Valuation of Large Variable Annuity Portfolios Under Nested Simulations: A Functional Data Approach

Abstract

Variable annuities are equity-linked annuity products that have rapidly grown in popularity around the world in recent years. Research up to date on variable annuity largely focuses on the valuation of guarantees embedded in a single variable annuity contract. However, methods developed for individual VA contracts based on option pricing theory cannot be extended to large variable annuity portfolios. Insurance companies currently use nested simulations to value guarantees for variable annuity portfolios but efficient valuation under nested simulations for a very large variable annuity portfolio has been a real challenge. The computation in nested simulations are highly intensive and often prohibitive. In this paper, we propose a novel method that combines a clustering technique with a functional data analysis technique to address this issue. We create a highly non-homogeneous synthetic variable annuity portfolio of 100,000 contracts and use it to estimate the dollar Deltas of the portfolio at each time step of outer loop scenarios under the nested simulation framework over a period of 30 years. Our test results show that the proposed method performs well in terms of accuracy and efficiency.

Keywords: Variable annuity, Monte Carlo simulation, Nested simulation, Stochastic-on-stochastic, Portfolio valuation, Clustering, Functional data analysis

JEL Classification: G12, G13