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

Abstract

Variable Annuity (VA) products expose insurance companies to considerable risk becauseof the guarantees they provide to buyers of these products. Managing and hedging these risks requireinsurers to find the values of key risk metrics for a large portfolio of VA products. In practice, manycompanies rely on nested Monte Carlo (MC) simulations to find key risk metrics. MC simulations arecomputationally demanding, forcing insurance companies to invest hundreds of thousands of dollars incomputational infrastructure per year. Moreover, existing academic methodologies are focused on fairvaluation of a single VA contract, exploiting ideas in option theory and regression. In most cases, thecomputational complexity of these methods surpasses the computational requirements of MC simulations.Therefore, academic methodologies cannot scale well to large portfolios of VA contracts. In thispaper, we present a framework for valuing such portfolios based on spatial interpolation. We providea comprehensive study of this framework and compare existing interpolation schemes. Our numericalresults show superior performance, in terms of both computational effciency and accuracy, for thesemethods compared to nested MC simulations. We also present insights into the challenge of findingan effective interpolation scheme in this framework, and suggest guidelines that help us build a fullyautomated scheme that is effcient and accurate.

Keywords

• variable annuity
• spatial interpolation
• Kriging
• inverse distance weighting
• radial basis function
• portfolio valuation