Empirical Analysis of Affine Versus Nonaffine Variance Specifications in Jump-Diffusion Models for Equity Indices

Abstract

This paper investigates several crucial issues that arise when modeling equity returns with stochastic variance. (i) Does the model need to include jumps even when using a nonaffine variance specification? We find that jump models clearly outperform pure stochastic volatility models. (ii) How do affine variance specifications perform when compared to nonaffine models in a jump diffusion setup? We find that nonaffine specifications outperform affine models, even after including jumps.Abstract This paper investigates several crucial issues that arise when modeling equity returns with stochastic variance. (i) Does the model need to include jumps even when using a nonaffine variance specification? We find that jump models clearly outperform pure stochastic volatility models. (ii) How do affine variance specifications perform when compared to nonaffine models in a jump diffusion setup? We find that nonaffine specifications outperform affine models, even after including jumps.

Equity index variance: Evidence from flexible parametric jump–diffusion models

“…First, we confirm findings in Ignatieva et al (2015) that jumps improve the in-sample performance, as models in the SV class consistently exhibit the highest DIC values, 16 whereas SVCJ specifications, except for AffineSqr, outperform SVJ. Secondly, non-affine diffusion models in general perform considerably better than affine models.…”

“…Chourdakis and Dotsis (2011) and Mijatovic and Schneider (2014) find evidence for non-linearities in the drift. Similarly, Christoffersen et al (2010) and Ignatieva, Rodrigues, and Seeger (2015) propose a set of non-affine stochastic volatility specifications and highlight the importance of non-linearity. 5 Our model includes various specifications mentioned above as a special case, by either allowing for more general dynamics of variance or extending the models by the possibility of jumps.…”

Model Complexity and Out-of-Sample Performance: Evidence from S&P 500 Index Returns

“…Andersen et al (2002) provide in-sample specification tests as well as option pricing implications. Kaeck (2013) and Ignatieva et al (2015) rely on the deviance information criterion, an in-sample Bayesian fit statistic developed in Spiegelhalter et al (2002). Christoffersen et al (2010) provide (in-sample) QQ plots as well scatter plots of variance level changes, and conclude that affine variance processes are rejected by the data.…”

“…2 Another strand of the literature studies multifactor variance specifications, as these support more erratic variance movements (see Chernov et al, 2003 or Kaeck andAlexander, 2012). The literature also presents convincing evidence in favor of non-affine variance dynamics (see Jones, 2003, Christoffersen et al, 2010, Mijatovic and Schneider, 2014, or Ignatieva et al, 2015, albeit often at the cost of tractability as these models do not allow for closed-form characteristic functions. Finally, discrete-time GARCH models as well as discrete-time stochastic volatility specifications provide alternative modeling frameworks; for recent surveys, we refer to Bauwens et al (2006) and Andersen et al (2009).…”

“…This is a surprising result, since numerous papers find that jump models outperform continuous stochastic volatility models in-sample (see focus on a much broader number of models and specification tests. Eraker et al (2003), Eraker (2004) or Ignatieva et al (2015)).…”