Unspanned Stochastic Volatility in Affine Models: Evidence from Eurodollar Futures and Options

Abstract

Unspanned stochastic volatility (USV) refers to the inability of bonds to replicate volatility-sensitive derivative securities. Affine term structure models require special restrictions on the parameters to exhibit USV. We use a joint Eurodollar futures and options data set to estimate affine three-factor models with and without USV restrictions. The unrestricted model captures prices of futures and options well. Option pricing errors are much larger in the USV model. The USV model is rejected in favor of the unrestricted model based on the likelihood ratio and Wald tests. We use the implications of the unrestricted model as a benchmark for understanding the extant evidence that favors USV. Specifically, we replicate extant tests in samples simulated from the unrestricted model. We show that none of the existing findings contradict the model without USV restrictions.