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CONSISTENT YIELD CURVE PREDICTION

Published online by Cambridge University Press:  05 February 2016

Josef Teichmann  and
Mario V. Wüthrich
Josef Teichmann*
Affiliation:
ETH Zurich, Department of Mathematics, 8092 Zurich, Switzerland
Mario V. Wüthrich
Affiliation:
ETH Zurich, RiskLab, Department of Mathematics, 8092 Zurich, Switzerland E-Mail: mario.wuethrich@math.ethz.ch
*
E-Mail: jteichma@math.ethz.ch
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Abstract

We present an arbitrage-free non-parametric yield curve prediction model which takes the full discretized yield curve data as input state variable. Absence of arbitrage is a particularly important model feature for prediction models in case of highly correlated data as, for instance, interest rates. Furthermore, the model structure allows to separate constructing the daily yield curve from estimating its volatility structure and from calibrating the market prices of risk. The empirical part includes tests on modeling assumptions, out-of-sample back-testing and a comparison with the Vasiček (1977) short-rate model.

Keywords

Yield curve predictionno-arbitrageHeath–Jarrow–Morton type modelvolatility scaling factors and return directions

Information

Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 46 , Issue 2 , May 2016 , pp. 191 - 224
Copyright
Copyright © Astin Bulletin 2016 

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References

Audrino, F. and Filipova, K. (2009) Yield curve predictability, regimes, and macroeconomic information: A data driven approach. University of St. Gallen. Discussion Paper no. 2009–10.Google Scholar
Barone-Adesi, G., Bourgoin, F. and Giannopoulos, K. (1998) Don't look back. Risk 08/1998, 100–103.Google Scholar
Björk, T. (1998) Interest rate theory. In Financial Mathematics, Bressanone 1996 (ed. Runggaldier, W.), pp. 53–122. Lecture Notes in Mathematics 1656, Springer.Google Scholar
Björk, T. and Landén, C. (2000) On the construction of finite dimensional realizations for nonlinear forward rate models. Working paper, Stockholm School of Economics.Google Scholar
Björk, T. and Svensson, L. (2001) On the existence of finite dimensional realizations for nonlinear forward rate models. Mathematical Finance, 11 (2), 205–243.Google Scholar
Black, F. and Karasinski, P. (1991) Bond and option pricing when short rates are lognormal. Financial Analysts Journal, 47 (4), 52–59.Google Scholar
Brigo, D. and Mercurio, F. (2006) Interest Rate Models - Theory and Practice. Berlin, Heidelberg: Springer.Google Scholar
Cairns, A.J.G. (1998) Descriptive bond-yield and forward-rate models for the British government securities' market. British Act. J., 4 (2), 265–321.CrossRefGoogle Scholar
Cairns, A.J.G. (2004) Interest Rate Models: An Introduction. Princeton, New Jersey: Princeton University Press.Google Scholar
Christensen, J.H.E., Diebold, F.X. and Rudebusch, G.D. (2007) The affine arbitrage-free class of Nelson-Siegel term structure models. Working Paper Series 2007-20, Federal Reserve Bank of San Francisco.Google Scholar
Christensen, J.H.E., Diebold, F.X. and Rudebusch, G.D. (2009) An arbitrage-free generalized Nelson-Siegel term structure model. Econometrics Journal, Royal Economic Society, 12 (3), C33–C64.Google Scholar
Cox, J.C., Ingersoll, J.E. and Ross, S.A. (1985) A theory of the term structure of interest rates. Econometrica, 53 (2), 385–407.Google Scholar
Dahl, M. (2007) A discrete-time model for reinvestment risk in the bond market. ASTIN Bulletin, 37 (2), 235–264.Google Scholar
Deguillaume, N., Rebonato, R. and Pogudin, A. (2013) The nature of the dependence of the magnitude of rate moves on the level of rates: A universal relationship. Quantitative Finance, 13 (3), 351–367.Google Scholar
Delbaen, F. and Schachermayer, W. (1994) A general version of the fundamental theorem of asset pricing. Mathematische Annalen, 300, 463–520.Google Scholar
Filipović, D. (1999) A note on the Nelson-Siegel family. Mathematical Finance, 9 (4), 349–359.CrossRefGoogle Scholar
Filipović, D. (2000) Exponential-polynomial families and the term structure of interest rates. Bernoulli, 6 (6), 1–27.Google Scholar
Filipović, D. (2009) Term-Structure Models. Berlin, Heidelberg: Springer.Google Scholar
Filipović, D. and Teichmann, J. (2004) On the geometry of the term structure of interest rates. Proceedings of The Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences, 460, 129–167.Google Scholar
Filipović, D. and Zabczyk, J. (2002) Markovian term structure models in discrete time. Annals of Applied Probability, 12 (2), 710–729.Google Scholar
Harms, P., Stefanovits, D., Teichmann, J. and Wüthrich, M.V. (2015) Consistent recalibration of yield curve models. Preprint on arXiv 1502.02926.Google Scholar
Heath, D., Jarrow, R. and Morton, A. (1990) Bond pricing and the term structure of interest rates: A discrete time approximation. Journal of Financial Quantitative Analysis, 25 (4), 419–440.Google Scholar
Heath, D., Jarrow, R. and Morton, A. (1992) Bond pricing and the term structure of interest rates: A new methodology. Econometrica, 60 (1), 77–105.Google Scholar
Hull, J. and White, A. (1990) Pricing interest-rate-derivative securities. Review of Financial Studies, 3 (4), 573–592.Google Scholar
Hull, J. and White, A. (1994) Branching out. Risk, 7, 34–37.Google Scholar
Jordan, T.J. (2009) SARON - an innovation for the financial markets. Launch event for Swiss Reference Rates, Zurich, August 25, 2009.Google Scholar
Müller, R. (2002) Zur Berechnung der Obligationenrenditen im Statistischen Montatsheft der SNB. Swiss National Bank Quartalsheft, 2, 64–73.Google Scholar
Nelson, C.R. and Siegel, A.F. (1987) Parsimonious modeling of yield curves. J. Business, 60 (4), 473–489.Google Scholar
Ortega, J.P., Pullirsch, R., Teichmann, J. and Wergieluk, J. (2009) A dynamic approach for scenario generation in risk management. Preprint on arXiv 0904.0624.Google Scholar
Stefanovits, D. and Wüthrich, M.V. (2014) Hedging of long term zero-coupon bonds in a market model with reinvestment risk. European Actuarial Journal, 4 (1), 49–75.Google Scholar
Svensson, L.E.O. (1994) Estimating and interpreting forward interest rates: Sweden 1992–1994. NBER Working Paper Series Nr. 4871.Google Scholar
Svensson, L.E.O. (1995) Estimating forward interest rates with the extended Nelson & Siegel method. Sveriges Riksbank Quarterly Review, 3, 13–26.Google Scholar
Vasiček, O. (1977) An equilibrium characterization of the term structure. Journal of Financial Economics, 5 (2), 177–188.Google Scholar
Wüthrich, M.V. (2016) Consistent re-calibration in yield curve modeling: An example. In: Causal Inference in Econometrics, 57–82. Huynh, V.-N., Kreinovich, V., Sriboonchitta, S. (eds.), Studies in computational Intelligence 622, Springer.Google Scholar