Multi-Curve HJM Modelling for Risk Management

63 Pages Posted: 16 Nov 2014 Last revised: 8 Oct 2015

See all articles by Chiara Sabelli

Chiara Sabelli

Scuola Normale Superiore

Michele Pioppi

UniCredit S.p.A.

Luca Sitzia

UniCredit S.p.A.

Giacomo Bormetti

University of Bologna - Department of Mathematics

Date Written: September 9, 2015

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.

Keywords: HJM, multiple-curve, scenario generation, PCA

JEL Classification: C32, C5, C51, G01, G10

Suggested Citation

Sabelli, Chiara and Pioppi, Michele and Sitzia, Luca and Bormetti, Giacomo, Multi-Curve HJM Modelling for Risk Management (September 9, 2015). Available at SSRN: https://ssrn.com/abstract=2524525 or http://dx.doi.org/10.2139/ssrn.2524525

Chiara Sabelli (Contact Author)

Scuola Normale Superiore ( email )

Piazza dei Cavalieri, 7
Pisa, 56126
Italy

Michele Pioppi

UniCredit S.p.A. ( email )

Piazza Gae Aulenti
Milan, 20154
Italy

Luca Sitzia

UniCredit S.p.A. ( email )

Piazza Gae Aulenti
Milan, 20154
Italy

Giacomo Bormetti

University of Bologna - Department of Mathematics ( email )

Piazza di Porta S. Donato , 5
Bologna, Bologna 40126
Italy

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