Estimate of Downside Risk with Fat‐Tailed and Skewed Models

Abstract

Asset returns are often not normally distributed and exhibit several stylized empirical facts: fat tails, skewness, finite variance, time scaling, and volatility clustering. Modeling the tail distribution of asset returns plays an essential role in downside risk management. The “left tail” of the distribution is where market crashes or crises occur. Downside risk can be measured in terms of conditional value-at-risk and estimated by fat-tailed and skewed models such as Levy stable, truncated Levy flight, skewed Student's t, mixture of normal distributions, and GARCH models. These fat-tailed and skewed models have different characteristics in describing the tail distribution of asset returns. The objective is to select appropriate ones that can accurately model the downside risk. Keywords: Levy stable; Student's t; mixture of normal distributions; GARCH; truncated Levy flight; fat tails; skewness; downside risk; Conditional value-at-risk; kurtosis; truncated Levy flight; monthly; weekly; weekly; The Random Character of Stock Market Prices