Case Study: Markov Chain

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Summary

“A.C.M.E” bank deals with both asset and liability products in retail bank industry. A big portfolio of the bank is based on loans. These loans make the majority of the total revenue earned by the bank. Hence, it is very essential for the bank to find the proportion of loans which have a high propensity to be paid in full and those which will finally become bad loans.

All the loans, which have been issued by the bank can be classified into the below four categories:

a. Good Loans: These are the loans which are in progress but are given to low risk customers. The expectation is most of these loans will be paid up in full with time.

b. Risky loans: These are also the loans which are in progress but are given to medium or high risk customers. It is expected a good number of these customers will default.

c. Bad loans: The customer to whom these loans were given have already defaulted.

d. Paid Up loans: These loans have already been paid in full.

It is assumed, the probabilities of different loans per year are as below:

From/To *         Good     Risky     Bad     Paid Up
————————————————————————
Good *               70%       5%         3%      22%
Risky *               5%          55%       35%    5%
Bad *                 0%          0%         100%  0%
Paid Up *          0%          0%         0%      100%

For a given time frame (in years), the model calculates the probabilities for different categories using a Markov Chain with the above values as the transition matrix.

Original source / documentation of model

Solve a business case using simple Markov Chain

Output Type

A list of values given below:

  • Good %
  • Risky %
  • Bad %
  • Paid up %

Libraries Used

  • Numpy

Equations Used

  • Matrix Multiplication