Asymptotic Behaviour of the Fractional Heston Model

15 Pages Posted: 30 Nov 2014

See all articles by Hamza Guennoun

Hamza Guennoun

Societe Generale

Antoine (Jack) Jacquier

Imperial College London; The Alan Turing Institute

Patrick Roome

Imperial College London - Department of Mathematics

Date Written: November 27, 2014

Abstract

We consider here the fractional version of the Heston model originally proposed by Comte, Coutin and Renault. Inspired by some recent ground-breaking work by Gatheral, Jaisson and Rosenbaum, who showed that fractional Brownian motion with short memory allows for a better calibration of the volatility surface (as opposed to the classical econometric approach of long memory of volatility), we provide a characterisation of the short- and long-maturity asymptotics of the implied volatility smile. Our analysis reveals that the short-memory property precisely provides a jump-type behaviour of the smile for short maturities, thereby fixing the well-known standard inability of classical stochastic volatility models to fit the short-end of the volatility skew.

Keywords: Fractional Heston model, Asymptotics, Implied Volatility

Suggested Citation

Guennoun, Hamza and Jacquier, Antoine and Roome, Patrick, Asymptotic Behaviour of the Fractional Heston Model (November 27, 2014). Available at SSRN: https://ssrn.com/abstract=2531468 or http://dx.doi.org/10.2139/ssrn.2531468

Hamza Guennoun

Societe Generale ( email )

52 Place de l'Ellipse
La Défense, 92000
France

Antoine Jacquier

Imperial College London ( email )

South Kensington Campus
London SW7 2AZ, SW7 2AZ
United Kingdom

HOME PAGE: http://wwwf.imperial.ac.uk/~ajacquie/

The Alan Turing Institute ( email )

British Library, 96 Euston Road
London, NW12DB
United Kingdom

Patrick Roome (Contact Author)

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
London SW7 2AZ, SW7 2AZ
United Kingdom

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