Local Volatility: Smooth Calibration and Fast Usage

14 Pages Posted: 20 Feb 2012 Last revised: 31 Dec 2015

See all articles by Adil Reghai

Adil Reghai

Natixis

Gilles Boya

Natixis

Ghislain Vong

Deutsche Bank AG - Global Equity Derivatives

Date Written: February 20, 2012

Abstract

This paper explores a powerful calibration technique of local volatility models based on the fixed point algorithm. It proves to be more robust and generic than the standard Dupire Approach. We also show how to dramatically increase the performance of Monte Carlo simulations by means of techniques borrowed from quantum physics. In particular, we use operator theory combined with fast discrete random generation to construct fast, efficient and robust algorithms for production purposes. This contribution is an engineering piece of work.

Keywords: Local volatility, calibration, fixed point algorithm, Operator Methods, Fast Discrete Random Number simulation, Magnus

JEL Classification: G13

Suggested Citation

Reghai, Adil and Boya, Gilles and Vong, Ghislain, Local Volatility: Smooth Calibration and Fast Usage (February 20, 2012). Available at SSRN: https://ssrn.com/abstract=2008215 or http://dx.doi.org/10.2139/ssrn.2008215

Adil Reghai (Contact Author)

Natixis ( email )

France

Gilles Boya

Natixis ( email )

47, quai d'Austerlitz
Paris, Paris 75013
France

Ghislain Vong

Deutsche Bank AG - Global Equity Derivatives ( email )

United Kingdom

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