Pricing Derivatives in Hermite Markets

Stoyanov, Stoyan V.; Rachev, Svetlozar T.; Mittnik, Stefan; Fabozzi, Frank J.

doi:10.1142/s0219024919500316

Cited by 6 publications

(2 citation statements)

References 63 publications

(87 reference statements)

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“…They appear as renormalized limits of sums of Gaussian sequences, so called non-central limit theorems, see Taqqu,Dobrushin-Major,Bai-T [Taq79, DM79,BT13a,GL20b] and are used in models trying to capture long range dependence, see e.g. Hermite_Markets [SRMF19]. Furthermore, one can define Wiener integrals with respect to them, see section section-preliminary…”

Section: Statement Of the Theoremsmentioning

confidence: 99%

Functional Limit Theorems of moving averages of Hermite processes and an application to homogenization

Gehringer

2020

Preprint

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We generalise the homogenisation theorem inGehringer-Li-homo,Gehringer-Li-tagged [GL19, GL20a] for passive tracer in a fractional Gaussian field to fractional non-Gaussian fields. We also obtain the limit theorems of normalized functionals of Hermite-Volterra processes, extending the result in Diu-Tran[DT18] to power series with fast decaying coefficients. We obtain either convergence to a Wiener process, in the short-range dependent case, or to a Hermite process, in the long-range dependent case. Furthermore, we prove convergence in the multivariate case with both, short and long-range dependent components and give an application to homogenization of fast/slow systems.

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Section: Statement Of the Theoremsmentioning

confidence: 99%

Functional Limit Theorems of moving averages of Hermite processes and an application to homogenization

Gehringer

2020

Preprint

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“…We refer the reader to [17] and [40] for a detailed review of the properties associated with selfsimilarity. In particular, the Rosenblatt process is used in finance [50,44,20] and statistical inference [31,13,35].…”

Section: Introductionmentioning

confidence: 99%

Fractal dimensions of the Rosenblatt process

Daw¹,

Kerchev²

2021

Preprint

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The paper concerns the image, level and sojourn time sets associated with sample paths of the Rosenblatt process. We obtain results regarding the Hausdorff (both classical and macroscopic), packing and intermediate dimensions, and the logarithmic and pixel densities. As a preliminary step we also establish the time inversion property of the Rosenblatt process, as well as some technical points regarding the distribution of Z.

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Nonparametric estimates of option prices via Hermite basis functions

Marinelli

d’Addona

2023

Ann Finance

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We consider approximate pricing formulas for European options based on approximating the logarithmic return’s density of the underlying by a linear combination of rescaled Hermite polynomials. The resulting models, that can be seen as perturbations of the classical Black-Scholes one, are nonpararametric in the sense that the distribution of logarithmic returns at fixed times to maturity is only assumed to have a square-integrable density. We extensively investigate the empirical performance, defined in terms of out-of-sample relative pricing error, of this class of approximating models, depending on their order (that is, roughly speaking, the degree of the polynomial expansion) as well as on several ways to calibrate them to observed data. Empirical results suggest that such approximate pricing formulas, when compared with simple nonparametric estimates based on interpolation and extrapolation on the implied volatility curve, perform reasonably well only for options with strike price not too far apart from the strike prices of the observed sample.

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Pricing Derivatives in Hermite Markets

Cited by 6 publications

References 63 publications

Functional Limit Theorems of moving averages of Hermite processes and an application to homogenization

Functional Limit Theorems of moving averages of Hermite processes and an application to homogenization

Fractal dimensions of the Rosenblatt process

Nonparametric estimates of option prices via Hermite basis functions

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