The quintic Ornstein-Uhlenbeck volatility model that jointly calibrates SPX & VIX smiles

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

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Abstract: The quintic Ornstein-Uhlenbeck volatility model is a stochastic volatility model where the volatility process is a polynomial function of degree five of a single Ornstein-Uhlenbeck process with fast mean reversion and large vol-of-vol. The model is able to achieve remarkable joint fits of the SPX-VIX smiles with only 6 effective parameters and an input curve that allows to match certain term structures. Even better, the model remains very simple and tractable for pricing and calibration: the VIX squared is again polynomial in the Ornstein-Uhlenbeck process, leading to efficient VIX derivative pricing by a simple integration against a Gaussian density; simulation of the volatility process is exact; and pricing SPX products can be done efficiently and accurately by standard Monte Carlo techniques with suitable antithetic and control variates.

Keywords: SPX and VIX modeling; Stochastic volatility; Pricing; Calibration (search for similar items in EconPapers)
Date: 2023-06-01
New Economics Papers: this item is included in nep-rmg
Note: View the original document on HAL open archive server: https://hal.science/hal-03909334v2
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Citations: View citations in EconPapers (3)

Published in Risk, 2023, Cutting edge section

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