Multi-Factor and Analytical Valuation of Treasury Bond Futures with an Embedded Quality Option∗

A closed-form pricing solution is proposed for the quality option embedded in Treasury bond futures contracts, under a multi-factor and Gaussian Heath, Jarrow, and Morton (1992) framework. Such an analytical solution can be obtained through a conditioning approximation, in the sense of Curran (1994) and Rogers and Shi (1995), or via a rank 1 approximation, following Brace and Musiela (1994). Monte Carlo simulations show that both approximations are extremely accurate and easy to calculate. Application of the proposed pricing model to the EUREX market, from January 2000 through May 2004, yields an excellent fit and an insignificant estimate of the quality option magnitude. On average, this delivery option accounts for only 0.04% of the futures prices.