The TMM process requires you first to determine your allowance segments, then establish loan states within each pool segment, essentially the sub-segments within a segment, between which you will track movement. By far, the most common active state drivers are risk ratings. In addition to the active states – risk ratings, delinquency, FICO scores and other default drivers – you will track movement to terminal states, that is, the end of the life of the loan, when it defaults or is paid off. A common transition matrix might have a six-point risk-rating scale and two categories for loans that have exited the transition.
Once you have established your loan states, look at the historical performance of your loans between the defined periods. Essentially, you are trying to determine the average probability of loans moving from one state to another by analyzing their historical transition, then averaging those transition rates over time. For example, if you have five years of historical data and five years of transitions, you can average those probabilities to apply to your current portfolio and project what the portfolio will look like going forward. This is when you run the Markov chain to see what your long-term probability is going to be. You eventually wind up migrating into the default or paid-off loan state, which is how the Markov chain process gets you from annual transition rates to a lifetime probability of default.
Your loss given default (LGD) calculates the losses you experience in cases of default. It is the simpler of the PD/LGD calculations. It is important to calculate the LGD by capturing the balance of loans at the time of default or just prior to default, then capture what losses occur to those loans following the default event. Eventual losses divided by balance prior to default equals LGD.