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The fractional and mixed-fractional CEV model
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.Comment: The final version of the paper, after the referee proces