Modeling and evaluating conditional quantile dynamics in VaR forecasts

TL;DR

This paper investigates the dynamic modeling of Value at Risk (VaR) quantiles, proposing a method that improves forecast accuracy by adjusting predictions only when violation frequencies deviate from expected levels, validated through simulations and empirical data.

Contribution

It introduces a novel approach for modeling and evaluating time-varying VaR quantiles using a data-driven adjustment mechanism and assesses forecast performance with the asymmetric Mean Absolute Deviation.

Findings

Significant improvements in VaR forecast accuracy using the proposed method.

The asymmetric Mean Absolute Deviation is effective for ranking forecast performance.

Empirical results on Fama-French portfolios demonstrate the method's practical utility.

Abstract

We focus on the time-varying modeling of VaR at a given coverage $\tau$, assessing whether the quantiles of the distribution of the returns standardized by their conditional means and standard deviations exhibit predictable dynamics. Models are evaluated via simulation, determining the merits of the asymmetric Mean Absolute Deviation as a loss function to rank forecast performances. The empirical application on the Fama-French 25 value-weighted portfolios with a moving forecast window shows substantial improvements in forecasting conditional quantiles by keeping the predicted quantile unchanged unless the empirical frequency of violations falls outside a data-driven interval around $\tau$.