An analysis of the true notional bond system applied to the CBOT T-bond futures

The conversion factor system (CFS) is used in the determination of the invoice price of the Chicago Board of Trade Treasury-bond futures. As an alternative to the CFS, Oviedo [Oviedo, R.A., 2006. Improving the design of Treasury-Bond futures contracts. The Journal of Business 79, 1293-1315] proposed the True Notional Bond System (TNBS), and showed that it outperforms the CFS when interest rates are deterministic. The main purpose of this paper is to compare the effectiveness of the two systems in a stochastic environment. In order to do so, we price the CBOT T-bond futures as well as all its embedded delivery options under both the CFS and the TNBS. Our pricing procedure is an adaptation of the Dynamic Programming algorithm described in Ben-Abdallah et al. [Ben-Abdallah, R., Ben-Ameur, H., Breton, M., 2007. Pricing CBOT Treasury Bond futures. Les Cahiers du GERAD G-2006-77]. Numerical illustrations show that, in a stochastic framework, TNBS does not always outperform the CFS. However, as the long-term mean moves away from the level of the notional rate, the TNBS performs increasingly better than the CFS.