Generalized Finite Integration Method with Laplace transform for European option pricing under Black–Scholes and Heston models

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...

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Vydáno v:Engineering analysis with boundary elements Ročník 164; s. 105751
Hlavní autoři: Ma, Y., Shi, C.Z., Hon, Y.C.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Ltd 01.07.2024
Témata:
Black–Scholes model
Generalized Finite Integration Method
Heston model
Laplace transform
Option pricing
Generalized Finite Integration Method
Laplace transform
Option pricing
Black–Scholes model
Heston model
ISSN:0955-7997
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Popis
Shrnutí: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.
ISSN:0955-7997
DOI:10.1016/j.enganabound.2024.105751