Reduced Models in Option Pricing

  • José P. Silva
  • E. Jan W. ter Maten
  • Michael Günther
  • Matthias Ehrhardt
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 26)

Abstract

We consider the computational efficiency of the backward vs. forward approaches and compare these with the respective ones resulting from a parametric reduced order model, whose speed-up can be put to good use in the calibration of the underlying dynamics. We apply a global Proper Orthogonal Decomposition in the time domain to obtain the reduced basis and the Modified Craig-Sneyd ADI and Chang-Cooper schemes to numerically solve the partial differential equations. The numerical results are presented for the Black-Scholes and Heston models.

Notes

Acknowledgements

The work of the authors was partially supported by the European Union in the FP7-PEOPLE-2012-ITN Program under Grant Agreement Number 304617 (FP7 Marie Curie Action, Project Multi-ITN STRIKE-Novel Methods in Computational Finance, http://www.itn-strike.eu). The authors would like to thank Prof. Karel in ’t Hout for providing the ADI MCS code for the Heston Model.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  • José P. Silva
    • 1
  • E. Jan W. ter Maten
    • 1
  • Michael Günther
    • 1
  • Matthias Ehrhardt
    • 1
  1. 1.Bergische Universität WuppertalWuppertalGermany

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