Efficient Multiple Time-Step Simulation of the SABR Model

  • Álvaro Leitao
  • Lech A. Grzelak
  • Cornelis W. Oosterlee
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 26)

Abstract

In this work, we present a multiple time-step Monte Carlo simulation technique for pricing options under the Stochastic Alpha Beta Rho (SABR) model. The proposed method is an extension of the one time-step Monte Carlo method that we proposed in Leitao et al. (Appl. Math. Comput. 293: 461–479, 2017). We call it the mSABR method. A highly efficient method results, with many interesting and nontrivial components, like Fourier inversion for the sum of log-normals, stochastic collocation, Gumbel copula, correlation approximation, that are not yet seen in combination within a Monte Carlo simulation. The present multiple time-step Monte Carlo method is especially useful for long-term or for exotic options. This paper is a short version of an already published paper (Leitao et al. On an efficient multiple time-step Monte Carlo simulation of the SABR model. Quantitative Finance.

Notes

Acknowledgements

Supported by the EU 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.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  • Álvaro Leitao
    • 1
    • 2
  • Lech A. Grzelak
    • 1
    • 3
  • Cornelis W. Oosterlee
    • 1
    • 2
  1. 1.Delft Institute of Applied MathematicsTU DelftDelftThe Netherlands
  2. 2.CWI-Centrum Wiskunde & InformaticaAmsterdamThe Netherlands
  3. 3.ING, Quantitative AnalyticsAmsterdamThe Netherlands

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