A flexible matrix Libor model with smiles

TL;DR

This paper introduces a flexible affine process-based Libor model capable of capturing smile effects in interest rate derivatives, providing semi-closed form pricing and tractability for complex instruments like swaptions.

Contribution

It extends existing affine Libor models by altering the state space, enabling better modeling of implied volatility smiles and analytical tractability for pricing derivatives.

Findings

The model can accurately describe the implied volatility surface.

Semi-closed form solutions are available for caps and floors.

The approach allows efficient pricing of swaptions using Edgeworth expansion.

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 of Wishart Libor model in describing the movements of the implied volatility surface.