Magic points in finance: Empirical integration for parametric option pricing

TL;DR

This paper introduces an efficient offline-online method for parametric option pricing using empirical magic point interpolation, significantly speeding up Fourier transform-based calculations in finance.

Contribution

It adapts the empirical magic point interpolation method to Fourier option pricing, enabling rapid and accurate computations for model calibration and real-time pricing.

Findings

Exponential decay of pricing error under analyticity assumptions

Significant efficiency gains demonstrated in numerical experiments

Method applicable beyond theoretical scope in practice

Abstract

We propose an offline-online procedure for Fourier transform based option pricing. The method supports the acceleration of such essential tasks of mathematical finance as model calibration, real-time pricing, and, more generally, risk assessment and parameter risk estimation. We adapt the empirical magic point interpolation method of Barrault, Nguyen, Maday and Patera (2004) to parametric Fourier pricing. In the offline phase, a quadrature rule is tailored to the family of integrands of the parametric pricing problem. In the online phase, the quadrature rule then yields fast and accurate approximations of the option prices. Under analyticity assumptions the pricing error decays exponentially. Numerical experiments in one dimension confirm our theoretical findings and show a significant gain in efficiency, even for examples beyond the scope of the theoretical results.