Unspanned Risks, Negative Local Time Risk Premiums, and Empirical Consistency of Models of Interest-Rate Claims

Abstract

We formalize the notion of local time risk premiums in the context of a theory in which the pricing kernel is a general diffusion process with spanned and unspanned components. We derive results pertaining to expected excess returns of options on bond futures. These results are organized around our finding that average returns of out-of-the-money puts and calls on bond futures are both negative, the consistency of which is examined through unconditional and conditional exercises. Our theoretical reconciliation warrants negative local time risk premiums, and our treatment considers models with market incompleteness, volatility uncertainty, and time-varying sign of futures risk premium.