Finite Difference Techniques for Arbitrage Free SABR

25 Pages Posted: 28 Feb 2014 Last revised: 13 Jan 2015

Fabien Le Floc'h

Calypso Technology; Independent

Gary J. Kennedy

Clarus Financial Technology

Date Written: May 8, 2014

Abstract

This paper presents various finite difference schemes applied to the SABR arbitrage free density problem. Hagan initially proposed a Crank-Nicolson discretization, which can lead to oscillations in the option price. Among a variety of finite difference schemes, it is found that the TR-BDF2 and Lawson-Swayne schemes stand out on this problem in terms of stability and speed.

Keywords: stochastic volatility, SABR, TR-BDF2, Crank-Nicolson, finite difference, finance

Suggested Citation

Le Floc'h, Fabien and Kennedy, Gary J., Finite Difference Techniques for Arbitrage Free SABR (May 8, 2014). Available at SSRN: https://ssrn.com/abstract=2402001 or http://dx.doi.org/10.2139/ssrn.2402001

Fabien Le Floc'h (Contact Author)

Calypso Technology ( email )

106 rue de la Boetie
Paris, 75008
France

Independent ( email )

France

Gary J. Kennedy

Clarus Financial Technology ( email )

8 Monkwell Square
London, EC2Y 5BN
United Kingdom

HOME PAGE: http://www.clarusft.com

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