Analytical Formulas for Local Volatility Model with Stochastic Rates

25 Pages Posted: 24 Oct 2009  

Eric Benhamou

Université Paris Est - Université Paris Est-Creteil

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

Université Paris Est - Université Paris Est-Creteil ( email )

61 avenue du Général de Gaulle
Créteil, 940000
France

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

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