2015/11/03 by Maximilian Gaß, Gaß, Maximilian, Kathrin Glau +3
Earth and Planetary Sciences · Economics, Econometrics and Finance · #65D30 #91G60 #Computational Finance (q-fin.CP) #FOS: Economics and business #Financial Risk and Volatility Modeling #Meteorological Phenomena and Simulations #Stochastic processes and financial applications #msc:65D30 #msc:91G60 #q-fin.CP
paper · pdf · doi:10.48550/arxiv.1511.00884
openalex publication_date 2015/11/03 · arxiv created 2016/11/04 · arxiv updated 2016/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.