Before revision: We ]  provide necessary and sufficient conditions for a multi-factor Cox-Ingersoll-Ross (CIR ) model to exhibit unspanned stochastic volatility (USV) . We then construct a class of three-factor CIR models that exhibit USV.
After revision: We ] showed that no two-factor Cox-Ingersoll-Ross (CIR) model can exhibit USV, it has been unknown to date whether CIR models with more than two factors can exhibit USV or not. We formally review USV and relate it to bond market incompleteness. We provide necessary and sufficient conditions for a multi-factor Cox-Ingersoll-Ross (CIR ) model to exhibit unspanned stochastic volatility (USV) . We then construct a class of three-factor CIR models that exhibit USV.