Differential Geometry, (m, lambda)-SABR and a Formula by Pierre-Henry Labordere

18 Pages Posted: 1 Dec 2010

See all articles by Ingo Fahrner

Ingo Fahrner

Landesbank Baden-W├╝rttemberg (LBBW)

Date Written: April 29, 2009

Abstract

We describe the heat kernel expansion which gives an approximation to the transition density of a diffusion. This leads to an approximation to the log-normal smile for general local volatility models. The Gyongy-Dupire theory enables us to extend this result to general stochastic volatility models. We apply the result to the (m; lambda)-SABR model.

Keywords: Smile expansion, (m, lambda)-SABR, heat kernel expansion

Suggested Citation

Fahrner, Ingo, Differential Geometry, (m, lambda)-SABR and a Formula by Pierre-Henry Labordere (April 29, 2009). Available at SSRN: https://ssrn.com/abstract=1717676 or http://dx.doi.org/10.2139/ssrn.1717676

Ingo Fahrner (Contact Author)

Landesbank Baden-W├╝rttemberg (LBBW) ( email )

Am Hauptbahnhof 2
Stuttgart, 70174
Germany

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
594
Abstract Views
2,131
rank
57,481
PlumX Metrics