Unspanned Stochastic Volatility in the Multi-Factor CIR Model
Mathematical Finance, Forthcoming
15 Pages Posted: 8 May 2017 Last revised: 16 Jan 2019
Date Written: April 13, 2018
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 Collin-Dufresne and Goldstein (2002) 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.
Keywords: multi-factor Cox-Ingersoll-Ross model, unspanned stochastic volatility, incomplete bond markets
JEL Classification: C32, G12, G13
Suggested Citation: Suggested Citation