Statistical emulators for pricing and hedging longevity risk products

Abstract

We propose the use of statistical emulators for the purpose of analyzing mortality-linked contracts in stochastic mortality models. Such models typically require (nested) evaluation of expected values of nonlinear functionals of multi-dimensional stochastic processes. Except in the simplest cases, no closed-form expressions are available, necessitating numerical approximation. To complement various analytic approximations, we advocate the use of modern statistical tools from machine learning to generate a flexible, non-parametric surrogate for the true mappings. This method allows performance guarantees regarding approximation accuracy and removes the need for nested simulation. We illustrate our approach with case studies involving (i) a Lee–Carter model with mortality shocks; (ii) index-based static hedging with longevity basis risk; (iii) a Cairns–Blake–Dowd stochastic survival probability model; (iv) variable annuities under stochastic interest rate and mortality.