Quantization Meets Fourier: A New Technology for Pricing Options

Abstract

In this paper we introduce a novel pricing methodology for a broad class of models for which the characteristic function of the log-asset price can be efficiently computed. The new method avoids the numerical integration required by the Fourier-based approaches and reveals to be fast and accurate, to the point that we can calibrate the models on real data. Our approach allows to price also American- style options, as it is possible to compute the transition probabilities for the underlying. This is accomplished through an efficient multinomial lattice discretization of the asset price based on a new quantization procedure which exploits the knowledge of the Fourier transform of the process at a given time. As a motivating example, we price an American Put option in a Tempered Stable model, with constitutes the first application of quantization to a pure jump process.