Tree-based Models for the Efficient Valuation of Large Variable Annuity Portfolios

Because of attractive guarantee features, variable annuities have become popular retirement and investment vehicles. Insurance companies often face the challenge of managing the financial risks associated with these guarantees. Dynamic hedging is a common practice among insurers but requires frequent valuation of the fair market values of the guarantees. Insurers rely on the use of Monte Carlo simulation, which is flexible but computationally intensive. Metamodels are increasing in popularity as efficient approaches for addressing the computational issues. In this paper, we use a synthetic dataset with 190,000 variable annuity contracts to empirically examine the performance of tree-based models for the valuation of the guarantees. In particular, we compare the predictive accuracy of five tree-based models that include traditional regression tree, ensemble methods, and trees based on unbiased recursive partitioning, as well as models based on ordinary kriging and GB2 regression. Our results indicate that tree-based models are generally very efficient in producing more accurate predictions and the gradient boosting ensemble method is considered the most superior.