A general HJM framework for multiple yield curve modeling

TL;DR

This paper introduces a comprehensive HJM framework for modeling multiple yield curves post-financial crisis, ensuring arbitrage-free dynamics and accommodating various modeling approaches.

Contribution

It develops a general semimartingale HJM approach for multiple yield curves, including arbitrage conditions and affine process specifications, unifying recent models.

Findings

Derives arbitrage-free drift and consistency conditions.

Provides a flexible Markovian structure with affine processes.

Unifies and extends existing multiple yield curve models.

Abstract

We propose a general framework for modeling multiple yield curves which have emerged after the last financial crisis. In a general semimartingale setting, we provide an HJM approach to model the term structure of multiplicative spreads between FRA rates and simply compounded OIS risk-free forward rates. We derive an HJM drift and consistency condition ensuring absence of arbitrage and, in addition, we show how to construct models such that multiplicative spreads are greater than one and ordered with respect to the tenor's length. When the driving semimartingale is specified as an affine process, we obtain a flexible Markovian structure. Finally, we show that the proposed framework allows to unify and extend several recent approaches to multiple yield curve modeling.