A simple approach to valuing the delivery options implicit in the US treasury bond futures contract

Abstract

The T-Bond futures contract has traded on the Chicago Board of Trade (CBOT) for approximately 20 years, and is now the most actively traded derivative product in the world. A voluminous amount of research has accordingly attempted to analyse the contract, and many have tried to establish a theoretical price which fully reflects all of the contract specifications. One factor that complicates this process is the series of delivery options which are embedded in the T-bond futures contract, and which give the short position some flexibility in their choice of the particular bond to be delivered as well as when delivery should be made. While the valuation of both the futures (and futures options) should obviously consider the value of these implicit delivery options, there is no existing methodology with which to estimate the values on an aggregate, and consistent basis. All of the previous methods for valuing the delivery options can be conveniently separated into two main groups, each having some distinct advantages and disadvantages. The first uses historical price data to simply measure the payoffs that would have accrued to an investor who follows a trading strategy that optimally utilises the delivery options available to a short futures position. Such an approach can usefully quantify the ex-post value of the options at expiration, and has the advantage that it does not require use of a particular option valuation formula. It is difficult however to generalise these results and does not provide any way to value the options prior to expiration on an ex-ante basis. That is the aim of the second approach, which specifies and applies a pricing model in an attempt to measure the amount by which futures prices should be bid down in equilibrium to reflect the options’ value. The success of the second approach obviously depends on the suitability of the specified valuation formula. It is clear that the current value of the delivery options is some function of the possible future changes to the values of the T-bonds that underlie the futures contract. These values are themselves dependant on innovations in the term structure of interest rates between the valuation date and the last day of trading in the futures contract. Accurate estimates of the value of the embedded options are therefore clearly reliant on the adequacy of the term structure model used in the analysis.