A multivariate Lévy process model with linear correlation
A multivariate Lévy process model with linear correlation
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DOI：
10.1080/14697680902744729
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发表时间：
2009-06
影响因子：
1.3
通讯作者：
Ray Kawai
中科院分区：
文献类型：
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作者：
Ray Kawai
本文建立了一个风险中性的多元L过程模型，并讨论了它在多资产波动率微笑背景下的适用性。我们的公式是基于独立的单变量Lévy过程的线性组合，并且可以很容易地校准为一维边缘分布的集合和给定的线性相关矩阵。我们推导了我们的公式和相关的校准过程是明确定义的条件，并提供了一些与允许闭式特征函数的特定Lévy过程相关的例子。给出了三种货币期权溢价的数值结果，以说明在不同线性相关结构下该公式的有效性。
In this paper, we develop a multivariate risk-neutral Lévy process model and discuss its applicability in the context of the volatility smile of multiple assets. Our formulation is based upon a linear combination of independent univariate Lévy processes and can easily be calibrated to a set of one-dimensional marginal distributions and a given linear correlation matrix. We derive conditions for our formulation and the associated calibration procedure to be well-defined and provide some examples associated with particular Lévy processes permitting a closed-form characteristic function. Numerical results of the option premiums on three currencies are presented to illustrate the effectiveness of our formulation with different linear correlation structures.