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Fast Exact Joint S&P 500/VIX Smile Calibration in Discrete and Continuous Time

Author

Listed:
  • Julien Guyon

    (CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - ENPC - École des Ponts ParisTech, MATHRISK - Mathematical Risk Handling - UPEM - Université Paris-Est Marne-la-Vallée - ENPC - École des Ponts ParisTech - Inria de Paris - Inria - Institut National de Recherche en Informatique et en Automatique)

  • Florian Bourgey

    (Bloomberg L.P.)

Abstract

We introduce the Newton--Sinkhorn and implied Newton algorithms which significantly speed up the Sinkhorn algorithm that [Guyon, The joint S&P 500/VIX smile calibration puzzle solved, Risk, April 2020] used to build the first arbitrage-free model exactly consistent with S&P 500 and VIX market data. Using a purely forward Markov functional model, we show how to build a continuous-time extension of the previous discrete-time model. We also compute model-free bounds on S&P 500 options that show the importance of taking VIX smile information into account. Extensive numerical tests are conducted.

Suggested Citation

  • Julien Guyon & Florian Bourgey, 2022. "Fast Exact Joint S&P 500/VIX Smile Calibration in Discrete and Continuous Time," Working Papers hal-03932808, HAL.
    • Handle: RePEc:hal:wpaper:hal-03932808
    DOI: 10.2139/ssrn.4315084
    as

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