Bond Futures and Their Options: More than the Cheapest-to-Deliver; Margining and Quality Option

Abstract

Even if the name futures indicate a simple instrument, bond futures are complex. Several special features are embedded in the instrument. In particular the future is not written on one specific bond but on a basket of bonds, from which the short side can choose the cheapest-to-deliver.

This paper focus on that feature, present in the main futures market, and its impact on the futures risk. A formula for the delivery option and the convexity adjustment due to the daily margining is proposed in the Gaussian HJM model. The approach is numerically very efficient and easy to implement. Based on this result a futures option formula is derived. The approach is similar to the one used for Canary swaptions.

Keywords: Bond future, option on bond futures, delivery option, marginning, HJM gaussian model, explicit formula, numerical integration

JEL Classification: G13, E43