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  • C.G. gratefully acknowledges financial support of Natural Sciences and Research Council (NSERC), Canada, and of the chair AXA/Risk Foundation: “Large Risks in Insurance.”

Address correspondence to C. Gourieroux, CREST, 15 boulevard Gabriel Peri, 92245, Malakoff Cedex, France; e-mail:


The Gaussian Affine Term Structure Model (ATSM) introduced by Duffie and Kan is often used in finance to price derivatives written on interest rates or to compute the reserve to hedge a portfolio of credits (CreditVaR), and in macroeconomic applications to study the links between real activity and financial variables. However, a standard three-factor ATSM, for instance, implies a deterministic affine relationship between any set of four rates, with different times-to-maturity, and these relationships are not observed in practice. In this paper, we introduce a new class of affine term structure models, called Bilinear Term Structure Model (BTSM). This extension breaks down the deterministic relationships between rates in structural factor models by introducing lagged factor values, and the linear dependence by considering quadratic effects of the factors.