Marginal consistent dependence modelling using weak subordination for Brownian motions
提出一种利用弱从属过程对指数Lévy市场模型进行依赖建模的方法，允许任意边际分布，并通过多元方差伽马模型实证表明其优于传统方法，可用于篮子期权定价。
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.