Volatility Is (Mostly) Path-Dependent

Guyon, Julien; Lekeufack, Jordan

doi:10.2139/ssrn.4174589

Cited by 7 publications

(13 citation statements)

References 30 publications

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“…To conclude, the rough Hawkes Heston model is able -in a tractable and parsimonious fashion -to jointly calibrate S&P 500 and VIX options. The parsimonious character of our model is an advantage compared to other models that jointly calibrate SPX/VIX options with either a large number of parameters [27,51] or based on martingale transport considerations [50]. The affine character of the rough Hawkes Heston model allows fast pricing using Fourier-techniques, instead of Monte Carlo or machine learning methods as those used for instance in [44,70].…”

Section: Discussionmentioning

confidence: 99%

“…This modeling challenge, known as the joint S&P 500/VIX calibration puzzle [49,50], has inspired the introduction of more sophisticated models, e.g. [44,50,51], that incorporate new features to the joint dynamics of the underlying and the volatility in order to solve the problem. In this paper we tackle the challenge by proposing a tractable affine model with rough volatility and volatility jumps that cluster and that have the opposite direction but occur at the same time as the jumps of the underlying prices.…”

Section: Introductionmentioning

confidence: 99%

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The Rough Hawkes Heston Stochastic Volatility Model

2022

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Rough Hawkes Heston Stochastic Volatility Model

2022

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“…Let us also refer to the paper by Guyon and Mustapha (2022), where a neural SDE model has been successfully jointly calibrated. Within the class of continuous, however not necessarily Markovian models, Guyon and Lekeufack (2022) conduct an empirical and statistical analysis as well as a joint calibration for a family of models where the volatility depends on the paths of the asset. These models can be turned into Markovian ones by using exponential kernels instead of general ones.…”

Section: State Of the Artmentioning

confidence: 99%

“…for some fixed ε > 0. In this case the value of the volatility process σ S at time t does not depend on the whole trajectory of the primary process X, but just on its evolution from t − ε to t. For an economically reasonable choice for ε the lags used in Section 3.4 of Guyon and Lekeufack (2022) can be adapted to the current setting.…”

Section: The Modelmentioning

confidence: 99%

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Joint calibration to SPX and VIX options with signature-based models

Cuchiero¹,

Gazzani²,

Möller³

et al. 2023

Preprint

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We consider a stochastic volatility model where the dynamics of the volatility are described by linear functions of the (time extended) signature of a primary underlying process, which is supposed to be some multidimensional continuous semimartingale. Under the additional assumption that this primary process is of polynomial type, we obtain closed form expressions for the VIX squared, exploiting the fact that the truncated signature of a polynomial process is again a polynomial process. Adding to such a primary process the Brownian motion driving the stock price, allows then to express both the log-price and the VIX squared as linear functions of the signature of the corresponding augmented process. This feature can then be efficiently used for pricing and calibration purposes. Indeed, as the signature samples can be easily precomputed, the calibration task can be split into an offline sampling and a standard optimization. For both the SPX and VIX options we obtain highly accurate calibration results, showing that this model class allows to solve the joint calibration problem without adding jumps or rough volatility.

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A Course on Rough Paths

2020

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show abstract

Volatility Is (Mostly) Path-Dependent

Cited by 7 publications

References 30 publications

The Rough Hawkes Heston Stochastic Volatility Model

The Rough Hawkes Heston Stochastic Volatility Model

Joint calibration to SPX and VIX options with signature-based models

A Course on Rough Paths

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