The good, the bad, and the asymmetric: Evidence from a new conditional density model

We propose a novel univariate conditional density model and decompose asset returns into a sum of copula-connected unobserved ‘good’ and ‘bad’ shocks. The novelty of this approach comes from two factors: we explicitly model correlation between unobserved shocks and allow for the presence of copula-connected discrete jumps. The proposed framework is very flexible and subsumes other models, such as ‘bad environments, good environments’. Our model shows certain hidden characteristics of returns, explains investors’ behaviour in greater detail, and yields better forecasts of risk measures. The in-sample and out-of-sample performance of our model is better than that of 40 popular GARCH variants. A Monte-Carlo simulation shows that the proposed model recovers the structural parameters of the unobserved dynamics. We estimate the model on S&P 500 data and find that time-dependent non-negative covariance between ‘good’ and ‘bad’ shocks with a leverage-like effect is an important component of total variance. Asymmetric reaction to shocks is present almost in all characteristics of returns. Conditional distribution of seems to be very time-dependent with skewness both in the centre and tails. We conclude that continuous shocks are more important than discrete jumps at least at daily frequency.