In this paper, we combine a recently developed Generalized Finite Integration Method (GFIM) with Laplace transform technique for pricing options under the Black Scholes model and Heston model respectively. Instead of using traditional time-stepping process, we first perform Laplace transform on the governing equation and boundary conditions to remove the temporal derivatives. The Generalized Finite Integration Method is then exploited to handle the spatial differential operators in the transformed space. From numerical Laplace inversion algorithm, we restore the required time-dependent option price. For verification, several option pricing models governed by one-dimensional Black–Scholes equation and two-dimensional extended Heston equation are constructed to demonstrate the efficiency and feasibility of the proposed approach.

中文翻译：

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Black-Scholes 和 Heston 模型下欧式期权定价的拉普拉斯变换广义有限积分法


在本文中，我们将最近开发的广义有限积分方法（GFIM）与拉普拉斯变换技术相结合，分别用于布莱克斯科尔斯模型和赫斯顿模型下的期权定价。我们没有使用传统的时间步进过程，而是首先对控制方程和边界条件进行拉普拉斯变换以消除时间导数。然后利用广义有限积分方法来处理变换空间中的空间微分算子。通过数值拉普拉斯反演算法，我们恢复了所需的时间相关期权价格。为了验证，构建了几个由一维 Black-Scholes 方程和二维扩展 Heston 方程控制的期权定价模型，以证明该方法的有效性和可行性。