Forecasting Value at Risk and Expected Shortfall in Equity Markets of High-Income and Latin American Countries

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 distributions are 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.

Keywords: Value at Risk, Expected Shortfall, GARCH Models, Heavy-Tailed Distributions, Latin American Countries, High-Income Countries, Equity Markets, Forex Markets.

JEL classification: C52, C53, G17

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