Efficient willow tree method for variable annuities valuation and risk management☆

Variable annuities (VAs) with various guarantees are popular retirement products in the past decades. However, due to the sophistication of the embedded guarantees, most existing methods only focus on the one of embedded guarantees underlying one specified stochastic model. The method to evaluate VAs with all guarantees and manage its risk is very limited, except for the Monte Carlo method. In this paper, we propose an efficient willow tree method to evaluate VAs embedded with all popular guarantees on the market underlying various stochastic models. Moreover, our tree structure is also applicable to compute dollar delta, value at risk (VaR) and conditional tail expectation (CTE) in hedging and risk-based capital calculation. Numerical experiments demonstrate the accuracy and efficiency of our method in pricing and managing the risk of VAs.