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: Empirical evidence suggests that fixed income markets exhibit unspanned stochastic volatility (USV), that is, that one cannot fully hedge volatility risk solely using a portfolio of bonds. While ] 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.