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, vol. 363, p. 106-123. ISSN 0377-0427. Available from: https://dx.doi.org/10.1016/j.cam.2019.06.006.

Basic information

• Original name: The fractional and mixed-fractional CEV model
• Authors: ARANEDA, Axel Alejandro.
• Edition: Journal of Computational and Applied Mathematics, AMSTERDAM, Elsevier Science, 2020, 0377-0427.

Other information

• Original language: English
• Type of outcome: Article in a journal
• Confidentiality degree: is not subject to a state or trade secret
• Impact factor: Impact factor: 2.621
• Doi: http://dx.doi.org/10.1016/j.cam.2019.06.006
• UT WoS: 000488995600007
• Keywords in English: fBM; mfBm; CEV; Fractional Fokker-Planck; Fractional Ito's calculus; Feller's process

Abstract

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.