Option Valuation in Multivariate SMM/SABR Models (with an Application to the CMS Spread)

27 Pages Posted: 11 Sep 2009 Last revised: 30 Jun 2010

See all articles by Joerg Kienitz

Joerg Kienitz

University of Wuppertal - Applied Mathematics; University of Cape Town (UCT); Quaternion Risk Management

Manuel Wittke

Deloitte & Touche - Financial Risk Solutions

Date Written: June 30, 2010

Abstract

We consider the joint dynamic of a basket of n-assets where each asset itself follows a Swap Market Model or SABR stochastic volatility model. Using the Markovian Projection methodology we approximate it by a univariate displaced diffusion SMM/SABR dynamic for the basket to price caps and floors in closed form. This enables us to consider not only the asset correlation but, in the case of the SABR model, as well the skew, the cross-skew and the decorrelation in our approximation. If for example spread options are considered the latter is not possible in alternative approximations. 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: SMM, SABR model, CMS, CMS Spread, Gyöngy Lemma, Markovian Projection, Displaced diffusion

JEL Classification: C63, G12, G13

Suggested Citation

Kienitz, Joerg and Wittke, Manuel, Option Valuation in Multivariate SMM/SABR Models (with an Application to the CMS Spread) (June 30, 2010). Available at SSRN: https://ssrn.com/abstract=1469554 or http://dx.doi.org/10.2139/ssrn.1469554

Joerg Kienitz (Contact Author)

University of Wuppertal - Applied Mathematics ( email )

Gaußstraße 20
42097 Wuppertal
Germany

University of Cape Town (UCT) ( email )

Private Bag X3
Rondebosch, Western Cape 7701
South Africa

Quaternion Risk Management ( email )

54 Fitzwilliam Square North
Dublin, D02X308
Ireland

Manuel Wittke

Deloitte & Touche - Financial Risk Solutions ( email )

Germany

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