The value of multivariate model sophistication: An application to pricing Dow Jones Industrial Average options

We assess the predictive accuracies of a large number of multivariate volatility models in terms of pricing options on the Dow Jones Industrial Average. We measure the value of model sophistication in terms of dollar losses by considering a set of 444 multivariate models that differ in their specification of the conditional variance, conditional correlation, innovation distribution, and estimation approach. All of the models belong to the dynamic conditional correlation class, which is particularly suitable because it allows consistent estimations of the risk neutral dynamics with a manageable amount of computational effort for relatively large scale problems. It turns out that increasing the sophistication in the marginal variance processes (i.e., nonlinearity, asymmetry and component structure) leads to important gains in pricing accuracy. Enriching the model with more complex existing correlation specifications does not improve the performance significantly. Estimating the standard dynamic conditional correlation model by composite likelihood, in order to take into account potential biases in the parameter estimates, generates only slightly better results. To enhance this poor performance of correlation models, we propose a new model that allows for correlation spillovers without too many parameters. This model performs about 60% better than the existing correlation models we consider. Relaxing a Gaussian innovation for a Laplace innovation assumption improves the pricing in a more minor way. In addition to investigating the value of model sophistication in terms of dollar losses directly, we also use the model confidence set approach to statistically infer the set of models that delivers the best pricing performances.