Local Volatility: Smooth Calibration and Fast Usage

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

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)

ADIA ( email )

211 Corniche
Abu Dhabi
United Arab Emirates

Gilles Boya

Natixis ( email )

Paris
France

Ghislain Vong

Credit Suisse Securities ( email )

One Cabot Square
London, E14 4QJ
United Kingdom

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