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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

In August 2020 we published "Comprehensive Internal Model Data for Three Portfolios" as an outcome of our work for the committee "Actuarial Data Science" of the German Actuarial Association. The data sets include realistic cash-flow models outputs used for proxy modelling of life and health insurers. Using these data, we implement the hitherto most promising model in proxy modeling consisting of ensembles of feed-forward neural networks and compare the results with the least squares Monte Carlo (LSMC) polynomial regression. To date, the latter represents—to our best knowledge—the most accurate proxy function productively in use by insurance companies. An additional goal of this publication is a more precise description of "Comprehensive Internal Model Data for Three Portfolios" for other researchers, practitioners and regulators interested in developing solvency capital requirement (SCR) proxy models. [ABSTRACT FROM AUTHOR]

In this paper, we take the point of view of an insurer dealing with life annuities, which aims at building up a (partial) internal model in order to quantify the impact of mortality risks, namely process and longevity risk, in view of taking appropriate risk management actions. We assume that a life table, providing a best-estimate assessment of annuitants' future mortality is available to the insurer; conversely, the insurer has no access to data sets and the methodology underlying the construction of the life table. Nonetheless, the insurer is aware that, in the presence of mortality risks, a stochastic approach is required. The (projected) life table, which provides a deterministic description of future mortality, should then be used as the basic input of a stochastic model. The model we propose focuses on the annual number of deaths in a given cohort, which we represent allowing for a random mortality rate. To this purpose, we adopt the widely used Poisson model, first assuming a Gamma-distributed random parameter, and second introducing time-dependence in the parameter itself Further, we define a Bayesian-inferential procedure for updating the parameters to experience in some situations. The setting we define does not demand advanced analytical tools, while allowing for process and longevity risk in a rigorous way. The model is then implemented for capital allocation purposes. We investigate the amount of the required capital for a given life annuity portfolio, based on solvency targets which could be adopted within internal models. The outcomes of such an investigation are compared with the capital required according to some standard rules, in particular those proposed within the Solvency 2 project. [ABSTRACT FROM AUTHOR]