Comparative Evaluation of VaR Models: Historical Simulation, GARCH-Based Monte Carlo, and Filtered Historical Simulation

Xin Tian

Papers from arXiv.org

Abstract: 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.

Date: 2025-05
New Economics Papers: this item is included in nep-ets, nep-for and nep-rmg
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/2505.05646 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2505.05646

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().