Fast Hybrid Schemes for Fractional Riccati Equations (Rough Is Not So Tough)

Giorgia Callegaro (), Martino Grasselli () and Gilles Paèes ()
Additional contact information
Giorgia Callegaro: Department of Mathematics “Tullio Levi Civita,” University of Padova, 35121 Padova, Italy
Martino Grasselli: Department of Mathematics “Tullio Levi Civita,” University of Padova, 35121 Padova, Italy; Department of Mathematics “Tullio Levi Civita,” University of Padova, 35121 Padova, Italy
Gilles Paèes: Laboratoire Probabilités, Statistique et Modélisation Aléatoire, Sorbonne Université, 75252 Paris, France

Mathematics of Operations Research, 2021, vol. 46, issue 1, 221-254

Abstract: We solve a family of fractional Riccati equations with constant (possibly complex) coefficients. These equations arise, for example, in fractional Heston stochastic volatility models, which have received great attention in the recent financial literature because of their ability to reproduce a rough volatility behavior. We first consider the case of a zero initial value corresponding to the characteristic function of the log-price. Then we investigate the case of a general starting value associated to a transform also involving the volatility process. The solution to the fractional Riccati equation takes the form of power series, whose convergence domain is typically finite. This naturally suggests a hybrid numerical algorithm to explicitly obtain the solution also beyond the convergence domain of the power series. Numerical tests show that the hybrid algorithm is extremely fast and stable. When applied to option pricing, our method largely outperforms the only available alternative, based on the Adams method.

Keywords: fractional Brownian motion; fractional Riccati equation; rough Heston model; power series representation (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (12)

Downloads: (external link)
https://doi.org/10.1287/moor.2020.1054 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:46:y:2021:i:1:p:221-254

Access Statistics for this article

More articles in Mathematics of Operations Research from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().