Monte Carlo-based VaR estimation and backtesting under Basel III

Value-at-Risk (VaR) is a key metric widely applied in market risk assessment and regulatory compliance under the Basel III framework. This study compares two Monte Carlo-based VaR models using publicly available equity data: a return-based model calibrated to historical portfolio volatility, and a CAPM-style factor-based model that simulates risk via systematic factor exposures. The two models are applied to a technology-sector portfolio and evaluated under historical and rolling backtesting frameworks. Under the Basel III backtesting framework, both initially fall into the red zone, with 13 VaR violations. With rolling-window estimation, the return-based model shows modest improvement but remains in the red zone (11 exceptions), while the factor-based model reduces exceptions to eight, placing it into the yellow zone. These results demonstrate the advantages of incorporating factor structures for more stable exception behavior and improved regulatory performance. The proposed framework, fully transparent and reproducible, offers practical relevance for internal validation, educational use, and model benchmarking.