The Rough Hawkes Heston Stochastic Volatility Model

Bondi, Alessandro; Pulido, Sergio; Scotti, Simone

doi:10.2139/ssrn.4253827

Cited by 3 publications

(6 citation statements)

References 62 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Here we consider call options written on the VIX on the trading day 02/06/2021, the same as in Guyon and Lekeufack (2022). We stress that for such recent dates the bid-ask spreads for VIX options are rather tight with respect to older dated options as considered for instance in Gatheral et al (2020); Bondi et al (2022b). The maturities are reported in the following table with the corresponding range of strikes (in percentage) with respect to the market's futures prices.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…(ii) The second approach is to consider T SPX = T VIX , i.e., to choose the same (or close together, see Remark 1.1) maturities both for SPX and VIX options. This perspective has been adopted for instance by Gatheral et al (2018); Rosenbaum and Zhang (2021); Grzelak (2022); Bondi et al (2022b).…”

Section: Numerical Resultsmentioning

confidence: 99%

“…In particular they allow for Fourier pricing after solving the related Riccati equations. This underlying structure is the building block of an extension with jumps investigated in Bondi et al (2022a) and recently employed in the context of the joint calibration in Bondi et al (2022b), where a rough Heston model with Hawkes-type jumps with Fourier pricing is employed.…”

Section: State Of the Artmentioning

confidence: 99%

“…Let us now consider the case of VIX options where Fourier pricing can be applied by computing the Fourier-Laplace transform of VIX squared, see also Sepp (2008); Papanicolaou and Sircar (2014); Cao et al (2020); Bondi et al (2022b) and references therein for a Fourier-based approach to pricing VIX options. Fix a labelling injective function L : {I : |I| ≤ n} → {1, .…”

Section: Spx As a Signature-based Modelmentioning

confidence: 99%

“…Analogous formulations in terms of the error function are also possible, see for instance Cao et al (2020); Bondi et al (2022b). In the same spirit one can also obtain a representation of future prices.…”

Section: Spx As a Signature-based Modelmentioning

confidence: 99%

See 4 more Smart Citations

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

Cuchiero¹,

Gazzani²,

Möller³

et al. 2023

Preprint

View full text Add to dashboard Cite

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.

show abstract

Section: Numerical Resultsmentioning

confidence: 99%

Section: Numerical Resultsmentioning

confidence: 99%