An ex post valuation of the quality option implicit in the treasury bond futures contract

Abstract

This paper develops three empirical estimates of the value of the quality delivery option implicit in the Treasury bond futures contract: (a) an ex ante value as given by the excess of forward price of the cheapest-to-deliver bond over its conversion factor times the futures price; (b) an ex post value equal to the payoffs to a strategy of buying and holding a short-futures long-forward position at the start and delivering the cheapest bond at the expiration of futures contract, and (c) another ex post value equal to the sum of payoffs to a continuous rollover strategy involving a short-futures long-forward position in the cheapest-to-deliver bonds. Three months prior to delivery the average values of the three estimates are $464, $329, and $2,075, respectively. The differences among the three estimates appear to be largely due to nonsynchronous spot-futures data.