Discrete-Time Dynamic Term Structure Models with Generalized Market Prices of Risk
University of North Carolina (UNC) at Chapel Hill - Finance Area
New York University, Leonard N. Stern School of Business
Kenneth J. Singleton
Stanford University-Graduate School of Business
7 March 2006
AFA 2007 Chicago Meetings Paper
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.
Number of Pages in PDF File: 39
Keywords: Nonlinear, Discrete time, Dynamic Term Structure Models, Esscher Transform, Generalized Market Prices of Risks
JEL Classification: C51, E43, E47, G12working papers series
Date posted: March 10, 2006
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