Consider a stock market with two stocks A and B. Stock A always sell for either $5 or $10; Stock B always sell for either $6 or $12. • If stock A is selling for $5 today, there is a 75 percent chance it will sell for $5 tomorrow. If stock A is selling for $10 today, there is a 90 percent chance it will sell for $10 tomorrow. • If stock B is selling for $6 today, there is a 90 percent chance it will sell for $6 tomorrow. If stock B is selling for $12 today, there is a 70 percent chance it will sell for $12 tomorrow. Based on this information. a) Write down the state vectors and transition matrices for the corresponding Markov systems for stock A and stock B. b) Markov chain model for stock A can be expressed for via the following dia- gram, in which circles denote the states and the arrows denote the transition probabilities: 0.75 $5 0.10 0.25 0.90 $10 Let us call this diagram transition diagram. Depict the Markov chain model for stock B using a similar transition diagram. c) Compute the average cost of stock A and the average cost of stock B. d) Suppose you have just purchased one unit of stock A and one unit of stock B at prices $5 and $6, respectively. This is your portfolio. What is the probability that the value of your portfolio is greater than $15 in two days. e) What is the long-run value of your portfolio?
Consider a stock market with two stocks A and B. Stock A always sell for either $5 or $10; Stock B always sell for either $6 or $12. • If stock A is selling for $5 today, there is a 75 percent chance it will sell for $5 tomorrow. If stock A is selling for $10 today, there is a 90 percent chance it will sell for $10 tomorrow. • If stock B is selling for $6 today, there is a 90 percent chance it will sell for $6 tomorrow. If stock B is selling for $12 today, there is a 70 percent chance it will sell for $12 tomorrow. Based on this information. a) Write down the state vectors and transition matrices for the corresponding Markov systems for stock A and stock B. b) Markov chain model for stock A can be expressed for via the following dia- gram, in which circles denote the states and the arrows denote the transition probabilities: 0.75 $5 0.10 0.25 0.90 $10 Let us call this diagram transition diagram. Depict the Markov chain model for stock B using a similar transition diagram. c) Compute the average cost of stock A and the average cost of stock B. d) Suppose you have just purchased one unit of stock A and one unit of stock B at prices $5 and $6, respectively. This is your portfolio. What is the probability that the value of your portfolio is greater than $15 in two days. e) What is the long-run value of your portfolio?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Show full answers and steps to part d) and e) using Markov Chain Theory. Please explain how you get to the answers without using excel, R or stata
![[5] Consider a stock market with two stocks A and B. Stock A always sell for either
$5 or $10; Stock B always sell for either $6 or $12.
• If stock A is selling for $5 today, there is a 75 percent chance it will sell for
$5 tomorrow. If stock A is selling for $10 today, there is a 90 percent chance
it will sell for $10 tomorrow.
• If stock B is selling for $6 today, there is a 90 percent chance it will sell for
$6 tomorrow. If stock B is selling for $12 today, there is a 70 percent chance
it will sell for $12 tomorrow.
Based on this information.
a) Write down the state vectors and transition matrices for the corresponding
Markov systems for stock A and stock B.
b) Markov chain model for stock A can be expressed for via the following dia-
gram, in which circles denote the states and the arrows denote the transition
probabilities:
0.75
$5
0.10
0.25
0.90
$10
Let us call this diagram transition diagram. Depict the Markov chain
model for stock B using a similar transition diagram.
c) Compute the average cost of stock A and the average cost of stock B.
d) Suppose you have just purchased one unit of stock A and one unit of stock
B at prices $5 and $6, respectively. This is your portfolio. What is the
probability that the value of your portfolio is greater than $15 in two days.
e) What is the long-run value of your portfolio?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa3574180-5be7-46af-9f18-c1fbb9ec682c%2Fce6ee914-070a-464b-8f03-c80ab3bc0fc6%2Fi7xxo4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:[5] Consider a stock market with two stocks A and B. Stock A always sell for either
$5 or $10; Stock B always sell for either $6 or $12.
• If stock A is selling for $5 today, there is a 75 percent chance it will sell for
$5 tomorrow. If stock A is selling for $10 today, there is a 90 percent chance
it will sell for $10 tomorrow.
• If stock B is selling for $6 today, there is a 90 percent chance it will sell for
$6 tomorrow. If stock B is selling for $12 today, there is a 70 percent chance
it will sell for $12 tomorrow.
Based on this information.
a) Write down the state vectors and transition matrices for the corresponding
Markov systems for stock A and stock B.
b) Markov chain model for stock A can be expressed for via the following dia-
gram, in which circles denote the states and the arrows denote the transition
probabilities:
0.75
$5
0.10
0.25
0.90
$10
Let us call this diagram transition diagram. Depict the Markov chain
model for stock B using a similar transition diagram.
c) Compute the average cost of stock A and the average cost of stock B.
d) Suppose you have just purchased one unit of stock A and one unit of stock
B at prices $5 and $6, respectively. This is your portfolio. What is the
probability that the value of your portfolio is greater than $15 in two days.
e) What is the long-run value of your portfolio?
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