Forecasting value at risk and expected shortfall in equity markets of high-income and Latin American countries

Abstract

Using daily equity market data for Latin American (Latam) and high-income (HI) countries over 2008-2023, this paper estimates GARCH and GJR models to forecast Value at Risk (VaR) and Expected Shortfall (ES). The performance of a broad set of heavy-tailed and asymmetric distributions is evaluated, including the Normal (N), Skewed Normal (skN), Student’s t (S), skewed S (skS), generalized hyperbolic skS (GHskS), normal inverse Gaussian (NIG), skewed NIG (skNIG), normal reciprocal inverse Gaussian (NRIG), and skewed NRIG (skNRIG). The key findings can be summarized as follows: (i) for VaR forecasting, asymmetric distributionsare preferred at both confidence levels, and at the 99% level heavy tails are also required; (ii) for ES forecasting, at both confidence levels the selected models rely on asymmetric heavy-tailed distributions, with GHskS emerging as the dominant specification; (iii) for VaR forecasting, modeling leverage effects is necessary for most HI countries, whereas this is required for only about half of the Latam countries; and (iv) for ES forecasting, volatility specification plays a more limited role than in VaR forecasting.