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Computing arbitrage-free yields in multi-factor Gaussian shadow-rate term structure models

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  • Marcel A. Priebsch

Abstract

This paper develops a method to approximate arbitrage-free bond yields within a term structure model in which the short rate follows a Gaussian process censored at zero (a "shadow-rate model" as proposed by Black, 1995). The censoring ensures that model-implied yields are constrained to be positive, but it also introduces non-linearity that renders standard bond pricing formulas inapplicable. In particular, yields are not linear functions of the underlying state vector as they are in affine term structure models (see Piazzesi, 2010). Existing approaches towards computing yields in shadow-rate models suffer from high computational burden or low accuracy. In contrast, I show that the technique proposed in this paper is sufficiently fast for single-step estimation of a three-factor shadow-rate term structure model, and sufficiently accurate to evaluate yields to within approximately half a basis point.

Suggested Citation

  • Marcel A. Priebsch, 2013. "Computing arbitrage-free yields in multi-factor Gaussian shadow-rate term structure models," Finance and Economics Discussion Series 2013-63, Board of Governors of the Federal Reserve System (U.S.).
  • Handle: RePEc:fip:fedgfe:2013-63
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    Cited by:

    1. Christensen, Jens H.E. & Lopez, Jose A. & Rudebusch, Glenn D., 2015. "A probability-based stress test of Federal Reserve assets and income," Journal of Monetary Economics, Elsevier, vol. 73(C), pages 26-43.
    2. Pasaogullari, Mehmet, 2015. "Forecasts from Reduced-form Models under the Zero-Lower-Bound Constraint," Working Paper 1512, Federal Reserve Bank of Cleveland.
    3. repec:eee:finana:v:52:y:2017:i:c:p:119-129 is not listed on IDEAS
    4. Kortela, Tomi, 2016. "A shadow rate model with time-varying lower bound of interest rates," Research Discussion Papers 19/2016, Bank of Finland.
    5. Lemke, Wolfgang & Vladu, Andreea, 2015. "A Shadow-Rate Term Structure Model for the Euro Area," Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 113159, Verein für Socialpolitik / German Economic Association.
    6. repec:bfr:rueban:2017:52 is not listed on IDEAS
    7. Monfort, Alain & Pegoraro, Fulvio & Renne, Jean-Paul & Roussellet, Guillaume, 2017. "Staying at zero with affine processes: An application to term structure modelling," Journal of Econometrics, Elsevier, vol. 201(2), pages 348-366.

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