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

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