Comparative Evaluation of VaR Models: Historical Simulation, GARCH-Based Monte Carlo, and Filtered Historical Simulation
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914072222498816 |
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| author | Tian, Xin |
| author_facet | Tian, Xin |
| contents | This report presents a comprehensive evaluation of three Value-at-Risk (VaR) modeling approaches: Historical Simulation (HS), GARCH with Normal approximation (GARCH-N), and GARCH with Filtered Historical Simulation (FHS), using both in-sample and multi-day forecasting frameworks. We compute daily 5 percent VaR estimates using each method and assess their accuracy via empirical breach frequencies and visual breach indicators. Our findings reveal severe miscalibration in the HS and GARCH-N models, with empirical breach rates far exceeding theoretical levels. In contrast, the FHS method consistently aligns with theoretical expectations and exhibits desirable statistical and visual behavior. We further simulate 5-day cumulative returns under both GARCH-N and GARCH-FHS frameworks to compute multi-period VaR and Expected Shortfall. Results show that GARCH-N underestimates tail risk due to its reliance on the Gaussian assumption, whereas GARCH-FHS provides more robust and conservative tail estimates. Overall, the study demonstrates that the GARCH-FHS model offers superior performance in capturing fat-tailed risks and provides more reliable short-term risk forecasts. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_05646 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Comparative Evaluation of VaR Models: Historical Simulation, GARCH-Based Monte Carlo, and Filtered Historical Simulation Tian, Xin Risk Management Econometrics Computational Finance Applications 91G70, 62P05, 60G10 91G70, 62P05, 60G1091G70, 62P05, 60G10 91G70, 62P05, 60G10 This report presents a comprehensive evaluation of three Value-at-Risk (VaR) modeling approaches: Historical Simulation (HS), GARCH with Normal approximation (GARCH-N), and GARCH with Filtered Historical Simulation (FHS), using both in-sample and multi-day forecasting frameworks. We compute daily 5 percent VaR estimates using each method and assess their accuracy via empirical breach frequencies and visual breach indicators. Our findings reveal severe miscalibration in the HS and GARCH-N models, with empirical breach rates far exceeding theoretical levels. In contrast, the FHS method consistently aligns with theoretical expectations and exhibits desirable statistical and visual behavior. We further simulate 5-day cumulative returns under both GARCH-N and GARCH-FHS frameworks to compute multi-period VaR and Expected Shortfall. Results show that GARCH-N underestimates tail risk due to its reliance on the Gaussian assumption, whereas GARCH-FHS provides more robust and conservative tail estimates. Overall, the study demonstrates that the GARCH-FHS model offers superior performance in capturing fat-tailed risks and provides more reliable short-term risk forecasts. |
| title | Comparative Evaluation of VaR Models: Historical Simulation, GARCH-Based Monte Carlo, and Filtered Historical Simulation |
| topic | Risk Management Econometrics Computational Finance Applications 91G70, 62P05, 60G10 91G70, 62P05, 60G1091G70, 62P05, 60G10 91G70, 62P05, 60G10 |
| url | https://arxiv.org/abs/2505.05646 |