Marginal Consistent Dependence Modeling Using Weak Subordination for Brownian Motions

26 Pages Posted: 2 Dec 2017

See all articles by Markus Michaelsen

Markus Michaelsen

Universität Hamburg

Alexander Szimayer

University of Hamburg - Faculty of Economics and Business Administration

Date Written: June 14, 2017

Abstract

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.

Keywords: Lévy processes, Dependence modeling, Weak multivariate subordination, Maximum likelihood estimation, Variance gamma, Normal inverse Gaussian

JEL Classification: C51, G12

Suggested Citation

Michaelsen, Markus and Szimayer, Alexander, Marginal Consistent Dependence Modeling Using Weak Subordination for Brownian Motions (June 14, 2017). Available at SSRN: https://ssrn.com/abstract=3079478 or http://dx.doi.org/10.2139/ssrn.3079478

Markus Michaelsen (Contact Author)

Universität Hamburg ( email )

Von-Melle-Park 5
Hamburg, 20146
Germany

Alexander Szimayer

University of Hamburg - Faculty of Economics and Business Administration ( email )

Von-Melle-Park 5
Hamburg, 20146
Germany

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