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.

Keywords: Expected Return of Options on Treasury Bond Futures, Unspanned Components of Pricing Kernel, Interest-Rate Models, Tanaka’s Formula, Local Time Risk Premiums

JEL Classification: G00, G12, G13, G15