Authors: Andrei Kostyrka and Dmitry Malakhov.
Abstract: We propose a univariate conditional density model where asset returns are decomposed into a sum of copula-connected unobserved positive and negative shocks, both continuous and discrete, thus yielding up to 4 distinct shocks. The ‘Bad environments, good environments’ model is a special case of our model with zero-mean uncorrelated shocks, dynamic shape parameters, and without jumps. We compare our models with different marginal distributions and copulæ to 40 well-established GARCH variants (4 distributions, 10 volatility dynamics) by backtesting them on a sample of S&P500 daily data. Our models with dynamic scale parameters and without jumps perform better both in sample and out of sample compared with standard models. However, all dynamic-shape models have on average poor out-of-sample performance. Using the best-performing model, we reveal some hidden characteristics of returns behaviour. We show that the independence assumption for signed shocks does not hold: models with correlated shocks perform better, covariance is an important component of total variance, and it is time-dependent with a leverage-like effect. Conditional skewness behaviour reveals naïve investors' expectations. The U.S. market on average has a propensity for bull trends and a lower possibility of a bear trend during crisis times. The relation between returns and volatility is either very non-linear or insignificant. In this draft we also show preliminary results for models with jumps which indicate that introduction of discrete jumps does not improve the model performance; however, negative jumps have greater sizes, and occur more frequently.