Pricing Options under Jump-Diffusion Models by Adaptive Radial Basic Functions

Ron Chan

Research output: Working paper

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Abstract

The aim of this paper is to show that option prices in jump-diffusion models can be computed using meshless methods based on Radial Basis Function (RBF) interpolation instead of traditional mesh-based methods like Finite Differences (FDM) or Finite Elements (FEM). The RBF technique is demonstrated by solving the partial integro-differential equation for American and European options on non-dividend-paying stocks in the Merton jump-diffusion model, using the Inverse Multiquadric Radial Basis Function (IMQ). The method can in principle be extended to Levy-models. Moreover, an adaptive method is proposed to tackle the accuracy problem caused by a singularity in the initial condition so that the accuracy in option pricing in particular for small time to maturity can be improved.
Original languageEnglish
Place of PublicationBath, U. K.
PublisherDepartment of Economics, University of Bath
Publication statusPublished - 7 Jun 2010

Publication series

NameBath Economics Research Working Papers
No.06/10

Keywords

  • the Merton Jump-diffusions Model
  • singularity
  • option pricing
  • adaptive method
  • Radial Basis Function
  • Levy processes
  • parabolic partial integro-differential equations

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    Chan, R. (2010). Pricing Options under Jump-Diffusion Models by Adaptive Radial Basic Functions. (Bath Economics Research Working Papers; No. 06/10). Department of Economics, University of Bath.