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

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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.

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  • 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. Dumas, Bernard & Savioz, Marcel René, 2020. "A Theory of the Nominal Character of Stock Securities," CEPR Discussion Papers 15507, C.E.P.R. Discussion Papers.
    2. 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.
    3. Mehmet Pasaogullari, 2015. "Forecasts from Reduced-form Models under the Zero-Lower-Bound Constraint," Working Papers (Old Series) 1512, Federal Reserve Bank of Cleveland.
    4. Schupp, Fabian, 2020. "The (ir)relevance of the nominal lower bound for real yield curve analysis," Working Paper Series 2476, European Central Bank.
    5. Schupp, Fabian & Geiger, Felix, 2018. "With a little help from my friends: Survey-based derivation of euro area short rate expectations at the effective lower bound," VfS Annual Conference 2018 (Freiburg, Breisgau): Digital Economy 181529, Verein für Socialpolitik / German Economic Association.
    6. Taisuke Nakata & Hiroatsu Tanaka, 2020. "Equilibrium Yield Curves and the Interest Rate Lower Bound," CARF F-Series CARF-F-482, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    7. Kortela, Tomi, 2016. "A shadow rate model with time-varying lower bound of interest rates," Bank of Finland Research Discussion Papers 19/2016, Bank of Finland.
    8. 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.
    9. Tunaru, Diana, 2017. "Gaussian estimation and forecasting of the U.K. yield curve with multi-factor continuous-time models," International Review of Financial Analysis, Elsevier, vol. 52(C), pages 119-129.
    10. Jacob Bjerre Skov & David Skovmand, 2021. "Dynamic term structure models for SOFR futures," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(10), pages 1520-1544, October.
    11. Kortela, Tomi, 2016. "A shadow rate model with time-varying lower bound of interest rates," Research Discussion Papers 19/2016, Bank of Finland.
    12. Lemke, Wolfgang & Vladu, Andreea, 2015. "A Shadow-Rate Term Structure Model for the Euro Area," VfS Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 113159, Verein für Socialpolitik / German Economic Association.
    13. repec:zbw:bofrdp:2016_019 is not listed on IDEAS

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