Can Unspanned Stochastic Volatility Models Explain the Cross Section of Bond Volatilities?

In fixed income markets, volatility is unspanned if volatility risk cannot be hedged with bonds. We first show that all affine term structure models with state space ${ℝ}_{+}^M\times {ℝ}^{N-M}$ can be drift normalized and show when the standard variance normalization can be obtained. Using this normalization, we find conditions for a wide class of affine term structure models to exhibit unspanned stochastic volatility (USV). We show that the USV conditions restrict both the mean reversions of risk factors and the cross section of conditional yield volatilities. The restrictions imply that previously studied affine USV models are unlikely to be able to generate the observed cross section of yield volatilities. However, more general USV models can match the cross section of bond volatilities.

This paper was accepted by Wei Xiong, finance.