. 6 - The Sierpinski triangle can be implemented in...Ch. 6 - The roots of a cubic equation a3x3+a2x2+a1x+a0=0...Ch. 6 - The overall grade in a course is determined from...Ch. 6 - A Keith number is a number (integer) that appears...Ch. 6 - The following MATLAB commands create a sine-shaped...
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- Business discussarrow_forwardBusiness discussarrow_forwardI just need to know why this is wrong below: What is the test statistic W? W=5 (incorrect) and What is the p-value of this test? (p-value < 0.001-- incorrect) Use the Wilcoxon signed rank test to test the hypothesis that the median number of pages in the statistics books in the library from which the sample was taken is 400. A sample of 12 statistics books have the following numbers of pages pages 127 217 486 132 397 297 396 327 292 256 358 272 What is the sum of the negative ranks (W-)? 75 What is the sum of the positive ranks (W+)? 5What type of test is this? two tailedWhat is the test statistic W? 5 These are the critical values for a 1-tailed Wilcoxon Signed Rank test for n=12 Alpha Level 0.001 0.005 0.01 0.025 0.05 0.1 0.2 Critical Value 75 70 68 64 60 56 50 What is the p-value for this test? p-value < 0.001arrow_forward
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