Marginal consistent dependence modelling using weak subordination for Brownian motions |
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Authors: | Markus Michaelsen Alexander Szimayer |
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Institution: | 1. Faculty of Business, Economics and Social Sciences, Universit?t Hamburg , Von-Melle-Park 5, Hamburg, 20146 Germany.markus.michaelsen@wiso.uni-hamburg.de;3. Faculty of Business, Economics and Social Sciences, Universit?t Hamburg , Von-Melle-Park 5, Hamburg, 20146 Germany. |
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Abstract: | We present an approach for modelling dependencies in exponential Lévy market models with arbitrary margins originated from time changed Brownian motions. Using weak subordination of Buchmann et al. Bernoulli, 2017], 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 multivariate variance gamma models on various market data and show that these models are highly preferable to traditional approaches. Consistent values of basket-options under given marginal pricing models are achieved using the Esscher transform, generating a non-flat implied correlation surface. |
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Keywords: | Lévy processes Dependence modelling Weak multivariate subordination Maximum likelihood estimation Variance gamma Normal inverse Gaussian |
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