A FRACTIONAL VERSION OF THE HESTON MODEL WITH HURST PARAMETER H ∈ (1/2, 1)

TitleA FRACTIONAL VERSION OF THE HESTON MODEL WITH HURST PARAMETER H ∈ (1/2, 1)
Publication TypeJournal Article
Year of Publication2017
AuthorsLEPINETTE EMMANUEL, MEHRDOUST FARSHID
JournalDynamic Systems and Applications
Volume26
Issue3&4
Start Page537
Pagination13
Date Published2017
ISSN1056-2176
AMS Subject Classification34F05, 37H10, 60H20
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.

PDFhttps://acadsol.eu/dsa/articles/26/34/9.pdf
DOI10.12732/dsa.v26i34.9
Refereed DesignationRefereed