  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.
