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Magic points in finance: Empirical integration for parametric option pricing

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  • Maximilian Ga{ss}
  • Kathrin Glau
  • Maximilian Mair

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.

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  • Maximilian Ga{ss} & Kathrin Glau & Maximilian Mair, 2015. "Magic points in finance: Empirical integration for parametric option pricing," Papers 1511.00884, arXiv.org, revised Nov 2016.
    • Handle: RePEc:arx:papers:1511.00884
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    References listed on IDEAS

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    Cited by:

    1. Philipp Harms, 2019. "Strong convergence rates for Markovian representations of fractional processes," Papers 1902.01471, arXiv.org, revised Aug 2020.

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