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@article{1676599, author = {Araneda, Axel Alejandro}, article_location = {AMSTERDAM}, doi = {http://dx.doi.org/10.1016/j.cam.2019.06.006}, keywords = {fBM; mfBm; CEV; Fractional Fokker-Planck; Fractional Ito's calculus; Feller's process}, language = {eng}, issn = {0377-0427}, journal = {Journal of Computational and Applied Mathematics}, title = {The fractional and mixed-fractional CEV model}, volume = {363}, year = {2020} }
TY - JOUR ID - 1676599 AU - Araneda, Axel Alejandro PY - 2020 TI - The fractional and mixed-fractional CEV model JF - Journal of Computational and Applied Mathematics VL - 363 SP - 106-123 EP - 106-123 PB - Elsevier Science SN - 03770427 KW - fBM KW - mfBm KW - CEV KW - Fractional Fokker-Planck KW - Fractional Ito's calculus KW - Feller's process N2 - 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. ER -
ARANEDA, Axel Alejandro. The fractional and mixed-fractional CEV model. \textit{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.
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