Generalized Finite Integration Method with Laplace Transform for European Option Pricing under Black-Scholes and Heston Models

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Original languageEnglish
Article number105751
Journal / PublicationEngineering Analysis with Boundary Elements
Volume164
Online published3 May 2024
Publication statusPublished - Jul 2024

Abstract

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 Hestonmodel respectively. Instead of using traditional time-stepping process, we first perform Laplacetransform on the governing equation and boundary conditions to remove the temporal derivatives. The Generalized Finite Integration Method is then exploited to handle the spatial differentialoperators in the transformed space. From numerical Laplace inversion algorithm, we restore therequired time-dependent option price. For verification, several option pricing models governedby one-dimensional Black–Scholes equation and two-dimensional extended Heston equation areconstructed to demonstrate the efficiency and feasibility of the proposed approach.