Model Selection and Averaging in Financial Risk Management

Abstract

Simulated asset returns are used in many areas of actuarial science. For example, life insurers use them to price annuities, life insurance, and investment guarantees. The quality of those simulations has come under increased scrutiny during the current financial crisis. When simulating the asset price process, properly choosing which model or models to use, and accounting for the uncertainty in that choice, is essential. We investigate how best to choose a model from a flexible set of models. In our regime-switching models the individual regimes are not constrained to be from the same distributional family. Even with larger sample sizes, the standard model-selection methods (AIC, BIC, and DIC) incorrectly identify the models far too often. Rather than trying to identify the best model and limiting the simulation to a single distribution, we show that the simulations can be made more realistic by explicitly modeling the uncertainty in the model-selection process. Specifically, we consider a parallel model-selection method that provides the posterior probabilities of each model being the best, enabling model averaging and providing deeper insights into the relationships between the models. The value of the method is demonstrated through a simulation study, and the method is then applied to total return data from the S&P 500.

Acknowledgments

This work was supported by a generous grant from The Actuarial Foundation. The authors would like to thank an anonymous reviewer, whose comments and suggestions greatly increased the quality of this article. The authors would also like to thank the attendees at the Statistical Society of Canada Annual Meeting in Guelph, the Actuarial Research Conference in Winnipeg, the Montreal Seminar of Actuarial and Financial Mathematics, and the statistics colloquium at Brigham Young University for their insightful comments and questions, namely, Paul Marriott, Daniel Alai, Jed Frees, Saeed Ahmadi, and Mary Hardy.