Bond futures: Delivery Option with Term Structure Modelling

Abstract

Bond futures are characterised by a set of underlying bonds; the short party has the option to deliver at expiry any of those underlying bonds. Consequently, bond futures embed a choice option between bonds with different maturities and coupons. The delivery mechanism also incorporates conversion factors that create an implicit strike. The option is impacted by different maturities and different moneyness for each bond. It is important to take into account the full term structure of volatility with smile. A recent paper Bang and Daboussi (2022) developed such an approach for swap rate based products like CMS. In this paper we extend their approach to cover futures and apply it to the specific case of bond futures. The method allows the analysis of the impact of smile, term structure of volatility and correlations between rates on the delivery option and convexity adjustment values. All of them have an impact on the valuation and risk management of bond futures.

Keywords: bond futures, delivery option, term structure, volatility smile, correlation

JEL Classification: G13, G15, G23, K12