Variance Gamma模型下欧式与美式期权的柳树法定价

Willow Tree Method for European and American Option Pricing Under Variance Gamma Model

摘要:

现有的Variance Gamma模型下期权定价方法计算复杂，工作量大，因此提出了欧式与美式期权的快速定价柳树法。在构建过程中，使用Johnson曲线构造服从VG过程的资产价格节点，并用傅里叶余弦级数近似的方法计算资产价格节点之间的转移概率。最后，从理论上证明柳树法定价欧式期权的收敛性。通过数值实验，表明柳树法与现有方法相比有相同的精度，但计算速度更快。

Abstract:

Existing methods for European and American option pricing under the VG model are quite complex and time consuming in calculation. Thus, an efficient and accurate Willow tree method is proposed in this paper. Johnson curve is used to construct the asset price nodes in the VG process and the FFT-COS method is used to calculate the transfer probability between asset price nodes. Besides, the theoretical convergence of the Willow tree method for European options is analyzed. Moreover, some numerical experiments are conducted to demonstrate the efficiency and accuracy of the proposed method.