Marginal consistent dependence modelling using weak subordination for Brownian motions
Marginal consistent dependence modelling using weak subordination for Brownian motions
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DOI：
10.1080/14697688.2018.1439182
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发表时间：
2018-11
影响因子：
1.3
通讯作者：
Markus Michaelsen;Alexander Szimayer
中科院分区：
文献类型：
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作者：
Markus Michaelsen;Alexander Szimayer
我们提出了一种方法来建模的依赖性指数Lévy市场模型的任意利润起源于时变布朗运动。使用Buchmann等人的弱从属[Bernoulli，2017]，我们面临一个新的依赖层，比基于路径从属的传统方法更上级，因为考虑到多元随机时间变化，弱从属过程不需要具有独立分量。我们应用一个从属能够纳入任何联合或特质的信息到达。我们强调多元方差伽玛和正常的逆高斯过程和状态明确的公式的Lévy特征。使用最大似然法，我们估计各种市场数据的多元方差伽马模型，并表明这些模型是非常可取的传统方法。在给定的边际定价模型下，使用Esscher变换实现了篮子期权的一致价值，生成了一个非平坦的隐含相关曲面。
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.