A Spatial Interpolation Framework for Efficient Valuation of Large Portfolios of Variable Annuities

TL;DR

This paper introduces a spatial interpolation framework that significantly reduces computational costs while accurately valuing large portfolios of variable annuities, outperforming traditional nested Monte Carlo methods.

Contribution

The paper proposes a novel spatial interpolation approach for large VA portfolio valuation, addressing scalability issues of existing academic methods and nested Monte Carlo simulations.

Findings

Interpolation schemes outperform nested MC in efficiency and accuracy

The framework enables scalable valuation of large VA portfolios

Guidelines for building automated, effective interpolation schemes

Abstract

Variable Annuity (VA) products expose insurance companies to considerable risk because of the guarantees they provide to buyers of these products. Managing and hedging these risks requires insurers to find the value of key risk metrics for a large portfolio of VA products. In practice, many companies rely on nested Monte Carlo (MC) simulations to find key risk metrics. MC simulations are computationally demanding, forcing insurance companies to invest hundreds of thousands of dollars in computational infrastructure per year. Moreover, existing academic methodologies are focused on fair valuation of a single VA contract, exploiting ideas in option theory and regression. In most cases, the computational complexity of these methods surpasses the computational requirements of MC simulations. Therefore, academic methodologies cannot scale well to large portfolios of VA contracts. In this paper, we present a framework for valuing such portfolios based on spatial interpolation. We provide a comprehensive study of this framework and compare existing interpolation schemes. Our numerical results show superior performance, in terms of both computational efficiency and accuracy, for these methods compared to nested MC simulations. We also present insights into the challenge of finding an effective interpolation scheme in this framework, and suggest guidelines that help us build a fully automated scheme that is efficient and accurate.