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. This answers in the affirmative the  previously open question whether CIR models with more than two factors can exhibit USVor not .
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 1] 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 CIR model to exhibit USV . We then construct a class of three-factor CIR models that exhibit USV. This answers in the affirmative the above previously open question . We also show that multi-factor CIR models with diagonal drift matrix cannot exhibit USV .
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We
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
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1
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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
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Cox-Ingersoll-Ross (CIR )
CIR
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unspanned stochastic volatility (USV)
USV
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above
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whether
. We also show that multi-factor
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more than two factors can exhibit USVor not
diagonal drift matrix cannot exhibit USV