Improving Value-at-Risk prediction under model uncertainty

TL;DR

This paper introduces G-VaR, a new VaR prediction method that accounts for model uncertainty by considering multiple distributions, and demonstrates its superior performance on major stock indices.

Contribution

The paper proposes G-VaR, a novel VaR predictor based on sublinear expectation theory, addressing model uncertainty in financial risk estimation.

Findings

G-VaR outperforms existing benchmark VaR predictors on NASDAQ and S&P500.

G-VaR effectively incorporates model uncertainty into risk prediction.

Experimental results show G-VaR's robustness and accuracy.

Abstract

Several well-established benchmark predictors exist for Value-at-Risk (VaR), a major instrument for financial risk management. Hybrid methods combining AR-GARCH filtering with skewed-$t$ residuals and the extreme value theory-based approach are particularly recommended. This study introduces yet another VaR predictor, G-VaR, which follows a novel methodology. Inspired by the recent mathematical theory of sublinear expectation, G-VaR is built upon the concept of model uncertainty, which in the present case signifies that the inherent volatility of financial returns cannot be characterized by a single distribution but rather by infinitely many statistical distributions. By considering the worst scenario among these potential distributions, the G-VaR predictor is precisely identified. Extensive experiments on both the NASDAQ Composite Index and S\&P500 Index demonstrate the excellent performance of the G-VaR predictor, which is superior to most existing benchmark VaR predictors.