Marginal Consistent Dependence Modeling Using Weak Subordination for Brownian Motions

We present an approach for modeling dependencies in exponential Lévy market models with arbitrary margins originated from time changed Brownian motions. Using weak subordination of Buchmann et al. (2016), we face a new layer of dependencies, superior to traditional approaches based on pathwise subordination, since weakly subordinated processes are not required to have independent components considering multivariate stochastic time changes. We apply a subordinator being able to incorporate any joint or idiosyncratic information arrivals. We emphasize multivariate variance gamma and normal inverse Gaussian processes and state explicit formulae for the Lévy characteristics. Using maximum likelihood, we estimate a multivariate variance gamma model on various market data and show that the model is highly preferable to traditional approaches. Consistent values of basket-options under given marginal pricing models are achieved using Esscher transform, generating a non-flat implied correlation surface