The aim of this paper is to propose a numerical method to price the Chicago Board of Trade Treasury-bond futures. This contract is one of the most traded in the world, largely because of its ability to hedge long term interest rate risk. The difficulty to price it arises from its multiple inter-dependent embedded delivery options, which can be exercised at various times and dates during the delivery month. We consider a continuous time model with a continuous underlying factor (the interest rate), moving according to a Markov diffusion process consistent with the no-arbitrage principle. We propose a model that can handle all the delivery rules embedded in the CBOT T-bond futures, interpreted here as an American-style interest rate derivative. Our pricing procedure is a backward numerical algorithm combining Dynamic Programming (DP), approximation by finite elements, and fixed point evaluation. Numerical illustrations are provided under the Vacisek and CIR models
