# An Arbitrage-Free Interest Rate Model Consistent with Economic Constraints for Long-Term Asset Liability Management

1
Nov

### 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.

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