Asymmetric Volatility Modeling with GJR-GARCH and TARCH
Summary
This article extends standard ARCH and GARCH approaches to account for the sign of market shocks. Symmetric GARCH treats positive and negative returns of equal size alike, while the leverage effect describes how negative returns can be followed by sharper volatility increases. The article discusses corporate leverage and investor behavior as possible explanations for this asymmetry.
GJR-GARCH adds an indicator-weighted term to conditional variance so negative shocks can receive extra weight. TARCH instead models conditional standard deviation, using a threshold to amplify shocks on one side and producing a piecewise linear response. The article describes MQL5 implementations, demonstrations using S&P 500 data, impact-curve comparisons, and an equity-versus-forex asymmetry test. It offers these models as tools for volatility forecasting and risk analysis, but gives no broad performance assessment; it also notes that parameter estimates differ between its MQL5 implementation and Python's arch package, possibly because their optimizers differ.
Key ideas
- Standard GARCH loses shock direction when it squares returns, so positive and negative shocks have equal effects.
- GJR-GARCH adds an indicator term that can increase conditional variance after negative returns.
- TARCH models conditional standard deviation and can respond linearly to shock magnitude with a threshold for asymmetry.
- News impact curves illustrate how symmetric GARCH, GJR-GARCH, and TARCH translate shocks into future volatility.
- Parameter estimates may vary between software implementations because their optimization procedures differ.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.