A Flexible Matrix Libor Model with Smiles

34 Pages Posted: 23 Mar 2012

See all articles by Alessandro Gnoatto

Alessandro Gnoatto

University of Verona - Department of Economics

Martino Grasselli

University of Padova - Department of Mathematics; Léonard de Vinci Pôle Universitaire, Research Center

José Da Fonseca

Auckland University of Technology - Faculty of Business & Law

Date Written: March 21, 2012

Abstract

We present a flexible approach for the valuation of interest rate derivatives based on Affine Processes. We extend the methodology proposed in Keller-Ressel et al. (2009) by changing the choice of the state space. We provide semi-closed-form solutions for the pricing of caps and floors. We then show that it is possible to price swaptions in a multifactor setting with a good degree of analytical tractability. This is done via the Edgeworth expansion approach developed in Collin-Dufresne and Goldstein (2002). A numerical exercise illustrates the flexibility ofWishart Libor model in describing the movements of the implied volatility surface.

Keywords: Affine processes, Wishart process, Libor market model, Fast Fourier Transform, Caps, Floors, Swaptions

JEL Classification: G13, C51

Suggested Citation

Gnoatto, Alessandro and Grasselli, Martino and Da Fonseca, José, A Flexible Matrix Libor Model with Smiles (March 21, 2012). Available at SSRN: https://ssrn.com/abstract=2027034 or http://dx.doi.org/10.2139/ssrn.2027034

Alessandro Gnoatto (Contact Author)

University of Verona - Department of Economics ( email )

Via dell'Artigliere, 8
37129 Verona
Italy

Martino Grasselli

University of Padova - Department of Mathematics ( email )

Via Trieste 63
Padova, Padova
Italy

Léonard de Vinci Pôle Universitaire, Research Center ( email )

Paris La Défense
France

José Da Fonseca

Auckland University of Technology - Faculty of Business & Law ( email )

3 Wakefield Street
Private Bag 92006
Auckland Central 1020
New Zealand
64 9 921 9999 5063 (Phone)

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