Discrete-Time Dynamic Term Structure Models with Generalized Market Prices of Risk

39 Pages Posted: 10 Mar 2006

See all articles by Qiang Dai

Qiang Dai

University of North Carolina (UNC) at Chapel Hill - Finance Area

Anh Le

New York University, Leonard N. Stern School of Business

Kenneth J. Singleton

Stanford University - Graduate School of Business

Date Written: 7 March 2006

Abstract

This paper develops a rich class of discrete-time, nonlinear dynamic term structure models (DTSMs). Under the risk-neutral measure, the distribution of the state vector Xt resides within a family of discrete-time affine processes that nests the exact discrete-time counter-parts of the entire class of continuous-time models in Duffie and Kan (1996) and Dai and Singleton (2000). Moreover, we allow the market price of risk, linking the risk-neutral and historical distributions of X, to depend generally on the state Xt. The conditional likelihood functions for coupon bond yields for the resulting nonlinear models under the historical measure are known exactly in closed form. As an illustration of our approach, we estimate a three factor model with a cubic term in the drift of the stochastic volatility factor and compare it to a model with a linear drift. Our results show that inclusion of a cubic term in the drift significantly improves the models statistical fit as well as its out-of-sample forecasting performance.

Keywords: Nonlinear, Discrete time, Dynamic Term Structure Models, Esscher Transform, Generalized Market Prices of Risks

JEL Classification: C51, E43, E47, G12

Suggested Citation

Dai, Qiang and Le, Anh and Singleton, Kenneth J., Discrete-Time Dynamic Term Structure Models with Generalized Market Prices of Risk (7 March 2006). AFA 2007 Chicago Meetings Paper. Available at SSRN: https://ssrn.com/abstract=889029 or http://dx.doi.org/10.2139/ssrn.889029

Qiang Dai

University of North Carolina (UNC) at Chapel Hill - Finance Area ( email )

Kenan-Flagler Business School
Chapel Hill, NC 27599-3490
United States
919-962-7182 (Phone)

Anh Le (Contact Author)

New York University, Leonard N. Stern School of Business ( email )

Stern School of Business
44 West 4th Street
New York, NY 10012-1126
United States
1-212-998-0321 (Phone)
1-212-995-4232 (Fax)

Kenneth J. Singleton

Stanford University - Graduate School of Business ( email )

Knight Management Center
655 Knight Way
Stanford, CA 94305-7298
United States
650-723-5753 (Phone)

HOME PAGE: http://www.stanford.edu/~kenneths

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