Economic Representative Scenarios for Variable Annuity Dynamic Hedging of GMMB and GMDB

Abstract

Variable annuities introduce significant risk for the insurers. To control this risk, insurers generally use dynamic hedging models. In practice, calculations for dynamic hedging models for variable annuities are computationally intensive since they require many nested stochastic scenario projections with outer and inner loops. In this article, we study the relationship between the hedging errors and the descriptive statistics of economic scenarios. Then, using the relationships between the hedging errors and the descriptive statistics of the economics scenarios, we present two novel scenario selection algorithms to determine economic representative scenarios (ERS) to run for dynamic risk hedging models. We do this for guaranteed minimum maturity benefit (GMMB) and guaranteed minimum death benefit (GMDB). We also benchmark these new algorithms against a control variate algorithm and Monte Carlo simulations. One of the two proposed novel scenario selection algorithms, the adapted Clara algorithm gives a lower mean absolute deviation of the conditional tail expectation (CTE) than the control variate method and Monte Carlo simulations for the same number of scenarios. Also, 500 representative scenarios selected by the adapted Clara algorithm generate a mean absolute deviation of the CTE95 of the hedging errors approximately equivalent to 1000 (or more in some cases) Monte Carlo simulations for 5 years GMMB and GMDB.