A Fractional Version of the Heston Model with Hurst Parameter H ∈ (1/2, 1)

12 Pages Posted: 13 Dec 2016

See all articles by Emmanuel Lepinette

Emmanuel Lepinette

Université Paris-Dauphine - CEREMADE, CNRS

Farshid Mehrdoust

Department of Applied Mathematics, Faculty of Mathematical Sciences University of Guilan,

Date Written: December 12, 2016

Abstract

We consider a fractional version of the Heston model where the two standard Brownian motions are replaced by two fractional Brownian motions with Hurst parameter H ∈ (1/2, 1). We show that the stochastic differential equation admits a unique positive solution by adapting and generalizing some results of Y. Hu, D. Nualart and X. Song on singular equations driven by rough paths. Moreover, we show that the fractional version of the variance, which is a version of the fractional Cox-Ingersoll-Ross model, is still a mean-reverting process.

Keywords: fractional Heston and Cox-Ingersoll-Ross models, fractional Brownian motion, singular equations driven by rough paths

Suggested Citation

Lepinette, Emmanuel and Mehrdoust, Farshid, A Fractional Version of the Heston Model with Hurst Parameter H ∈ (1/2, 1) (December 12, 2016). Available at SSRN: https://ssrn.com/abstract=2884010 or http://dx.doi.org/10.2139/ssrn.2884010

Emmanuel Lepinette (Contact Author)

Université Paris-Dauphine - CEREMADE, CNRS ( email )

Place du Marechal de Lattre de Tassigny
Paris Cedex 16, 75775
France

Farshid Mehrdoust

Department of Applied Mathematics, Faculty of Mathematical Sciences University of Guilan, ( email )

P.O. Box 1841
Rasht, Guilan
Iran

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