Bivariate Laplace Conditional Distributions for Modeling Non-Linearly Dependent Volatile Price Changes

In the spirit of the solution of for modeling price changes in high-volatility markets for univariate commodities, here we generalize an approach to the case of modeling price changes jointly for two related commodities. Often, conditional distributions are more easily understood in financial markets, where the fluctuations in one commodity can shed significant light on the behavior of a related commodity. With this observation, we enhance and characterize the entire family of bivariate joint densities for which both the conditional distributions are specified to be of the Laplace form. Such bivariate distributions will be referred to as bivariate Laplace conditional (BLC) distributions. We study the marginals of the BLC distributions and establish that they are not only sub-Gaussian but also super-Laplacian and, hence, super-Cauchy, i.e., they have heavier tails than Gaussian distributions but lighter tails than the usual Laplace and Cauchy distributions. Distance correlation is suggested as a measure of the association between the two marginal variables, as their product moment correlation is zero but they may be non-linearly dependent. A real-life data set is analyzed to illustrate the use of BCL distributions in practice. We believe that this is the first work using conditional specifications in bivariate financial data analysis.