Option Valuation in Multivariate SABR Models

Jörg Kienitz and Manuel Wittke
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Jörg Kienitz: Deutsche Postbank AG
Manuel Wittke: University of Bonn

No 272, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: We consider the joint dynamic of a basket of n-assets where each asset itself follows a SABR stochastic volatility model. Using the Markovian Projection methodology we approximate a univariate displaced diffusion SABR dynamic for the basket to price caps and floors in closed form. This enables us to consider not only the asset correlation but also the skew, the cross-skew and the decorrelation in our approximation. The latter is not possible in alternative approximations to price e.g. spread options. We illustrate the method by considering the example where the underlyings are two constant maturity swap (CMS) rates. Here we examine the influence of the swaption volatility cube on CMS spread options and compare our approximation formulae to results obtained by Monte Carlo simulation and a copula approach.

Keywords: SABR; CMS spread; displaced diffusion; Markovian projection; Gyongy Lemma (search for similar items in EconPapers)
JEL-codes: C63 G12 G13 (search for similar items in EconPapers)
Pages: 26 pages
Date: 2010-02-01
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Citations: View citations in EconPapers (5)

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