Efficient Valuation of Variable Annuity Portfolios with Dynamic Programming

Abstract

The valuation of variable annuity (VA) portfolios presents major challenges for life insurers. Recent studies propose approximation methods based on selecting a few representative guarantees. In contrast, I present a bottom-up valuation approach using recursive dynamic programming (RDP). An in-depth numerical analysis shows that the RDP estimation is able to value a large VA portfolio with a high degree of accuracy and within a few seconds---even under stochastic interest rates and volatility---since the heavy computational burden can be fully front-loaded (in a one-time effort at the guarantee's pricing stage). The RDP approach outperforms competing methods in both speed and accuracy and is thus ideally suited for various VA-related applications, including the computation of GAAP reserves, statutory reserves and capital requirements, as well as to determine the insurer's hedging position. Moreover, RDP can naturally incorporate optimal policyholder behavior into the insurer's valuation.