Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Quantile-based modeling of scale dynamics in financial returns for Value-at-Risk and Expected Shortfall forecasting

Xiaochun Liu, Richard Luger

Abstract

We introduce a semiparametric approach for forecasting Value-at-Risk (VaR) and Expected Shortfall (ES) by modeling the conditional scale of financial returns, defined as the difference between two specified quantiles, via restricted quantile regression. Focusing on downside risk, VaR is derived from the left-tail quantile of rescaled returns, and ES is approximated by averaging quantiles below the VaR level. The method delivers robust, distribution-free estimates of extreme losses and captures skewness, heavy tails, and leverage effects. Simulation experiments and empirical analysis show that it often outperforms established models, including GARCH and joint VaR-ES conditional-quantile approaches. An application to daily returns on major international stock indices, spanning the COVID-19 period, highlights its effectiveness in capturing risk dynamics.

Quantile-based modeling of scale dynamics in financial returns for Value-at-Risk and Expected Shortfall forecasting

Abstract

We introduce a semiparametric approach for forecasting Value-at-Risk (VaR) and Expected Shortfall (ES) by modeling the conditional scale of financial returns, defined as the difference between two specified quantiles, via restricted quantile regression. Focusing on downside risk, VaR is derived from the left-tail quantile of rescaled returns, and ES is approximated by averaging quantiles below the VaR level. The method delivers robust, distribution-free estimates of extreme losses and captures skewness, heavy tails, and leverage effects. Simulation experiments and empirical analysis show that it often outperforms established models, including GARCH and joint VaR-ES conditional-quantile approaches. An application to daily returns on major international stock indices, spanning the COVID-19 period, highlights its effectiveness in capturing risk dynamics.
Paper Structure (14 sections, 43 equations, 2 figures, 42 tables)

This paper contains 14 sections, 43 equations, 2 figures, 42 tables.

Table of Contents

  1. Introduction
  2. Quantile-based modeling
  3. Background
  4. Conditional dynamics
  5. Estimating VaR
  6. Approximating ES
  7. Simulation experiments
  8. Simulation design
  9. Benchmark models
  10. Numerical results
  11. Empirical Application
  12. Evaluation of VaR forecasts
  13. Joint evaluation of VaR and ES forecasts
  14. Conclusion

Figures (2)

  • Figure 1: Time series plots of the daily log returns for the S&P 500, DJIA, NASDAQ, and EURO STOXX 50 indices over the sample period. Each plot represents the percentage daily returns computed from adjusted closing prices.
  • Figure 2: Time series plots of the daily log returns for the FTSE 100, DAX, CAC 40, and TSX indices over the sample period. Each plot displays percentage daily returns based on adjusted closing prices.