Journal of Risk Model Validation

A mean-reverting scenario design model to create lifetime forecasts and volatility assessments for retail loans

Sisi Liang and Joseph Breeden

  • Implementation of the new CECL and IFRS9 accounting standards for lifetime loss forecasting are best met by using mean-reverting scenarios in stress test models that incorporate loss probability versus the age of the loan.
  • Forecasts based upon mean-reverting scenarios provide point-in-time estimates initially and relax onto through-the-cycle estimates in the long-run.
  • Lifetime loss forecasts with mean-reverting scenarios are ideal for loan pricing and economic capital estimation.


Lifetime loan forecasting has become essential to lender risk management and profitability. Loan-pricing models require forecasts over the life of the loan. Current expected credit loss (CECL) calculations proposed by the US Financial Accounting Standards Board (FASB) (2012) and included in International Financial Reporting Standard 9 (IFRS9) require lifetime forecasts. In both cases, we cannot create forecasts that assume the current or historic environment persists for many years into the future. Instead, a more reasonable approach is to use macroeconomic scenarios for the near term and then relax onto the long-run average for future years. In the current paper, we develop a modeling framework that can incorporate mean-reverting scenarios into any scenario-based forecasting model. Using prior economic conditions, we create an environmental index with which to calibrate a discrete version of an Ornstein-Uhlenbeck (OU) mean-reverting model. OU models are best applied to stationary processes, which is true for the environment function derived from age-period-cohort-type (APC-type) models. The mean-reverting model is used to transition from the near-term macroeconomic scenario to the long-run average to provide stable lifetime estimates for long-duration loans. We demonstrate this framework with a loan-level forecasting model using an age-vintage-time structure for retail loans, in this case, a small auto loan portfolio. The loan-level age-vintage-time model is similar in structure to an APC model, but it is estimated at the loan-level for greater robustness on small portfolios. The environment function of time is correlated to macroeconomic factors, and it is then extrapolated backward in time before the performance data to stabilize the trend of the environment function. This framework is in line with the explicit goals of the new FASB loan-loss accounting guidelines. In addition, this model provides a simple mechanism to facilitate the transition between point-in-time and through-the-cycle economic capital estimates with an internally consistent model.