Treasury option returns and models with unspanned risks

We document the phenomenon that average excess returns of out-of-the-money puts and calls on bond futures are negative, both unconditionally and conditionally on economic states. To explain these findings, we develop economically motivated restrictions in the context of a theory in which the pricing kernel is a general diffusion process with spanned and unspanned components. Our reconciliation is a framework that introduces market incompleteness and priced unspanned volatility risks, allowing for time-varying downside and upside futures risk premiums. The estimated model shows consistency with data on bond yields, yield volatilities, bond futures return volatilities, option prices, and option risk premiums.