Hybrid Laplace transform and finite difference methods for pricing American options under complex models

Jingtang Ma, Zhiqiang Zhou, Zhenyu Cui

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we propose a hybrid Laplace transform and finite difference method to price (finite-maturity) American options, which is applicable to a wide variety of asset price models including the constant elasticity of variance (CEV), hyper-exponential jump–diffusion (HEJD), Markov regime switching models, and the finite moment log stable (FMLS) models. We first apply Laplace transforms to free boundary partial differential equations (PDEs) or fractional partial differential equations (FPDEs) governing the American option prices with respect to time, and obtain second order ordinary differential equations (ODEs) or fractional differential equations (FDEs) with free boundary, which is named as the early exercise boundary in the American option pricing. Then, we develop an iterative algorithm based on finite difference methods to solve the ODEs or FDEs together with the unknown free boundary values in the Laplace space. Both the early exercise boundary and the prices of American options are recovered through inverse Laplace transforms. Numerical examples demonstrate the accuracy and efficiency of the method in CEV, HEJD, Markov regime switching models and the FMLS models.

Original languageEnglish
Pages (from-to)369-384
Number of pages16
JournalComputers and Mathematics with Applications
Volume74
Issue number3
DOIs
StatePublished - Aug 1 2017

ASJC Scopus subject areas

  • Modeling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

Keywords

  • American option pricing
  • Finite difference methods
  • Fractional partial differential equations
  • Laplace transform methods
  • Partial differential equations

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