Analytical Formulas for Local Volatility Model with Stochastic Rates

25 Pages Posted: 24 Oct 2009  

Eric Benhamou

A.I. Square Connect; LAMSADE- Paris Dauphine University

Emmanuel Gobet

Ecole Polytechnique, Paris - Centre de Mathematiques Appliquees

Mohammed Miri

Thomson Reuters

Date Written: October 21, 2009

Abstract

This paper presents new approximation formulae of European options in a local volatility model with stochastic interest rates. This is a companion paper to our work on perturbation methods for local volatility models http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1275872 for the case of stochastic interest rates. The originality of this approach is to model the local volatility of the discounted spot and to obtain accurate approximations with tight estimates of the error terms. This approach can also be used in the case of stochastic dividends or stochastic convenience yields. We finally provide numerical results to illustrate the accuracy with real market data.

Keywords: asymptotic expansion, local volatility model, HJM framework, Hull and White model, Malliavin calculus, small diffusion process, CEV model

JEL Classification: G13

Suggested Citation

Benhamou, Eric and Gobet, Emmanuel and Miri, Mohammed, Analytical Formulas for Local Volatility Model with Stochastic Rates (October 21, 2009). Available at SSRN: https://ssrn.com/abstract=1492054 or http://dx.doi.org/10.2139/ssrn.1492054

Eric Benhamou

A.I. Square Connect ( email )

35 Boulevard d'Inkermann
Neuilly sur Seine, 92200
France

LAMSADE- Paris Dauphine University ( email )

Place du Marechal de Lattre de Tassigny
Pais, 75016
France

HOME PAGE: http://https://www.lamsade.dauphine.fr/

Emmanuel Gobet (Contact Author)

Ecole Polytechnique, Paris - Centre de Mathematiques Appliquees ( email )

Palaiseau Cedex, 91128
France

Mohammed Miri

Thomson Reuters ( email )

6 Bd Haussman
France, FL 75009
France

Register to save articles to
your library

Register

Paper statistics

Downloads
648
rank
36,569
Abstract Views
2,745
PlumX