Risk Metrics Evaluation for Variable Annuities with Various Guaranteed Benefits

Abstract

Variable annuities (VAs) are popularly traded around the world. Thus, the risk metrics for VAs are critical in risk management, reserves, and risk-based capital calculation for insurance companies. However, there is no efficient method to compute these metrics of VAs with various benefits, except for nested simulations. In this article, the authors apply a derivative pricing technique, the willow tree, to solve this common insurance problem. An efficient and accurate approach is proposed based on the willow tree structure. Numerical experiments illustrate the efficiency and effectiveness of their method. Moreover, it is observed that mortality risk and interest rate risk are two key risk factors for the liability of VAs. In order to manage the risk of VAs effectively, insurance companies should hedge the downside risk of interest rates and implement hedging strategies based on the ages of policyholders, rather than the type of guaranteed benefits. The numerical approach starts from the definition of risk metrics; thus, the proposed idea can also be applied to estimate the VaR and expected shortfall of financial derivatives.

TOPICS: Derivatives, options, VAR and use of alternative risk measures of trading risk

Key Findings

• • We propose a universal efficient lattice algorithm for computing two commonly used risk metrics, value-at-risk (VaR) and conditional tail expectation (CTE), for the liability of VAs with various guaranteed benefits from the insurer’s perspective.

• • Our article is the first one to study the VaR and CTE of the net liability based on a derivative pricing technique, the willow tree method.

• • Our method starts from the definition of VaR and CTE with basic probability knowledge, so it can be extended to evaluate risk metrics for other derivatives.