Cosine Willow Tree Structure under Lévy Processes with Application to Pricing Variance Derivatives
Cosine Willow Tree Structure under Lévy Processes with Application to Pricing Variance Derivatives
复制标题
DOI：
10.3905/jod.2021.1.140
复制
发表时间：
2021-09
期刊：
影响因子：
--
通讯作者：
Junmei Ma;Wei Xu;Yingdong Yao
中科院分区：
文献类型：
--
作者：
Junmei Ma;Wei Xu;Yingdong Yao
Lévy过程模型可以捕捉突发外生事件导致的价格大幅变化，可以更好地展现金融数据的高峰和重尾特征。傅里叶变换方法因其效率、如何将模型与收益函数分离以及如何处理具有特征函数的模型而以 Lévy 过程下的衍生品定价而闻名，但因其对路径依赖的限制而受到批评。在本文中，我们提出了一种统一的余弦柳树方法，它继承了变换方法的优点但克服了其缺点。此外，对冲希腊人可以作为树结构的副产品以较小的额外成本获得。还讨论了一些流行的方差导数，以证明所提出的方法在处理路径依赖方面的灵活性。最后，分析了各种 Lévy 过程模型的理论收敛性。
Lévy process models can capture the large price changes on sudden exogenous events and can better demonstrate the high peak and heavy tail characteristics of financial data. The Fourier transformation method is famous for pricing derivatives under the Lévy processes beause of its efficiency, how it separates models from payoff function, and how it handles models with characteristic functions, but it is criticized for its restriction on path dependency. In this article, we propose a unified cosine willow tree method, which inherits the merits of the transformation method but overcomes its shortcomings. Moreover, the hedging Greeks can be obtained as a by-product from the tree structure with minor extra cost. Some popular variance derivatives are also discussed to demonstrate the flexibility of the proposed method in handling path dependency. Finally, the theoretical convergence is analyzed for various Lévy process models.