The affine LIBOR models

TL;DR

This paper introduces a flexible affine factor process approach to LIBOR modeling that ensures non-negativity, analytical tractability, and unified advantages of forward price and classical LIBOR models, with practical applications demonstrated.

Contribution

It develops a general affine LIBOR model framework that guarantees non-negativity and tractability, unifying forward price and classical LIBOR models with explicit formulas.

Findings

Affine LIBOR models ensure non-negative rates.

Closed-form formulas for caps and swaptions using CIR process.

Prototypical volatility smiles demonstrated.

Abstract

We provide a general and flexible approach to LIBOR modeling based on the class of affine factor processes. Our approach respects the basic economic requirement that LIBOR rates are non-negative, and the basic requirement from mathematical finance that LIBOR rates are analytically tractable martingales with respect to their own forward measure. Additionally, and most importantly, our approach also leads to analytically tractable expressions of multi-LIBOR payoffs. This approach unifies therefore the advantages of well-known forward price models with those of classical LIBOR rate models. Several examples are added and prototypical volatility smiles are shown. We believe that the CIR-process based LIBOR model might be of particular interest for applications, since closed form valuation formulas for caps and swaptions are derived.