Value at Risk Estimation for Life Insurance Using Monte Carlo Simulation Based on an ARIMA Model with a Generalized Error Distribution (GED) Assumption

Abstract

Extreme increases in life insurance claims can threaten an insurer’s solvency and liquidity. This study estimates the Value at Risk (VaR) of monthly life insurance claims in Indonesia using an Autoregressive Integrated Moving Average (ARIMA) model with a Generalized Error Distribution (GED) innovation, combined with Monte Carlo simulation. Monthly aggregate claims data from the Financial Services Authority (OJK), comprising 107 log-return observations, were used. A three-stage procedure (parameter significance, residual white-noise, and minimum AIC) selected ARIMA(0,0,1) as the best mean model, with no remaining autocorrelation or conditional heteroscedasticity. Maximum Likelihood Estimation yielded a GED shape parameter of ν̂ = 0.731368, indicating heavier tails than the normal distribution. Because the relevant risk for an insurer is a surge in claims, VaR was estimated on the upper tail of the one-month-ahead return distribution through 110,000 Monte Carlo replications. At the 99% confidence level, the estimated VaR was 0.91646 in log-return terms, equivalent to a potential increase of approximately IDR 21.07 trillion above the reference month’s claim value. Kupiec’s backtest confirmed the model’s validity (LR = 2.1508, p = 0.1425). The ARIMA-GED model with Monte Carlo simulation thus provides a statistically valid basis for estimating extreme claim-surge risk in Indonesian life insurance.