ZABR -- Expansions for the Masses

16 Pages Posted: 7 Jan 2012

Date Written: December 24, 2011

Abstract

We extend the widely used SABR model (Hagan et al (2002)) to include a general volatility function and a CEV power on the stochastic volatility process itself. Using a short time expansion we derive results for the Dupire local volatility which in turn is inserted into a single time step finite difference scheme to generate arbitrage free option prices. Our approach has a number of advantages over the standard SABR model: a. it eliminates arbitrage for low and high strikes, b. it allows for an exact fit to a set of discrete option quotes, and c. it gives more explicit control over the wings, both for low (and potentially negative) strikes and for very high strikes. All of this without sacrificing speed in the implementation.

Keywords: Option pricing, volatility smiles

JEL Classification: G13

Suggested Citation

Andreasen, Jesper and Huge, Brian Norsk, ZABR -- Expansions for the Masses (December 24, 2011). Available at SSRN: https://ssrn.com/abstract=1980726 or http://dx.doi.org/10.2139/ssrn.1980726

Jesper Andreasen (Contact Author)

Saxo Bank ( email )

Philip Heymans Alle 15
Hellerup, 2900
Denmark

Brian Norsk Huge

Danske Bank ( email )

DK-1092 Copenhagen K
Denmark

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