Quantile uncertainty and value-at-risk model risk

Area of Science:

• Quantitative Finance
• Risk Management
• Statistical Modeling

Background:

• Quantile estimates are widely used for risk assessment across disciplines.
• Value-at-Risk (VaR) is a key tool in banking risk management.
• Regulatory frameworks like Basel II highlight the need to address model risk.

Purpose of the Study:

• To develop a methodology for quantifying model risk in quantile risk estimates.
• To provide a framework for adjusting risk estimates based on model risk.
• To inform regulatory capital add-ons for financial institutions.

Main Methods:

• Development of a novel framework for adjusting quantile estimates for model risk.
• Utilizing a benchmark representing the authority's state of knowledge.
• Conducting simulation experiments with controlled model risk.
• Applying the methodology to empirical data from a large bank.

Main Results:

• A simulation experiment demonstrated the quantification of Value-at-Risk model risk.
• The study computed the required regulatory capital add-on for banks.
• An empirical example illustrated the practical application of the methodology.

Conclusions:

• The developed methodology effectively quantifies model risk in quantile estimates.
• The framework can be practically applied using readily available bank data.
• Potential applications extend to non-financial risk assessments.