Introduction to Markov Chain Analysis: The video explains the concept of Markov Chain analysis, focusing on a small example related to the financial crisis of 2007-08, particularly analyzing housing inventory over three stages: current on mortgage, delinquent in payment, and default.
Explanation of Stages and Matrix: The three stages are described as follows: current on mortgage (loan or housing currently on mortgage), delinquent in payment (payments might or might not be made in the second month), and default (loan not paid). The matrix representing these stages is a 3x3 matrix, and the sum of probabilities in the matrix equals one.
Step-by-Step Calculation Using Excel: The video demonstrates how to calculate the next stage using Excel functions. By using the MMULT function, the current stock values (100,000 in mortgage, 20,000 delinquent, 5,000 default) are multiplied with the probability matrix to predict the stock values for the next stage.
Finding Steady State: The steady state is reached when the output equals the input after multiple iterations. In the example, this occurs around the 18th stage. The video shows how to perform these calculations in Excel and freeze cells using dollar signs to find the steady state.
Reverse Engineering with Inverse Matrix: The video also covers how to use the inverse matrix (MINVERSE function) in Excel to predict previous stages from a given stage, demonstrating that reverse engineering is possible in Markov Chain analysis.