Transforming Volatility - Multi Curve Cap and Swaption Volatilities

22 Pages Posted: 22 Jan 2013 Last revised: 27 Mar 2013

See all articles by Joerg Kienitz

Joerg Kienitz

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

Date Written: March 22, 2013


In this document we consider the problem of deriving volatilities of non-standard tenors given quotes for standard tenors. Especially, we aim to derive volatilities for caps and swaptions from given quotes for a short tenor, for instance 3m, and derive volatilties for a longer tenor, for instance 6m. Furthermore, we also consider the other way of transforming long tenor volatilities to short tenor ones. We fi rst consider the single curve framework and then transferring the results to a multi curve framework which is the standard market approach after 2007. We apply a displaced di ffusion approach for the volatility transformation. Finally, we give several examples and outline the transfer algorithm.

Keywords: Cap, Swaption, Displaced Diffusion, Volatility, Multi Curve, Money Market Basis

JEL Classification: C13, C63

Suggested Citation

Kienitz, Joerg, Transforming Volatility - Multi Curve Cap and Swaption Volatilities (March 22, 2013). Available at SSRN: or

Joerg Kienitz (Contact Author)

University of Wuppertal - Applied Mathematics ( email )

Gaußstraße 20
42097 Wuppertal

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

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