## Service

## Methodology

RRAS (Roll Rate Analytic System) methodology modifies a set of techniques with a special focus on the Markov chain approach and vintage analysis. Implementation of a dual-time approach for transition matrix decomposition helps to produce forecasts of credit portfolio losses and to assess future portfolio distribution. Consequently, accurate values of future credit portfolio reserves can more accurately be obtained, allowing for better stress testing and, hence, better risk model validation.

A uniform method for credit portfolio stress-testing is one of the primary outcomes of the presented approaches. Using dual-time transition matrix decomposition, and together with vintage segmentation, we can significantly increase accuracy of credit portfolio behaviour forecasting, gross charge-off, cash flow, and stress-testing. Moreover, using the method subsequently introduced by V. Babikov (The Theory and practice of Retail Credit), we can simultaneously investigate the behaviour of different significant factors, such as prepayments, vintage quality, and the macroeconomic environment. Furthermore, we can generate many additional analytic reports.

Description of methodology requires a suitable terminology. A glossary of terms has already been developed, although it does not cover all credit portfolio behaviors we are interested in. We will now try to put in order the mix of internationally used definitions and designations. This is necessary to explain the RRAS methodology our company has developed.

Let us represent the main definitions and introduce acronyms we are going to use. (You can find out all about the terminology in the Glossary).

**Vintage** – loans of a certain vintage have unique characteristics of quality, prepayment and revolvement. These unique characteristics are a result of the pooling of underlying assets. Most grouping assumes that underlying assets are pooled across certain geographical regions with similar terms for maturity, interest rates, and origination period. We subsequently assume vintages pool their underlying assets across a certain month of origination.

**RC (risk class)** – A delinquency bucket that depends on the number of days past a due date (DPD), defined as follows:

RC0 – 0~DPD;

RC1 – 1-30~DPD;

RC2 – 31-60~DPD, and so on.

As an example, Figure 1 shows the Markov chain graph for a close-end portfolio, where charge-off is defined as 120+ DPD. There are two absorption states: Charge-off (C/O) and Pay-Down (P-D).

Figure 1. Markov chain graph for close-end portfolios without restructuring.

**Month on book (MOB)** – vintage age in months.

**Days past due (DPD)** – time overdue.

**Tenor (Term)** – a pooling of the underlying assets across a certain term to maturity. Significant changes in the tenor structure of a portfolio can become an impediment to the process of risk assessment and credit portfolio modelling

**Basic matrix** – in accordance with the Markov chain graph in Figure 1, each element xij(k) of the matrix X0ij(k) is the average (across all the vintages) probability of the transition between risk class i and risk class j at month k on book:

Each matrix element xij(k) is a function of frequency of transition from risk class i to risk class j of k, where k is a vintage age (month on book). Let us call this functions xij(k) as the “Maturation function”. Credits’ transitions between risk classes are heterogeneous, partially due to maturation effect (MOB effect upon frequency of transition between risk classes). Maturation functions can be calculated in case of enough statistics. The Roll Rate Analytic System’s specialized algorithms automatically compute maturation functions for different loan types.

The next step in RRAS modeling is to determine and study main risk factors: vintage quality, macroeconomic impact, prepayment, revolving … (see Publications for more information).

Finally, RRAS helps us to create business and macroeconomic scenarios.

Roll Rate Analytic System also produces a wide assortment of reports, assessing a credit portfolio’s behavior from different angles. Read the Service section for more on reports.

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