René Aïd, Olivier Féron, Nizar Touzi, Christine Vialas
This paper proposes an Heath-Jarrow-Morton model of the yield curve that can fit the particular requirements of long-term asset and liability management (ALM). In particular, the proposed HJM model can reproduce expected long-term statistical properties of any two interest rates, while still satisfying the no-arbitrage constraints. We describe the methodology to calibrate the model in this particular constrainted setting, i.e. to find the model parameters as a function of the expected statistical properties. We precisely give the constraints on these expectations to ensure the existence of a solution.