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 a), b) & c) in this exercise using Markov Chain’s Theory. Please explain how you get to the answers without using R, excel or stata
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