Journal of Computational Finance

Risk.net

Error analysis in Fourier methods for option pricing

Fabián Crocce, Juho Häppölä, Jonas Kiessling and Raúl Tempone

  • We present an error analysis in using Fourier methods for pricing European options when the underlying asset follows an exponential Levy process.
  • The derived bound is minimised to achieve optimal parameters for the numerical method.
  • We propose a scheme to use the error bound in choosing parameters in a systematic fashion to meet a pre-described error tolerance at minimal cost.
  • Using numerical examples, we present results comparable to or superior to relevant points of comparison

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.