Speed and Biases of Fourier-Based Pricing Choices: A Numerical Analysis

International Journal of Computer Mathematics. https://doi.org/10.1080/00207160.2017.1322691

20 Pages Posted: 28 Jul 2016 Last revised: 13 May 2018

See all articles by Ricardo Crisóstomo

Ricardo Crisóstomo

Comisión Nacional del Mercado de Valores (CNMV); Universidad Nacional de Educacion a Distancia (UNED)

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Date Written: November 22, 2016

Abstract

We compare the CPU effort and pricing biases of seven Fourier-based implementations. Our analyses show that truncation and discretization errors significantly increase as we move away from the Black–Scholes–Merton framework. We rank the speed and accuracy of the competing choices, showing which methods require smaller truncation ranges and which are the most efficient in terms of sampling densities. While all implementations converge well in the Bates jump-diffusion model, Attari's formula is the only Fourier-based method that does not blow up for any Variance Gamma parameter values. In terms of speed, the use of strike vector computations significantly improves the computational burden, rendering both fast Fourier transforms (FFT) and plain delta-probability decompositions inefficient. We conclude that the multi-strike version of the COS method is notably faster than any other implementation, whereas the strike-optimized Carr Madan's formula is simultaneously faster and more accurate than the FFT, thus questioning its use.

Keywords: Jump processes, Bates model, Variance Gamma, Fourier transforms, pricing errors, speed comparisons

JEL Classification: G13, C52, C63

Suggested Citation

Crisóstomo, Ricardo, Speed and Biases of Fourier-Based Pricing Choices: A Numerical Analysis (November 22, 2016). International Journal of Computer Mathematics. https://doi.org/10.1080/00207160.2017.1322691 . Available at SSRN: https://ssrn.com/abstract=2815371 or http://dx.doi.org/10.2139/ssrn.2815371

Ricardo Crisóstomo (Contact Author)

Comisión Nacional del Mercado de Valores (CNMV) ( email )

C/ Edison, 4
Madrid, Madrid 28006
Spain

Universidad Nacional de Educacion a Distancia (UNED)

Calle Bravo Murillo, 38
Madrid, Madrid 28015
Spain

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