An Analysis of the True Notional Bond System Applied to the CBOT T-Bonds Futures

Abstract

The main purpose of this paper is to apply the True Notional Bond System (TNBS) proposed by Oviedo (2006) for the theoretical pricing of the Chicago Board of Trade Treasury-bond futures, one of the most traded derivatives in the world. This system is proposed as an alternative to the current conversion factor system (CFS), whose poor performance is well known. In this paper, we price the CBOT T-bond futures as well as all its embedded delivery options and compare the corresponding results under the CFS in a stochastic interest rate framework. Our pricing procedure is an adaptation of the Dynamic Programming (DP) algorithm described in Ben-Abdallah et al. (2006), giving the value of the futures contract under the TNBS as a function of time and current short-term interest rate. Numerical illustrations, provided under the Vacisek and CIR models, show that the TNBS reduces dramatically the value of all the delivery options embedded in the CBOT T-bond futures.