Model complexity and out-of-sample performance: evidence from S&P 500 index returns

We apply a range of out-of-sample specification tests to more than forty competing stochastic volatility models to address how model complexity affects out-of-sample performance. Using daily S&P 500 index returns, model confidence set estimations provide strong evidence that the most important model feature is the non-affinity of the variance process. Despite testing alternative specifications during the turbulent market regime of the global financial crisis of 2008, we find no evidence that either finite- or infinite-activity jump models or other previously proposed model extensions improve the out-of-sample performance further. Applications to Value-at-Risk demonstrate the economic significance of our results. Furthermore, the out-of-sample results suggest that standard jump diffusion models are misspecified.