Comparison of Value at Risk (VaR) Multivariate Forecast Models.

Area of Science:

• Quantitative Finance
• Risk Management
• Econometrics

Background:

• Accurate Value at Risk (VaR) forecasting is crucial for financial risk management.
• Traditional methods like Historical Simulation (HS) are often compared against more sophisticated models.
• Understanding model performance across different market conditions and estimation parameters is essential.

Purpose of the Study:

• To evaluate and compare the performance of various multivariate VaR forecasting models.
• To assess the impact of different significance levels, rolling windows, and portfolio weighting strategies on VaR accuracy.
• To determine the optimal model balancing risk overestimation and underestimation costs.

Main Methods:

• Comparison of HS, DCC-GARCH, GO-GARCH, and Vine copula models for VaR estimation.
• Application of normal, Student's t, and skewed Student's t marginal distributions for copula models.
• Portfolio construction using 6 and 12 Ibovespa stocks with two weighting strategies.
• Utilized rolling windows (500, 1000 observations) and significance levels (1%, 2.5%, 5%) for risk estimation.
• Performance evaluation based on realized loss and cost metrics.

Main Results:

• VaR model performance is highly sensitive to chosen significance levels, rolling window sizes, and portfolio weighting strategies.
• The model offering the best balance between overestimation and underestimation costs did not align with the model indicated by realized loss.
• Different multivariate models exhibited varying degrees of accuracy and cost-efficiency.

Conclusions:

• No single VaR model universally outperforms others across all tested configurations.
• The choice of parameters (significance level, window size, weighting strategy) significantly influences risk forecast outcomes.
• A comprehensive evaluation considering both realized loss and estimation costs is necessary for selecting appropriate VaR models.