Evaluating VaR for Equity-Linked Annuities by Forecasting Volatility of S&P 500 Index Return

This paper provides empirical results showing Value-at-Risk(VaR) for equity-linked annuities(ELA) calculated by different volatility models: GARCH, EGARCH, and GJR-GARCH models. We will use two procedures to calculate VaR for ELA. The first procedure examines the performance of various GARCH-type models with regard to forecasting the future volatility of S\&P 500 index daily returns. We use the three GARCH-type models mentioned above to forecast volatility. To further the robustness of estimating results, we compare the empirical performances of the three GARCH-type models for the both in-sample and out-of-sample tests. The second is to calculate VaR for S\&P 500 index return and ELA using the forecasting results of each GARCH-type model. We also calculate the value of ELA and VaR under the Student's t-distribution. Additionally, we analyze the effect of contract terms of ELA on the VaR in this procedure.