Title: An asymmetrical opposite-signed-shocks GARCH model
Authors: Dmitry Malakhov - National Research University Higher School of Economics (Russia)
Andrei Kostyrka - University of Luxembourg (Luxembourg) [presenting]
Abstract: A new general GARCH-like framework is proposed. Asset returns are decomposed into a sum of copula-connected unobserved positive and negative shocks, possibly with discrete jumps (yielding up to 4 distinct shocks, continuous and discrete, of both signs). We model return distributions in a flexible manner using several parametric families of signed shocks and copulae with dynamic parameters. The model subsumes the Bad environments, good environments model as a special case. We compare our models with 40 well-established GARCH variants by estimating and backtesting them on a total of 19.5 years of S\&P500 daily data. Our models perform better both out of sample (according to Christoffersen and Engle-Manganelli VaR forecast tests) and in sample (according to the non-nested LR tests and information criteria). For Diebold-Mariano forecast accuracy tests for volatilities, the picture is mixed; however, a subset of our models that have the best in-sample results and pass the VaR tests produces forecasts that are not worse than those of the GARCH variants that pass the same tests. Using these models, we reveal the information structure of returns and investors behaviour, e.g., market reaction to positive and negative shocks. Given the complexity of the new models, we use multiple numerical stabilisation techniques, including fail-safe numerical integration, stochastic and deterministic optimisation, robustified numerical derivatives, and parallel-capable estimation routines.