We propose a two-dimensional fast Fourier transform (FFT) network to retrieve the prices of options that depend on two Levy processes. Applications include, but are not limited to, the valuation of options on two stocks under the Levy processes, and options on a single stock under a random time-change Levy process. The proposed numerical scheme can be applied to different multivariate Levy constructions such as subordination and linear combination provided that the joint characteristic function is available. The proposed FFT-network can be thought of as a lattice approach implemented through the characteristic function. With the prevalent implementation of FFT, the network approach results in significant computational time reduction while maintaining satisfactory accuracy. Furthermore, we investigate option pricing on a single asset where the asset return and its volatility are driven by a pair of dependent Levy processes. Such a model is also called the random time-changed Levy process. Numerical examples are given to demonstrate the efficiency and accuracy of FFT-network applied to exotic and American-style options.

中文翻译：

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用于二元 Lévy 期权定价的 FFT 网络

我们提出了一个二维快速傅立叶变换 (FFT) 网络来检索依赖于两个 Levy 过程的期权价格。应用包括但不限于在 Levy 过程下对两只股票的期权进行估值，以及在随机时变 Levy 过程下对一只股票的期权进行估值。只要联合特征函数可用，所提出的数值方案可以应用于不同的多元 Levy 构造，例如从属和线性组合。所提出的 FFT 网络可以被认为是通过特征函数实现的格子方法。随着 FFT 的普遍实施，网络方法显着减少了计算时间，同时保持了令人满意的精度。此外，我们研究了单个资产的期权定价，其中资产回报及其波动性由一对相关的 Levy 过程驱动。这种模型也称为随机时变 Levy 过程。给出了数值例子来证明 FFT 网络应用于奇异和美式期权的效率和准确性。