Affine multiple yield curve models

TL;DR

This paper introduces a comprehensive affine process-based framework for multi-curve interest rate modeling, enabling exact fit, tractable valuation, and the integration of existing models with new developments like Wishart-driven short rate models.

Contribution

It unifies various affine multi-curve models into a single framework, allowing for ordered spreads, exact initial fit, and new models with closed-form pricing formulas.

Findings

Framework fits initial term structures exactly

Derives closed-form caplet pricing for Wishart-driven models

Calibrates models successfully to market data

Abstract

We provide a general and tractable framework under which all multiple yield curve modeling approaches based on affine processes, be it short rate, Libor market, or HJM modeling, can be consolidated. We model a numeraire process and multiplicative spreads between Libor rates and simply compounded OIS rates as functions of an underlying affine process. Besides allowing for ordered spreads and an exact fit to the initially observed term structures, this general framework leads to tractable valuation formulas for caplets and swaptions and embeds all existing multi-curve affine models. The proposed approach also gives rise to new developments, such as a short rate type model driven by a Wishart process, for which we derive a closed-form pricing formula for caplets. The empirical performance of two specifications of our framework is illustrated by calibration to market data.