The quintic Ornstein-Uhlenbeck volatility model that jointly calibrates SPX & VIX smiles - Archive ouverte HAL
Article Dans Une Revue Risk Magazine Année : 2023

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

Résumé

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.
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Dates et versions

hal-03909334 , version 1 (21-12-2022)
hal-03909334 , version 2 (09-05-2023)

Identifiants

  • HAL Id : hal-03909334 , version 2

Citer

Eduardo Abi Jaber, Camille Illand, Shaun Xiaoyuan Li. The quintic Ornstein-Uhlenbeck volatility model that jointly calibrates SPX & VIX smiles. Risk Magazine, 2023, Cutting edge section. ⟨hal-03909334v2⟩
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