We are pleased to share with you our Detra Note 2021-1 on the "A Heath-Jarrow-Morton model compliant with Solvency II? Promises and pitfalls".
In this working paper, we adapt the Heath-Jarrow Morton (HJM) framework by considering a constraint of convergence of future forward rates toward a constant exogeneous rate set e.g. by a regulator. This limit rate, called “ultimate forward risk” or UFR, was introduced by the EIOPA in 2015 to extrapolate the initial yield curve for maturities beyond the last liquid point. We show that adding a constraint of convergence in the HJM model impacts not only the term structure of interest rates but also the future variance of zero-coupon bonds.