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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

References listed on IDEAS
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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!]
    Other versions:
  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. 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:
  6. Markus Leippold & Liuren Wu, 1999. "The Potential Approach to Bond and Currency Pricing," Finance 9903004, EconWPA. [Downloadable!]
  7. Bekaert, Geert & Hodrick, Robert J. & Marshall, David A., 2001. "Peso problem explanations for term structure anomalies," Journal of Monetary Economics, Elsevier, vol. 48(2), pages 241-270, October. [Downloadable!] (restricted)
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  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. Bekaert, Geert & Hodrick, Robert J. & Marshall, David A., 1997. "On biases in tests of the expectations hypothesis of the term structure of interest rates," Journal of Financial Economics, Elsevier, vol. 44(3), pages 309-348, June. [Downloadable!] (restricted)
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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)
  11. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(04), pages 657-681, October. [Downloadable!]
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  15. 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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  16. 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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  18. 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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  19. 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. Martin D. Evans & Karen K. Lewis, 1992. "Do Stationary Risk Premia Explain It All? Evidence from the Term Structure," Working Papers 92-11, New York University, Leonard N. Stern School of Business, Department of Economics.
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  21. repec:cup:etheor:v:12:y:1996:i:4:p:657-81 is not listed on IDEAS
  22. Moraleda, Juan M. & Vorst, Ton C. F., 1997. "Pricing American interest rate claims with humped volatility models," Journal of Banking & Finance, Elsevier, vol. 21(8), pages 1131-1157, August. [Downloadable!] (restricted)
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  24. 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. 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!]
  2. 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!]
  3. Marco Realdon, 2006. "Equity Valuation Under Stochastic Interest Rates," Discussion Papers 06/12, Department of Economics, University of York. [Downloadable!]
  4. Markus Leippold & Liuren Wu, 2002. "Asset Pricing Under The Quadratic Class," Finance 0207015, EconWPA. [Downloadable!]
    Other versions:
  5. Konstantijn Maes, 2004. "Modeling the Term Structure of Interest Rates: Where Do We Stand?," Research series 200402, National Bank of Belgium. [Downloadable!]
    Other versions:
  6. 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!]
  7. 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:
  8. Enlin Pan & Liuren Wu, 2004. "Taking Positive Interest Rates Seriously," Finance 0409013, EconWPA. [Downloadable!]
  9. Li Chen & H. Vincent Poor, 2003. "Credit Risk Modeling and the Term Structure of Credit Spreads," Finance 0312009, EconWPA. [Downloadable!]
  10. Li Chen & H. Vincent Poor, 2003. "Markovian Quadratic Term Structure Models For Risk-free And Defaultable Rates," Finance 0303008, EconWPA. [Downloadable!]
  11. 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!]
  12. Marco Realdon, 2006. "Quadratic Term Structure Models in Discrete Time," Discussion Papers 06/01, Department of Economics, University of York. [Downloadable!]
  13. 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!]
  14. Marco Realdon, 2007. "Extended-Gaussian Term Structure Models and Credit Risk Applications," Discussion Papers 07/27, Department of Economics, University of York. [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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