The fractional and mixed-fractional CEV model

Araneda, Axel A.

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.

Más información

Título según WOS: ID WOS:000488995600007 Not found in local WOS DB
Título de la Revista: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volumen: 363
Editorial: ELSEVIER SCIENCE BV
Fecha de publicación: 2020
Página de inicio: 106
Página final: 123
DOI:

10.1016/j.cam.2019.06.006

Notas: ISI