A Monte Carlo Simulation Approach to Forecasting Multi-period Value-at-Risk and Expected Shortfall Using the FIGARCH-skT Specification

Abstract

In financial literature, Value-at-Risk (VaR) and Expected Shortfall (ES) modelling is focused on producing 1-step ahead conditional variance forecasts. The present paper provides a methodological contribution to the multi-step VaR and ES forecasting through a new adaptation of the Monte Carlo simulation approach for forecasting multi-period volatility to a fractionally integrated GARCH framework for leptokurtic and asymmetrically distributed portfolio returns. Accounting for long memory within the conditional variance process with skewed Student-t (skT) conditionally distributed innovations, accurate 95% and 99% VaR and ES forecasts are calculated for multi-period time horizons. The results show that the FIGARCH-skT model has a superior multi-period VaR and ES forecasting performance.

Keywords: Expected Shortfall, FIGARCH, Forecasting, stock indices, skewed Student-t, Volatility, Long Memory, Value-at-Risk, VaR

JEL Classification: G17; G15; C15; C32; C53