Validation of Long-term Equity Return Models for Equity-linked Guarantees

A number of models have been proposed for the equity return process for equity-linked guarantees, following the introduction of stochastic modeling requirements by the Canadian Institute of Actuaries and the American Academy of Actuaries. In this paper we present some of the models that have become well known and discuss the use of residuals to test the fit. After showing that the use of the static, ‘‘actuarial approach’’ to risk management can result in two models with very similar likelihood and residuals giving very different capital requirements, we propose an extension of the bootstrap to compare all the models and to determine whether the optimistic or pessimistic view of the long-term left tail risk is more consistent with the data. Our context is the determination of capital requirements, so we are concerned in this work with real-world rather than riskneutral processes.