Affine LIBOR models driven by real-valued affine processes

TL;DR

This paper introduces a modification to affine LIBOR models allowing the use of real-valued affine processes, enabling the modeling of volatility smiles while maintaining arbitrage-free, nonnegative interest rates, and analytical pricing.

Contribution

It presents a novel approach to incorporate real-valued affine processes into LIBOR models without losing nonnegativity of interest rates.

Findings

Models can produce pronounced volatility smiles.

Maintains arbitrage-free and nonnegative interest rates.

Analytical formulas for caplet and swaption prices are available.

Abstract

The class of affine LIBOR models is appealing since it satisfies three central requirements of interest rate modeling. It is arbitrage-free, interest rates are nonnegative and caplet and swaption prices can be calculated analytically. In order to guarantee nonnegative interest rates affine LIBOR models are driven by nonnegative affine processes, a restriction, which makes it hard to produce volatility smiles. We modify the affine LIBOR models in such a way that real-valued affine processes can be used without destroying the nonnegativity of interest rates. Numerical examples show that in this class of models pronounced volatility smiles are possible.