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Design and Estimation of Quadratic Term Structure Models

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Author Info
Markus Leippold (University of Zurich)
Liuren Wu (Fordham University)

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Abstract

We consider the design and estimation of quadratic term structure models. We start with a list of stylized facts on interest rates and interest rate derivatives, classified into three layers: (1) general statistical properties, (2) forecasting relations, and (3) conditional dynamics. We then investigate the implications of each layer of property on model design and strive to establish a mapping between evidence and model structures. We calibrate a two­factor model that approximates these three layers of properties well, and illustrate how the model can be applied to pricing interest rate derivatives.

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Paper provided by EconWPA in its series Finance with number 0207014.

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Length: 49 pages
Date of creation: 30 Aug 2002
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Handle: RePEc:wpa:wuwpfi:0207014

Note: Type of Document - pdf; prepared on MikTex; to print on postscript; pages: 49 ; figures: included. produced via dvipdfm
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Related research
Keywords: quadratic model term structure positive interest rates humps expectation hy­pothesis GMM caps and floors.

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Find related papers by JEL classification:
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Determination of Interest Rates; Term Structure of Interest Rates

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  1. Constantinides, George M, 1992. "A Theory of the Nominal Term Structure of Interest Rates," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 5(4), pages 531-52. [Downloadable!] (restricted)
  2. Markus Leippold & Liuren Wu, 2002. "Asset Pricing Under The Quadratic Class," Finance 0207015, EconWPA. [Downloadable!]
  3. Newey, Whitney K & West, Kenneth D, 1987. "A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix," Econometrica, Econometric Society, vol. 55(3), pages 703-08, May. [Downloadable!] (restricted)
    Other versions:
  4. Campbell, John Y, 1995. "Some Lessons from the Yield Curve," Journal of Economic Perspectives, American Economic Association, vol. 9(3), pages 129-52, Summer. [Downloadable!] (restricted)
    Other versions:
  5. Geert Bekaert & Robert J. Hodrick & David A. Marshall, 1997. ""Peso problem" explanations for term structure anomalies," Working Paper Series, Issues in Financial Regulation WP-97-7, Federal Reserve Bank of Chicago.
    Other versions:
  6. Dybvig, Philip H & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1996. "Long Forward and Zero-Coupon Rates Can Never Fall," Journal of Business, University of Chicago Press, vol. 69(1), pages 1-25, January. [Downloadable!] (restricted)
    Other versions:
  7. Markus Leippold & Liuren Wu, 1999. "The Potential Approach to Bond and Currency Pricing," Finance 9903004, EconWPA. [Downloadable!]
  8. Mishkin, F.S., 1988. "The Information In The Term Structure: Some Further Results," Papers fb-_88-26, Columbia - Graduate School of Business.
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  9. Geert Bekaert & Robert J. Hodrick & David Marshall, 1996. "On biases in tests of the expectations hypothesis of the term structure of interest rates," Working Paper Series, Issues in Financial Regulation 96-3, Federal Reserve Bank of Chicago.
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  10. David K. Backus, 2001. "Affine Term Structure Models and the Forward Premium Anomaly," Journal of Finance, American Finance Association, vol. 56(1), pages 279-304, 02. [Downloadable!] (restricted)
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  14. Backus, David & Foresi, Silverio & Mozumdar, Abon & Wu, Liuren, 2001. "Predictable changes in yields and forward rates," Journal of Financial Economics, Elsevier, vol. 59(3), pages 281-311, March. [Downloadable!] (restricted)
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  15. Fabio Mercurio & Juan M. Moraleda, 1996. "A Family of Humped Volatility Structures," Tinbergen Institute Discussion Papers 96-169/2, Tinbergen Institute. [Downloadable!]
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  17. Jean-Philippe Bouchaud, Nicolas Sagna, Rama Cont, Nicole El-Karoui, Marc Potters, 1999. "Phenomenology of the interest rate curve," Applied Mathematical Finance, Taylor and Francis Journals, vol. 6(3), pages 209-232, September. [Downloadable!] (restricted)
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  18. Bent Jesper Christensen & Tomas Björk, . "Interest Rate Dynamics and Consistent Forward Rate Curves," Management Working Papers 1999-4, School of Economics and Management, University of Aarhus. [Downloadable!]
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  20. repec:cup:etheor:v:12:y:1996:i:4:p:657-81 is not listed on IDEAS
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    Other versions:
  23. Dong-Hyun Ahn & Robert F. Dittmar, 2002. "Quadratic Term Structure Models: Theory and Evidence," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 15(1), pages 243-288, March.
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Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Marco Realdon, 2006. "Equity Valuation Under Stochastic Interest Rates," Discussion Papers 06/12, Department of Economics, University of York. [Downloadable!]
  2. Markus Leippold & Liuren Wu, 2002. "Asset Pricing Under The Quadratic Class," Finance 0207015, EconWPA. [Downloadable!]
  3. Konstantijn Maes, 2004. "Modeling the Term Structure of Interest Rates: Where Do We Stand?," Research series 200402, National Bank of Belgium. [Downloadable!]
    Other versions:
  4. Don H. Kim, 2008. "Zero bound, option-implied PDFs, and term structure models," Finance and Economics Discussion Series 2008-31, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
  5. Li Chen & H. Vincent Poor, 2003. "Credit Risk Modeling and the Term Structure of Credit Spreads," Finance 0312009, EconWPA. [Downloadable!]
  6. Marco Realdon, 2006. "Quadratic Term Structure Models in Discrete Time," Discussion Papers 06/01, Department of Economics, University of York. [Downloadable!]
  7. Marco Realdon, 2007. "Extended-Gaussian Term Structure Models and Credit Risk Applications," Discussion Papers 07/27, Department of Economics, University of York. [Downloadable!]
  8. Don H Kim, 2007. "Spanned stochastic volatility in bond markets: a reexamination of the relative pricing between bonds and bond options," BIS Working Papers 239, Bank for International Settlements. [Downloadable!]
  9. Samson Assefa, 2007. "Calibration and Pricing in a Multi-Factor Quadratic Gaussian Model," Research Paper Series 197, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
  10. Olivier Scaillet., 2003. "Linear-Quadratic Jump-Diffusion Modelling with Application to Stochastic Volatility," THEMA Working Papers 2003-29, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise. [Downloadable!]
    Other versions:
  11. Enlin Pan & Liuren Wu, 2004. "Taking Positive Interest Rates Seriously," Finance 0409013, EconWPA. [Downloadable!]
  12. Li Chen & H. Vincent Poor, 2003. "Markovian Quadratic Term Structure Models For Risk-free And Defaultable Rates," Finance 0303008, EconWPA. [Downloadable!]
  13. Feng Zhao & Robert Jarrow & Haitao Li, 2004. "Interest Rate Caps Smile Too! But Can the LIBOR Market Models Capture It?," Econometric Society 2004 North American Winter Meetings 431, Econometric Society. [Downloadable!]
  14. Massoud Heidari & Liuren Wu, 2002. "Term Structure of Interest Rates, Yield Curve Residuals, and the Consistent Pricing of Interest Rates and Interest Rate Derivatives," Finance 0207010, EconWPA, revised 05 Sep 2002. [Downloadable!]
  15. Marco Realdon, 2007. "A Two Factor Black-Karasinski Credit Default Swap Pricing Model (forthcoming in the Icfai Journal of Derivatives Markets, Vol IV, No 4, October 2007; all copyrights rest with the Icfai University Pres," Discussion Papers 07/25, Department of Economics, University of York. [Downloadable!]
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