Capital models often establish dependencies among asset and liability risks using links to shared economic factors, such as inflation, interest rates, exchange rates, credit spreads, equity prices, etc. Generating scenarios for the factors thus becomes a core driver of the models. But financial models of such factors are often built for trading purposes rather than risk analysis, focusing on distributions skewed towards building in risk prices instead of real world expectations.

We review recent literature in model construction and fitting and propose testing methodologies for comparing candidate models and calibrations. Somewhat different approaches are favored for single-year vs. multi-year scenario generation. For the latter, auto-correlations of individual factors and similar concepts across factors are more critical and so calibration to historical time series is important. For the single-year horizon, models calibrated just to beginning states can give reasonable distributions of end-of-year values.