**Roll Rate Models**

The roll rate model is the most commonly used modeling practice for the loss forecasting in the consumer banking arena built at the portfolio level instead of at the individual account level.

In this modeling practice, the whole portfolio is segmented by various delinquency buckets, e.g. Current, 30-DPD, 60-DPD, 90-DPD, 120-DPD, 150-DPD, and charge-off. The purpose is to evaluate the probability of an account in a specific delinquency bucket flowing into the next stage of delinquency status during the course of 1 month. The table below demonstrates the scheme of a basic roll rate model. In the table below, projected rolling rates are shown in the bottom two rows highlighted in red. The projected rate for each delinquency bucket is simply the moving average of previous 3 months.

Due to its nature of simplicity, the roll rate model is able to fit into various business scenarios, e.g. delinquency tracking and loss forecasting, and across different consumer products, e.g. installment loans and revolving credits. However, since the rolling rate for a specific delinquency bucket is estimated on the moving-average basis without being able to incorporate exogenous risk factors and economic drivers, a roll rate model is most applicable to the short-term loss forecasting, e.g. usually within 3 months, and also not able to estimate the portfolio loss in a stressed economic scenario.

**Vintage Loss Models**

A vintage loss model is another widely used modeling technique for the loss forecasting and is similar to the roll rate model in that they both are portfolio-based instead of account-based. However, in the vintage loss model, the whole portfolio is segmented by various origination vintages instead of delinquency buckets.

In this modeling practice, once the vintage criterion is determined, each delinquency performance, e.g. from 30-DPD through Charge-off, of every segment can be tracked over time through the full life cycle. For instance, in the case of loss estimation, the loss rate of a specific vintage can be formulated as

**Ln(Loss_Rate / (1 – Loss_Rate)) = A * Vintage_Quality + B * Economy_Driver + S(Maturation)**

In the model specification above, while vintage_quality, e.g. origination credit score or loan-to-value, and economy_driver, e.g. unemployment rate or housing price index, are linear components, Maturation, e.g. months on book, is a non-parametric term to reflect the nonlinearity of a maturity curve.

Compared with the roll rate model, the vintage loss model demonstrates a twofold benefit. First of all, with the inclusion of maturation information, the loss trend can be captured and utilized to improve the forecasting in a longer term. Secondly, incorporated with the economic information, the model can also be used to perform the stress testing in various economic scenarios. However, a caveat is that the vintage loss model is more suitable for installment loans than for revolving credits in loss forecasting due to impacts of various business practices such as balance transfers and teaser rates.

**Expected Losses Models**

Albeit easy to understand and simple to implement, two methods introduced above are all under the criticism of not being able to incorporate loan-specific characteristics and a finer level of economic information. Significantly different from roll rate models and vintage loss curves, expected loss (EL) estimation is a modern modeling practice developed on the basis of 3 risk parameters, namely probability of default (PD), exposure at default (EAD), and loss given default (LGD).

In this modeling practice, each risk parameter is modeled separately with account-level risk factors and economic indicators. For each individual account, the expected loss during the course of next 12 months can be formulated as

**EL = PD * EAD * LGD**

This modeling methodology not only is in line with Basel framework but also has following advantages over traditional methods for loss forecasting, including roll rate models and vintage loss models.

1. The account-level modeling practice provides a more granular risk profiling for each individual borrower.

2. Each risk parameter is driven by a separate set of economic factors independently, allowing a more dynamic view of economic impacts

3. The modeling methodology is in line with statistical techniques prevailing in the consumer lending arena and intuitively adoptable by most model developers.

Since this methodology heavily relies on statistical modeling concepts, the loss estimation is subject to specific statistical assumptions on distributions and functional forms.