Delivery Options in the Pricing and Hedging of Treasury Bond and Note Futures

Abstract

An arbitrage-free stochastic term structure model is used here to determine the equilibrium Treasury bond futures price in terms of the option to deliver one of many eligible bonds as well as the appropriate quantity of Treasury bond futures required to hedge the bond identified initially as cheapest to deliver. If interest rates are close to 6%, the rate used to determine Treasury bond futures conversion factors, the proper hedging quantity can differ significantly from a more standard duration-based quantity that ignores the option to switch delivery to a more optimal bond. If interest rates are significantly different from 6%, the option to switch will have little if any value, and hedging quantities that ignore the option to switch will be much more accurate.