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Asset Pricing Under The Quadratic Class

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

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Abstract

We identify and characterize a class of term structure models where bond yields are quadratic functions of the state vector. We label this class the quadratic class and aim to lay a solid theoretical foundation for its future empirical application. We consider asset pricing in general and derivative pricing in particular under the quadratic class. We provide two general transform methods in pricing a wide variety of fixed income derivatives in closed or semi­closed form. We further illustrate how the quadratic model and the transform methods can be applied to more general settings.

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File URL: http://129.3.20.41/eps/fin/papers/0207/0207015.pdf
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Paper provided by EconWPA in its series Finance with number 0207015.

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Length: 46 pages
Date of creation: 30 Aug 2002
Date of revision:
Handle: RePEc:wpa:wuwpfi:0207015

Note: Type of Document - pdf; prepared on MikTex; to print on postscript; pages: 46 ; figures: included. produced via dvipdfm
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Web page: http://129.3.20.41

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Related research
Keywords: quadratic class; interest rates; term structure models; state price density; Markov process.;

Other versions of this item:

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
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. 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. David K. Backus & Chris I. Telmer & Liuren Wu, 1999. "Design and Estimation of Affine Yield Models," GSIA Working Papers 5, Carnegie Mellon University, Tepper School of Business. [Downloadable!]
    Other versions:
  3. Björk, Tomas & Christensen, Bent Jesper, 1997. "Interest Rate Dynamics and Consistent Forward Rate Curves," Working Paper Series in Economics and Finance 209, Stockholm School of Economics. [Downloadable!]
    Other versions:
  4. Markus Leippold & Liuren Wu, 1999. "The Potential Approach to Bond and Currency Pricing," Finance 9903004, EconWPA. [Downloadable!]
  5. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 9(1), pages 69-107. [Downloadable!] (restricted)
  6. David Backus & Silverio Foresi & Abon Mozumdar & Liuren Wu, 1998. "Predictable Changes in Yields and Forward Rates," NBER Working Papers 6379, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  7. 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)
  8. Michael W. Brandt & Amir Yaron, 2003. "Time-Consistent No-Arbitrage Models of the Term Structure," NBER Working Papers 9458, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  9. David A. Chapman & Neil D. Pearson, 2000. "Is the Short Rate Drift Actually Nonlinear?," Journal of Finance, American Finance Association, vol. 55(1), pages 355-388, 02. [Downloadable!] (restricted)
  10. Markus Leippold & Liuren Wu, 2002. "Design and Estimation of Quadratic Term Structure Models," Finance 0207014, EconWPA. [Downloadable!]
  11. David A. Chapman & Neil D. Pearson, 1998. "Is the Short Rate Drift Actually Nonlinear?," Finance 9808005, EconWPA. [Downloadable!]
  12. 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.
  13. Bates, David S., 2000. "Post-'87 crash fears in the S&P 500 futures option market," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 181-238. [Downloadable!] (restricted)
  14. Pfann, Gerard A. & Schotman, Peter C. & Tschernig, Rolf, 1996. "Nonlinear interest rate dynamics and implications for the term structure," Journal of Econometrics, Elsevier, vol. 74(1), pages 149-176, September. [Downloadable!] (restricted)
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  15. Chacko, George & Viceira, Luis M., 2003. "Spectral GMM estimation of continuous-time processes," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 259-292. [Downloadable!] (restricted)
  16. Ait-Sahalia, Yacine, 1996. "Testing Continuous-Time Models of the Spot Interest Rate," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 9(2), pages 385-426. [Downloadable!] (restricted)
    Other versions:
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. Peter Carr & Liuren Wu, 2002. "Time-Changed Levy Processes and Option Pricing," Finance 0207011, EconWPA. [Downloadable!]
    Other versions:
  2. 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!]
  3. Gaspar, Raquel M. & Schmidt, Thorsten, 2005. "Quadratic Portfolio Credit Risk models with Shot-noise Effects," Working Paper Series in Economics and Finance 616, Stockholm School of Economics. [Downloadable!]
  4. 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!]
  5. Markus Leippold & Liuren Wu, 2002. "Design and Estimation of Quadratic Term Structure Models," Finance 0207014, EconWPA. [Downloadable!]
  6. Luca Benati, . "Affine term structure models for the foreign exchange risk premium," Bank of England working papers 291, Bank of England. [Downloadable!]
  7. Bertholon, H. & Monfort, A. & Pegoraro, F., 2008. "Econometric Asset Pricing Modelling," Documents de Travail 223, Banque de France. [Downloadable!]
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  8. Niels Rom-Poulsen, 2007. "Semi-analytical MBS Pricing," The Journal of Real Estate Finance and Economics, Springer, vol. 34(4), pages 463-498, May. [Downloadable!] (restricted)
  9. Konstantijn Maes, 2004. "Modeling the Term Structure of Interest Rates: Where Do We Stand?," Research series 200402, National Bank of Belgium. [Downloadable!]
    Other versions:
  10. Daniel R. Smith & Christophe Parignon, 2004. "Modeling Yield-Factor Volatility," Econometric Society 2004 Australasian Meetings 307, Econometric Society. [Downloadable!]
  11. 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:
  12. Andrew Ang & Jean Boivin & Sen Dong & Rudy Loo-Kung, 2009. "Monetary Policy Shifts and the Term Structure," NBER Working Papers 15270, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  13. Enlin Pan & Liuren Wu, 2004. "Taking Positive Interest Rates Seriously," Finance 0409013, EconWPA. [Downloadable!]
  14. Jing-zhi Huang & Liuren Wu, 2004. "Specification Analysis of Option Pricing Models Based on Time-Changed Levy Processes," Econometric Society 2004 North American Winter Meetings 405, Econometric Society. [Downloadable!]
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  15. Li Chen & H. Vincent Poor, 2003. "Credit Risk Modeling and the Term Structure of Credit Spreads," Finance 0312009, EconWPA. [Downloadable!]
  16. Li Chen & H. Vincent Poor, 2003. "Markovian Quadratic Term Structure Models For Risk-free And Defaultable Rates," Finance 0303008, EconWPA. [Downloadable!]
  17. Monfort, A. & Pegoraro, F., 2007. "Switching VARMA Term Structure Models - Extended Version," Documents de Travail 191, Banque de France. [Downloadable!]
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  18. Peter Carr & Liuren Wu, 2002. "The Finite Moment Log Stable Process and Option Pricing," Finance 0207012, EconWPA. [Downloadable!]
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  19. Marco Realdon, 2006. "Quadratic Term Structure Models in Discrete Time," Discussion Papers 06/01, Department of Economics, University of York. [Downloadable!]
  20. Nour Meddahi, 2001. "An Eigenfunction Approach for Volatility Modeling," CIRANO Working Papers 2001s-70, CIRANO. [Downloadable!]
  21. Marco Realdon, 2007. "Extended-Gaussian Term Structure Models and Credit Risk Applications," Discussion Papers 07/27, Department of Economics, University of York. [Downloadable!]
  22. Gaspar, Raquel M., 2004. "General Quadratic Term Structures of Bond, Futures and Forward Prices," Working Paper Series in Economics and Finance 559, Stockholm School of Economics. [Downloadable!]
  23. Massoud Heidari & Liuren WU, 2002. "Are Interest Rate Derivatives Spanned by the Term Structure of Interest Rates?," Finance 0207013, EconWPA. [Downloadable!]
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