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A Stochastic Volatility Alternative to SABR

Part of: Mathematical economics Markov processes Applications Special processes

Published online by Cambridge University Press:  14 July 2016

L. C. G. Rogers  and
L. A. M. Veraart
L. C. G. Rogers*
Affiliation:
University of Cambridge
L. A. M. Veraart*
Affiliation:
Princeton University
*
∗Postal address: Statistical Laboratory, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WB, UK. Email address: l.c.g.rogers@statslab.cam.ac.uk
∗∗Current address: Institut für Stochastik, Universität Karlsruhe (TH), Kaiserstr. 89, 76133 Karlsruhe, Germany.
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Abstract

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We present two new stochastic volatility models in which option prices for European plain-vanilla options have closed-form expressions. The models are motivated by the well-known SABR model, but use modified dynamics of the underlying asset. The asset process is modelled as a product of functions of two independent stochastic processes: a Cox-Ingersoll-Ross process and a geometric Brownian motion. An application of the models to options written on foreign currencies is studied.

Keywords

SABREuropean optionvolatility smile

MSC classification

Secondary: 91B70: Stochastic models 60K99: None of the above, but in this section 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) 62P05: Applications to actuarial sciences and financial mathematics
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 4 , December 2008 , pp. 1071 - 1085
Copyright
Copyright © Applied Probability Trust 2008 

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