The fractional and mixed-fractional CEV model

ARANEDA, Axel Alejandro. The fractional and mixed-fractional CEV model. Journal of Computational and Applied Mathematics. AMSTERDAM: Elsevier Science, 2020, roč. 363, s. 106-123. ISSN 0377-0427. Dostupné z: https://dx.doi.org/10.1016/j.cam.2019.06.006.

Základní údaje

Originální název

The fractional and mixed-fractional CEV model

Autoři

ARANEDA, Axel Alejandro

Vydání

Journal of Computational and Applied Mathematics, AMSTERDAM, Elsevier Science, 2020, 0377-0427

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Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Utajení

není předmětem státního či obchodního tajemství

Impakt faktor

Impact factor: 2.621

DOI

http://dx.doi.org/10.1016/j.cam.2019.06.006

UT WoS

000488995600007

Klíčová slova anglicky

fBM; mfBm; CEV; Fractional Fokker-Planck; Fractional Ito's calculus; Feller's process

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Anotace

V originále

The continuous observation of the financial markets has identified some 'stylized facts' which challenge the conventional assumptions, promoting the born of new approaches. On the one hand, the long-range dependence has been faced replacing the traditional Gauss-Wiener process (Brownian motion), characterized by stationary independent increments, by a fractional version. On the other hand, the CEV model addresses the Leverage effect and smile-skew phenomena, efficiently. In this paper, these two insights are merging and both the fractional and mixed-fractional extensions for the CEV model, are developed. Using the fractional versions of both the Ito's calculus and the Fokker-Planck equation, the transition probability density function of the asset price is obtained as the solution of a non-stationary Feller process with time-varying coefficients, getting an analytical valuation formula for a European Call option. Besides, the Greeks are computed and compared with the standard case. (C) 2019 Elsevier B.V. All rights reserved.