Time-Consistent No-Arbitrage Models of the Term Structure

38 Pages Posted: 31 Jan 2003 Last revised: 7 May 2021

See all articles by Amir Yaron

Amir Yaron

University of Pennsylvania -- Wharton School of Business; National Bureau of Economic Research (NBER)

Michael W. Brandt

Duke University - Fuqua School of Business; National Bureau of Economic Research (NBER)

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Date Written: January 2003

Abstract

We present an econometric procedure for calibrating no-arbitrage term structure models in a way that is time-consistent and robust to measurement errors. Typical no-arbitrage models are time-inconsistent because their parameters are assumed constant for pricing purposes despite the fact that the parameters change whenever the model is recalibrated. No-arbitrage models are also sensitive to measurement errors because they fit exactly each potentially contaminated bond price in the cross-section. We overcome both problems by evaluating bond prices using the joint dynamics of the factors and calibrated parameters and by locally averaging out the measurement errors. Our empirical application illustrates the trade-off between fitting as well as possible and overfitting the cross-section of bond prices due to measurement errors. After optimizing this trade-off, our approach fits almost exactly the cross-section of bond prices at each date and produces out-of-sample forecast errors that beat a random walk benchmark and are comparable to the results in the affine term structure literature. We find that non-linearities in the pricing kernel are important, lending support to quadratic term structure models.

Suggested Citation

Yaron, Amir and Brandt, Michael W., Time-Consistent No-Arbitrage Models of the Term Structure (January 2003). NBER Working Paper No. w9458, Available at SSRN: https://ssrn.com/abstract=375310

Amir Yaron

University of Pennsylvania -- Wharton School of Business ( email )

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Michael W. Brandt (Contact Author)

Duke University - Fuqua School of Business ( email )

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