25 Pages Posted: 28 Feb 2014 Last revised: 13 Jan 2015
Date Written: May 8, 2014
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: 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