Abstract
Multivariate return distributions consistent with bilateral gamma marginals are formulated and termed multivariate bilateral gamma (MBG). Tail probability distances and Wasserstein Distances between return data, model simulations and their squares evaluate model performance. A full Gaussian copula (FGC) is taken as an alternate test model and the MBG delivers a comparatively better performance for equity pairs. The MBG is however inadequate for the S&P 500 index return when paired with VIX returns. Applying MBG to the S&P 500 index and regressions residuals of the VIX on the S&P 500 index return is successful. This model is termed MBGR. If the residual are taken independent bilateral gamma delivers the model MBGIR. Characteristic function estimations are employed to develop asset specific VIX levels and their joint returns with the asset return are studied. The CBOE skew index is generalized to be asset specific and triples of returns for the asset, its VIX and its Skew are studied using all four models and performance statistics. The model MBGR continues to deliver a good performance.
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