Error analysis in Fourier methods for option pricing

Bibliography:

F. Crocce, J. Happola, J. Kiessling, R. Tempone, Error analysis in Fourier methods for option pricing, Accepted for publication in the Journal of Computational Finance (JCF), Dec. 2015

Authors:

F. Crocce, J. Happola, J. Kiessling, R. Tempone

Keywords:

Error analysis, Option pricing, Fourier methods, Spectral methods, Levy processes, Stochastic processes, Hardy functions, Trapezoidal quadrature

Year:

2015

Abstract:

We provide a bound for the error committed when using a Fourier method to price European options when the underlying follows an exponential \levy 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 that can be solved analytically in terms of the characteristic exponent of the \levy process. Then, a numerical inverse Fourier transform allows us to obtain the option price. We present a novel bound for the error and use this bound to set the parameters for the numerical method. We analyse the properties of the bound for a dissipative and pure-jump example. The bound presented is independent of the asymptotic behaviour of option prices at extreme asset prices. The error bound can be decomposed into a product of terms resulting from the dynamics and the option payoff, respectively. The analysis is supplemented by numerical examples that demonstrate results comparable to and superior to the existing literature.

The role of applied mathematics in finance

ISSN:

2015

http://arxiv.org/abs/1503.00019