Error analysis in fourier methods for option pricing

Fabian Crocce Flores, Juho Happola*, Jonas Kiessling, Raul Tempone

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We provide a bound for the error committed when using a Fourier method to price European options, when the underlying follows an exponential Lévy dynamic. The price of the option is described by a partial integro-differential equation (PIDE). Applying a Fourier transformation to the PIDE yields an ordinary differential equation (ODE) that can be solved analytically in terms of the characteristic exponent of the Lévy process. Then, a numerical inverse Fourier transform allows us to obtain the option price. We present a bound for the error and use this bound to set the parameters for the numerical method. We analyze the properties of the bound and demonstrate the minimization of the bound to select parameters for a numerical Fourier transformation method in order to solve the option price efficiently.

Original languageEnglish (US)
Pages (from-to)53-82
Number of pages30
JournalJournal of Computational Finance
Volume21
Issue number1
DOIs
StatePublished - Jun 1 2017

Keywords

  • Error analysis
  • European options
  • Fourier methods
  • Lévy processes
  • Trapezoid quadrature

ASJC Scopus subject areas

  • Finance
  • Computer Science Applications
  • Applied Mathematics

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