Abstract

http://ssrn.com/abstract=1367955
 
 

References (37)



 
 

Citations (13)



 


 



Time Dependent Heston Model


Eric Benhamou


Pricing Partners

Emmanuel Gobet


Ecole Polytechnique, Paris - Centre de Mathematiques Appliquees

Mohammed Miri


Pricing Partners

March 24, 2009


Abstract:     
The use of the Heston model is still challenging because it has a closed formula only when the parameters are constant [Hes93] or piecewise constant [MN03]. Hence, using a small volatility of volatility expansion and Malliavin calculus techniques, we derive an accurate analytical formula for the price of vanilla options for any time dependent Heston model (the accuracy is less than a few bps for various strikes and maturities). In addition, we establish tight error estimates. The advantage of this approach over Fourier based methods is its rapidity (gain by a factor 100 or more), while maintaining a competitive accuracy. From the approximative formula, we also derive some corollaries related first to equivalent Heston models (extending some work of Piterbarg on stochastic volatility models [Pit05]) and second, to the calibration procedure in terms of ill-posed problems.

Number of Pages in PDF File: 37

Keywords: asymptotic expansion, Malliavin calculus, small volatility of volatility, time dependent Heston model

working papers series


Download This Paper

Date posted: March 25, 2009  

Suggested Citation

Benhamou, Eric and Gobet, Emmanuel and Miri, Mohammed, Time Dependent Heston Model (March 24, 2009). Available at SSRN: http://ssrn.com/abstract=1367955 or http://dx.doi.org/10.2139/ssrn.1367955

Contact Information

Eric Benhamou
Pricing Partners ( email )
Paris Cybervillage
204 Rue de crimée
Paris, 75019
France
Emmanuel Gobet (Contact Author)
Ecole Polytechnique, Paris - Centre de Mathematiques Appliquees ( email )
Palaiseau Cedex, 91128
France
Mohammed Miri
Pricing Partners ( email )
Paris Cybervillage
204 Rue de crimée
Paris, 75019
France
HOME PAGE: http://www-ljk.imag.fr/membres/Mohammed.Miri/
Feedback to SSRN


Paper statistics
Abstract Views: 6,237
Downloads: 2,149
Download Rank: 2,911
References:  37
Citations:  13

© 2014 Social Science Electronic Publishing, Inc. All Rights Reserved.  FAQ   Terms of Use   Privacy Policy   Copyright   Contact Us
This page was processed by apollo4 in 0.469 seconds