Statistical Emulators for Pricing and Hedging Longevity Risk Products

TL;DR

This paper introduces statistical emulators using machine learning techniques to efficiently value mortality-linked contracts in complex stochastic models, reducing computational costs and improving accuracy.

Contribution

It presents a novel application of machine learning-based statistical emulators for pricing and hedging longevity risk, replacing traditional nested simulation methods.

Findings

Emulators achieve high approximation accuracy.

Significant reduction in computational time.

Effective in diverse mortality models.

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.