Statistical Emulators for Pricing and Hedging Longevity Risk Products

Abstract: We propose the use of statistical emulators for the purpose of valuing 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. Rather than building ad hoc 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.