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

See all articles by Luís Oliveira

Luís Oliveira

Instituto Superior de Ciências do Trabalho e da Empresa (ISCTE) - ISCTE Business School

João Pedro Vidal Nunes

ISCTE Business School

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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

Oliveira, Luís and Nunes, João Pedro Vidal, Multi-Factor and Analytical Valuation of Treasury Bond Futures with an Embedded Quality Option. Journal of Futures Markets, Vol. 27, No. 3, 2007, Available at SSRN: https://ssrn.com/abstract=943972

Luís Oliveira

Instituto Superior de Ciências do Trabalho e da Empresa (ISCTE) - ISCTE Business School ( email )

Complexo Indeg/Iscte
Av. Professor Anibal Bettencourt
Lisboa, 1600-189
Portugal

João Pedro Vidal Nunes (Contact Author)

ISCTE Business School ( email )

Ed. INDEG/ISCTE
Av. Prof. Anibal Bettencourt
Lisboa, 1600-189
Portugal
+351 21 790 39 32 (Phone)
+351 21 793 87 09 (Fax)

HOME PAGE: http://iscte.pt/~jpvn/

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