Efficient valuation of variable annuity portfolios with dynamic programming

The valuation of variable annuity portfolios presents major challenges for US life insurers. Recent studies propose machine learning and metamodeling techniques based on selecting a few representative guarantees. However, these methods face a critical trade‐off between speed and accuracy. In contrast, I propose a recursive dynamic programming approach and demonstrate its ability to value a large and highly heterogeneous variable annuity 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). This makes the dynamic programming approach ideally suited for all variable annuity applications, including the computation of reserves and capital requirements and to determine the insurer's hedging position. Moreover, dynamic programming can naturally incorporate optimal policyholder behavior into the insurer's valuation.