A general HJM framework for multiple yield curve modeling

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.

(40 pages, 4 figures)

References in corpus (3)

• Convergence of local supermartingales and Novikov-Kazamaki type conditions for processes with jumps
• On multicurve models for the term structure
• When roll-overs do not qualify as numéraire: bond markets beyond short rate paradigms

Cited by in corpus (8)

• No free lunch for markets with multiple numéraires
• Multiple Yield Curve Modeling and Forecasting using Deep Learning
• A pure-jump mean-reverting short rate model
• Term structure modeling for multiple curves with stochastic discontinuities
• A stochastic control perspective on term structure models with roll-over risk
• Invariant cones for jump-diffusions in infinite dimensions
• The geometry of multi-curve interest rate models
• The Jarrow & Turnbull setting revisited