Communications in Information and Systems

Volume 15 (2015)

Number 1

Stochastic volatility models with volatility driven by fractional Brownian motions

Pages: 47 – 55

DOI: https://dx.doi.org/10.4310/CIS.2015.v15.n1.a4

Authors

T. E. Duncan (Department of Mathematics, University of Kansas, Lawrence, Ks., U.S.A.)

J. Jakubowski (Institute of Mathematics, University of Warsaw, Poland)

B. Pasik-Duncan (Department of Mathematics, University of Kansas, Lawrence, Ks., U.S.A.)

Abstract

In this paper the price of a risky asset that has a stochastic volatility being a function of a fractional Brownian motion is considered. Such models can provide a long range dependence for the volatility. The probability density function for the price at a given time is given explicitly under some natural, verifiable conditions. An option pricing model is also considered with some explicit results.

Keywords

stochastic volatility, fractional Brownian motion, financial models

2010 Mathematics Subject Classification

60H30, 91B25, 91G20, 91G80

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Published 18 November 2015