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

Julien Guyon and Florian Bourgey
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Julien Guyon: CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - ENPC - École nationale des ponts et chaussées, MATHRISK - Mathematical Risk Handling - UPEM - Université Paris-Est Marne-la-Vallée - ENPC - École nationale des ponts et chaussées - Centre Inria de Paris - Inria - Institut National de Recherche en Informatique et en Automatique
Florian Bourgey: Bloomberg L.P.

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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.

Keywords: Joint S&; P 500/VIX smile calibration; Newton-Sinkhorn; Implied Newton; Martingale interpolation; Martingale optimal transport (search for similar items in EconPapers)
Date: 2024-02-01
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Published in Risk, 2024, ⟨10.2139/ssrn.4315084⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03932808

DOI: 10.2139/ssrn.4315084

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