Speed and Biases of Fourier-Based Pricing Choices: Analysis of the Bates and Asymmetric Variance Gamma Models

46 Pages Posted: 7 Jun 2019 Last revised: 15 Jun 2019

See all articles by Ricardo Crisóstomo

Ricardo Crisóstomo

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

Multiple version iconThere are 2 versions of this paper

Date Written: 2016

Abstract

This paper compares the CPU effort and numerical biases of six Fourier-based implementations. Our analyses focus on two jump models that can consistently price options with different strikes and maturities: (i) the Bates jump-diffusion model, which combines jumps with stochastic volatility and (ii) the Asymmetric Variance Gamma (AVG) model, a pure-jump process where an infinite number of jumps can occur in any interval of time. We show that both truncation and discretization errors significantly increase as we move away from the diffusive Black-Scholes-Merton dynamics. While most pricing choices converge to the Bates reference values, Attari’s formula is the only Fourier-based method that does not completely blow up in any AVG problematic region. In terms of CPU speed, the strike vector computations proposed by Zhu (2010) significantly improve the computational burden, rendering the use of fast Fourier transforms and plain delta-probability decompositions inefficient.

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: Analysis of the Bates and Asymmetric Variance Gamma Models (2016). CNMV Working Paper No. 64, 2017. Available at SSRN: https://ssrn.com/abstract=3400683 or http://dx.doi.org/10.2139/ssrn.3400683

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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