On VIX futures in the rough Bergomi model

Jacquier, Antoine; Martini, Claude; Muguruza, Aitor

doi:10.1080/14697688.2017.1353127

Cited by 60 publications

(41 citation statements)

References 17 publications

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“…In this section we show and comment some plots related to the estimation of VIX Futures prices. We set the values H = 0.1 and ν = 1.18778 for the parameters and investigate three different initial forward variance curves v 0 (•), as in [22]: Scenario 1. v 0 (t) = 0.234 2 ; Scenario 2. v 0 (t) = 0.234 2 (1 + t) 2 ; Scenario 3. v 0 (t) = 0.234 2 √ 1 + t.…”

Section: Pricing and Comparison With Monte Carlomentioning

confidence: 99%

“…In all these cases, v 0 is an increasing function of time, whose value at zero is close to the square of the reference value of 0.25. One of the most recent and effective way to compute the price of VIX Futures is a Monte-Carlo-simulation method based on Cholesky decomposition, for which we refer to [22,Section 3.3.2]. It can be considered as a good approximation of the true price when the number M of computed paths is large.…”

Section: Pricing and Comparison With Monte Carlomentioning

confidence: 99%

“…However, they each suffer from several drawbacks, which the new generation of rough volatility models seems to overcome. For VIX Futures pricing, the rough version of Bergomi's model was thoroughly investigated in [22], showing accurate results. Nothing comes for free though and the new challenges set by rough volatility models lie on the numerical side, as new tools are needed to develop fast and accurate numerical techniques.…”

Section: Introductionmentioning

confidence: 99%

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Functional quantization of rough volatility and applications to the VIX

Bonesini¹,

Callegaro²,

Jacquier³

2021

Preprint

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We develop a product functional quantization of rough volatility. Since the quantizers can be computed offline, this new technique, built on the insightful works by Luschgy and Pagès, becomes a strong competitor in the new arena of numerical tools for rough volatility. We concentrate our numerical analysis to pricing VIX Futures in the rough Bergomi model and compare our results to other recently suggested benchmarks.

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Section: Pricing and Comparison With Monte Carlomentioning

confidence: 99%

Section: Pricing and Comparison With Monte Carlomentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Functional quantization of rough volatility and applications to the VIX

Bonesini¹,

Callegaro²,

Jacquier³

2021

Preprint

Self Cite

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“…Still, [31] showed that the rough Bergomi model is too close to lognormal to jointly calibrate both markets. Its younger sister [30] added a stochastic volatility of volatility component, generating a smile sandwiched between the bid-ask prices when calibrating VIX, but the joint calibration is not provided.…”

Section: Introductionmentioning

confidence: 99%

Rough multifactor volatility for SPX and VIX options

Jacquier¹,

Muguruza²,

Pannier³

2021

Preprint

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We provide explicit small-time formulae for the at-the-money implied volatility, skew and curvature in a large class of models, including rough volatility models and their multi-factor versions. Our general setup encompasses both European options on a stock and VIX options, thereby providing new insights on their joint calibration. The tools used are essentially based on Malliavin calculus for Gaussian processes. We develop a detailed theoretical and numerical analysis of the two-factor rough Bergomi model and provide insights on the interplay between the different parameters for joint SPX-VIX smile calibration.

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“…In order to price options under an rBergomi model, Bayer et al [6] proposed hierarchical adaptive sparse grids, Jacquier et al [7] developed pricing algorithms for VIX futures and options, and McCrickerd and Pakkanen [8] developed a "turbocharged" Monte Carlo pricing method. A number of short-term approximations have been proposed to obtain fast approximations for short maturities-see, for example, Fukasawa [3], El Euch et al [9], Bayer et al [10], and Friz et al [11].…”

Section: Introductionmentioning

confidence: 99%

Markovian Approximation of the Rough Bergomi Model for Monte Carlo Option Pricing

et al. 2021

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The recently developed rough Bergomi (rBergomi) model is a rough fractional stochastic volatility (RFSV) model which can generate a more realistic term structure of at-the-money volatility skews compared with other RFSV models. However, its non-Markovianity brings mathematical and computational challenges for model calibration and simulation. To overcome these difficulties, we show that the rBergomi model can be well-approximated by the forward-variance Bergomi model with wisely chosen weights and mean-reversion speed parameters (aBergomi), which has the Markovian property. We establish an explicit bound on the L2-error between the respective kernels of these two models, which is explicitly controlled by the number of terms in the aBergomi model. We establish and describe the affine structure of the rBergomi model, and show the convergence of the affine structure of the aBergomi model to the one of the rBergomi model. We demonstrate the efficiency and accuracy of our method by implementing a classical Markovian Monte Carlo simulation scheme for the aBergomi model, which we compare to the hybrid scheme of the rBergomi model.

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On VIX futures in the rough Bergomi model

Cited by 60 publications

References 17 publications

Functional quantization of rough volatility and applications to the VIX

Functional quantization of rough volatility and applications to the VIX

Rough multifactor volatility for SPX and VIX options

Markovian Approximation of the Rough Bergomi Model for Monte Carlo Option Pricing

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