Effective Forecasting of Insurer Capital Requirements: ARMA-GARCH, ARMA-GARCH-EVT, and DCC-GARCH Approaches

Abstract

This research paper presents a comprehensive analysis of three prominent volatility and dependence models for financial time series: ARMA-GARCH, GARCH-EVT, and DCC-GARCH. These models are employed to assess and forecast capital requirements for life and non-life insurer investments. This study evaluates the models' performance in forecasting Value-at-Risk, using daily data on key Thai financial indicators (representing permissible insurer investment assets) from March 2009 to March 2024. Specifically, 1-day and 10-day VaR forecasts are generated using the ARMA-GARCH and DCC-GARCH models, while the ARMA-GARCH-EVT model is employed for 1-day VaR forecasting. Our findings indicate that the ARMA-GARCH model effectively captures time-varying volatility, while the GARCH-EVT approach enhances tail risk estimation, particularly relevant for stress testing. Additionally, the DCC-GARCH model allows for the examination of dynamic conditional correlations between assets, providing insights into portfolio diversification benefits. Rigorous backtesting procedures, employing Kupiec and Christoffersen tests with a rolling window of 1,000 out-of-sample observations, confirm that the majority of models accurately forecast VaR at their respective horizons, with only a very small subset of 10-day VaR models exhibiting limitations. These results highlight that ARMA-GARCH, ARMA-GARCH-EVT, and DCC-GARCH models offer insurers robust tools for estimating minimum capital requirements, forecasting investment risk, and guiding strategic asset allocation decisions. This research underscores the effectiveness of these models for practical application in the insurance industry while also emphasizing the importance of continued model validation, particularly for extended forecasting horizons. Doi: 10.28991/ESJ-2024-08-06-03 Full Text: PDF