Abstract: In accordance with the principles of the present invention, an apparatus, simulation method, and system for modeling loss in a term structured financial portfolio are provided. An historical date range, time unit specification, maturity duration, evaluation horizon, random effects specification, and set of portfolio covariates are selected. Historical data is then segmented into infinitely many cumulative loss curves according to a selected covariate predictive of risk. The s-shaped curves are modeled according to a nonlinear kernel. Nonlinear kernel parameters are regressed against time units up to the maturity duration and against selected portfolio covariates. The final regression equations represent the central moment models necessary for prior distribution specification in the hierarchical Bayes model to follow.