Working Papers

2013-07 | June 2013


Estimating Shadow-Rate Term Structure Models with Near-Zero Yields


Standard Gaussian affine dynamic term structure models do not rule out negative nominal interest rates—a conspicuous defect with yields near zero in many countries. Alternative shadow-rate models, which respect the nonlinearity at the zero lower bound, have been rarely used because of the extreme computational burden of their estimation. However, by valuing the call option on negative shadow yields, we provide the first estimates of a three-factor shadow-rate model. We validate our option-based results by closely matching them using a simulation-based approach. We also show that the shadow short rate is sensitive to model fit and specification.

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Article Citation

Christensen, Jens H. E, and Glenn D. Rudebusch. 2013. "Estimating Shadow-Rate Term Structure Models with Near-Zero Yields," Federal Reserve Bank of San Francisco Working Paper 2013-07. Available at