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

39 Pages Posted: 3 Nov 2008

See all articles by Qiang Dai

Qiang Dai

New York University

Anh Le

New York University, Leonard N. Stern School of Business

Kenneth J. Singleton

Stanford University - Graduate School of Business

Date Written: 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 ¤t, linking the risk-neutral and historical distributions of X, to depend generally on the state Xt. The conditionallikelihood functions for coupon bond yields for the resulting nonlinear models under thehistorical 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-sampleforecasting performance.

Suggested Citation

Dai, Qiang and Le, Anh and Singleton, Kenneth J., Discrete-Time Dynamic Term Structure Models with Generalized Market Prices of Risk (March 2006). NYU Working Paper No. FIN-06-007, Available at SSRN: https://ssrn.com/abstract=1293639

Qiang Dai

New York University

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Anh Le

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

Stern School of Business
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Kenneth J. Singleton

Stanford University - Graduate School of Business ( email )

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