Multi-Factor and Analytical Valuation of Treasury Bond Futures with an Embedded Quality Option
Journal of Futures Markets, Vol. 27, No. 3, 2007
Posted: 12 Nov 2006
There are 2 versions of this paper
Abstract
A closed-form pricing solution is proposed for the quality option embedded in Treasury bond futures contracts, under a multi-factor and D. Heath, R. Jarrow, and A. Morton (1992) Gaussian framework. Such an analytical solution can be obtained through a conditioning approximation, in the sense of M. Curran (1994) and L. Rogers and Z. Shi (1995), or via a rank 1 approximation, following A. Brace and M. 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.
Keywords: Gaussian HJM multi-factor models, Quality option, Consistent forward rate curves, Treasury bond futures, EUREX market
JEL Classification: C15, E43, G13
Suggested Citation: Suggested Citation