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Pré-Publication, Document De Travail Année : 2022

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

Résumé

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.
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Dates et versions

hal-03932808 , version 1 (10-01-2023)

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Julien Guyon, Florian Bourgey. Fast Exact Joint S&P 500/VIX Smile Calibration in Discrete and Continuous Time. 2022. ⟨hal-03932808⟩
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