A Flexible Matrix Libor Model with Smiles
34 Pages Posted: 23 Mar 2012
Date Written: March 21, 2012
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
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