Joint SPX-VIX calibration with Gaussian polynomial volatility models: deep pricing with quantization hints

Eduardo Abi Jaber (), Camille Illand and Shaun Li
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Eduardo Abi Jaber: CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique
Camille Illand: AXA Investment Managers, Multi Asset Client Solutions, Quantitative Research - AXA
Shaun Li: UP1 - Université Paris 1 Panthéon-Sorbonne, AXA Investment Managers, Multi Asset Client Solutions, Quantitative Research - AXA, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique

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Abstract: We consider the joint SPX-VIX calibration within a general class of Gaussian polynomial volatility models in which the volatility of the SPX is assumed to be a polynomial function of a Gaussian Volterra process defined as a stochastic convolution between a kernel and a Brownian motion. By performing joint calibration to daily SPX-VIX implied volatility surface data between 2012 and 2022, we compare the empirical performance of different kernels and their associated Markovian and non-Markovian models, such as rough and non-rough pathdependent volatility models. In order to ensure an efficient calibration and a fair comparison between the models, we develop a generic unified method in our class of models for fast and accurate pricing of SPX and VIX derivatives based on functional quantization and Neural Networks. For the first time, we identify a conventional one-factor Markovian continuous stochastic volatility model that is able to achieve remarkable fits of the implied volatility surfaces of the SPX and VIX together with the term structure of VIX futures. What is even more remarkable is that our conventional one-factor Markovian continuous stochastic volatility model outperforms, in all market conditions, its rough and non-rough path-dependent counterparts with the same number of parameters.

Keywords: SPX and VIX modeling; Stochastic volatility; Gaussian Volterra processes; Quantization; Neural Networks (search for similar items in EconPapers)
Date: 2024-11
New Economics Papers: this item is included in nep-rmg
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Published in Mathematical Finance, 2024

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Persistent link: https://EconPapers.repec.org/RePEc:hal:cesptp:hal-03902513

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