Multi-curve HJM modelling for risk management

TL;DR

This paper introduces a discrete multi-curve HJM model for risk management, approximating continuous dynamics with VAR(1), enabling volatility estimation and risk assessment from daily empirical data.

Contribution

It develops a discrete HJM framework approximated by VAR(1), facilitating volatility and correlation estimation for multi-curve risk management.

Findings

Model accurately captures yield curve dynamics

Effective in forecasting Euro area yield curves

Simplifies covariance structure via PCA

Abstract

We present a HJM approach to the projection of multiple yield curves developed to capture the volatility content of historical term structures for risk management purposes. Since we observe the empirical data at daily frequency and only for a finite number of time-to-maturity buckets, we propose a modelling framework which is inherently discrete. In particular, we show how to approximate the HJM continuous time description of the multi-curve dynamics by a Vector Autoregressive process of order one. The resulting dynamics lends itself to a feasible estimation of the model volatility-correlation structure and market risk-premia. Then, resorting to the Principal Component Analysis we further simplify the dynamics reducing the number of covariance components. Applying the constant volatility version of our model on a sample of curves from the Euro area, we demonstrate its forecasting ability through an out-of-sample test.