Time-varying mixture GARCH models and asymmetric volatility

Abstract

The class of mixed normal conditional heteroskedastic (MixN-GARCH) models, which couples a mixed normal distributional structure with GARCH-type dynamics, has been shown to offer a plausible decomposition of the contributions to volatility, as well as excellent out-of-sample forecasting performance, for financial asset returns. In this paper, we generalize the MixN-GARCH model by relaxing the assumption of constant mixing weights. Two different specifications with time-varying mixing weights are considered. In particular, by relating current weights to past returns and realized (component-wise) likelihood values, an empirically reasonable representation of Engle and Ng's (1993) news impact curve with an asymmetric impact of unexpected return shocks on future volatility is obtained. An empirical out-of-sample study confirms the usefulness of the new approach and gives evidence that the leverage effect in financial returns data is closely connected, in a non-linear fashion, to the time-varying interplay of mixture components representing, for example, various groups of market participants. The class of mixed normal conditional heteroskedastic (MixN-GARCH) models, which couples a mixed normal distributional structure with GARCH-type dynamics, has been shown to offer a plausible decomposition of the contributions to volatility, as well as excellent out-of-sample forecasting performance, for financial asset returns. In this paper, we generalize the MixN-GARCH model by relaxing the assumption of constant mixing weights. Two different specifications with time-varying mixing weights are considered. In particular, by relating current weights to past returns and realized (component-wise) likelihood values, an empirically reasonable representation of Engle and Ng's (1993) news impact curve with an asymmetric impact of unexpected return shocks on future volatility is obtained. An empirical out-of-sample study confirms the usefulness of the new approach and gives evidence that the leverage effect in financial returns data is closely connected, in a non-linear fashion, to the time-varying interplay of mixture components representing, for example, various groups of market participants.

Enhancing Portfolio Performance and VIX Futures Trading Timing with Markov-Switching GARCH Models

“…This means that we estimated a stochastic process with only a scale (standard deviation) regime-switching parameter. This is done to achieve a more stable and feasible solution in the estimation method [28][29][30][31].…”

“…By the fact that VIX futures could be an important diversification and risk hedging tool, we propose the use of MS models to determine the timing of VIX futures investing. More specifically, we propose the use of MS models, and their extension with Generalized Autoregressive Conditional Heteroskedaticity (MS-GARCH) variances [28][29][30][31]. This, to forecast the regime-specific smoothed probabilities (ξ s=i,t+1 ) at t + 1.…”

An investigation of higher order moments of empirical financial data and their implications to risk

“…To understand the origins of these different scaling relations we simulate a GARCH-normal(1,1) model and a GARCH-double-normal(1,1) model, used before in, [10] , [28] , [29] . We first simulate a GARCH model with a given conditional distribution and a given set of time-independent parameters for a large number of events.…”

Asymmetric stable Paretian distribution testing

“…where 0 λ 1 and f N denotes the normal pdf. The use of the MixN for modeling financial asset returns has a substantial history; see Haas et al (2004), Haas et al (2013), Paolella (2013), and the references therein. The next is a two-component SαS mixture:…”