The fractional and mixed-fractional CEV model

被引:11
作者
Araneda, Axel A. [1 ]
机构
[1] Frankfurt Inst Adv Studies, D-60438 Frankfurt, Germany
关键词
fBM; mfBm; CEV; Fractional Fokker-Planck; Fractional Ito's calculus; Feller's process; LONG-TERM-MEMORY; CONSTANT ELASTICITY; BROWNIAN-MOTION; BLACK-SCHOLES; ITO FORMULA; OPTION; CALCULUS; TESTS; DISTRIBUTIONS; CONVERGENCE;
D O I
10.1016/j.cam.2019.06.006
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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.
引用
收藏
页码:106 / 123
页数:18
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