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The sub-fractional CEV model

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ARANEDA Axel Alejandro NILS Bertschinger

Year of publication 2021
Type Article in Periodical
Magazine / Source Physica A: Statistical Mechanics and its Applications
MU Faculty or unit

Faculty of Economics and Administration

Keywords CEV model; Econophysics; Long-range dependence; Option pricing; Sub-fractional Brownian motion; Sub-fractional Fokker–Planck
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Description The sub-fractional Brownian motion (sfBm) is a stochastic process, characterized by non-stationarity in their increments and long-range dependence, considered as an intermediate step between the standard Brownian motion (Bm) and the fractional Brownian motion (fBm). The mixed process, a linear combination between a Bm and an independent sfBm, called mixed sub-fractional Brownian motion (msfBm), keeps the features of the sfBm adding the semi-martingale property for H>3/4, is a suitable candidate to use in price fluctuation modeling, in particular for option pricing. In this note, we arrive at the European Call price under the Constant Elasticity of Variance (CEV) model driven by a mixed sub-fractional Brownian motion. Empirical tests show the capacity of the proposed model to capture the temporal structure of option prices across different maturities.
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