IDEAS home Printed from https://ideas.repec.org/a/eee/dyncon/v35y2011i6p815-824.html
   My bibliography  Save this article

Discrete time Wishart term structure models

Author

Listed:
  • Gourieroux, Christian
  • Sufana, Razvan

Abstract

This paper reveals that the class of Affine Term Structure Models (ATSMs) introduced by Duffie and Kan (1996) is larger than previously considered in the literature. In the framework of risk factors following a Wishart autoregressive process, we define the Wishart Term Structure Model (WTSM) as an extension of a subclass of Quadratic Term Structure Models (QTSMs), derive simple parameter restrictions that ensure positive bond yields at all maturities, and observe that the usual constraint on affine processes requiring that the volatility matrix be diagonal up to a path independent linear invertible transformation can be considerably relaxed.

Suggested Citation

  • Gourieroux, Christian & Sufana, Razvan, 2011. "Discrete time Wishart term structure models," Journal of Economic Dynamics and Control, Elsevier, vol. 35(6), pages 815-824, June.
  • Handle: RePEc:eee:dyncon:v:35:y:2011:i:6:p:815-824
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165-1889(11)00008-X
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Qiang Dai & Kenneth J. Singleton, 2000. "Specification Analysis of Affine Term Structure Models," Journal of Finance, American Finance Association, vol. 55(5), pages 1943-1978, October.
    2. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    3. Das, Sanjiv R., 2002. "The surprise element: jumps in interest rates," Journal of Econometrics, Elsevier, vol. 106(1), pages 27-65, January.
    4. Markus Leippold & Liuren Wu, 2003. "Design and Estimation of Quadratic Term Structure Models," Review of Finance, European Finance Association, vol. 7(1), pages 47-73.
    5. Leippold, Markus & Wu, Liuren, 2002. "Asset Pricing under the Quadratic Class," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 37(2), pages 271-295, June.
    6. C. Gourieroux, 2006. "Continuous Time Wishart Process for Stochastic Risk," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 177-217.
    7. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    8. Dai, Qiang & Singleton, Kenneth J., 2003. "Fixed-income pricing," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 20, pages 1207-1246, Elsevier.
    9. Ahn, Chang Mo & Thompson, Howard E, 1988. " Jump-Diffusion Processes and the Term Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 43(1), pages 155-174, March.
    10. Chen, Ren-Raw & Scott, Louis O, 1992. "Pricing Interest Rate Options in a Two-Factor Cox-Ingersoll-Ross Model of the Term Structure," Review of Financial Studies, Society for Financial Studies, vol. 5(4), pages 613-636.
    11. Qiang Dai & Kenneth J. Singleton & Wei Yang, 2007. "Regime Shifts in a Dynamic Term Structure Model of U.S. Treasury Bond Yields," Review of Financial Studies, Society for Financial Studies, vol. 20(5), pages 1669-1706, 2007 12.
    12. Gourieroux, Christian & Sufana, Razvan, 2010. "Derivative Pricing With Wishart Multivariate Stochastic Volatility," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(3), pages 438-451.
    13. Monfort, A. & Pegoraro, F., 2007. "Switching VARMA Term Structure Models - Extended Version," Working papers 191, Banque de France.
    14. Gregory R. Duffee, 2002. "Term Premia and Interest Rate Forecasts in Affine Models," Journal of Finance, American Finance Association, vol. 57(1), pages 405-443, February.
    15. Longstaff, Francis A., 1989. "A nonlinear general equilibrium model of the term structure of interest rates," Journal of Financial Economics, Elsevier, vol. 23(2), pages 195-224, August.
    16. Alain Monfort & Fulvio Pegoraro, 2007. "Switching VARMA Term Structure Models," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 5(1), pages 105-153.
    17. Gray, Stephen F., 1996. "Modeling the conditional distribution of interest rates as a regime-switching process," Journal of Financial Economics, Elsevier, vol. 42(1), pages 27-62, September.
    18. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    19. Ravi Bansal & Hao Zhou, 2002. "Term Structure of Interest Rates with Regime Shifts," Journal of Finance, American Finance Association, vol. 57(5), pages 1997-2043, October.
    20. L. C. G. Rogers, 1997. "The Potential Approach to the Term Structure of Interest Rates and Foreign Exchange Rates," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 157-176, April.
    21. Dijkstra, Theo K. & Yao, Yong, 2002. "Moment generating function approach to pricing interest rate and foreign exchange rate claims," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 163-178, October.
    22. Andrea Buraschi & Paolo Porchia & Fabio Trojani, 2010. "Correlation Risk and Optimal Portfolio Choice," Journal of Finance, American Finance Association, vol. 65(1), pages 393-420, February.
    23. Qiang Dai & Kenneth Singleton, 2003. "Term Structure Dynamics in Theory and Reality," Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 631-678, July.
    24. Ahn, Dong-Hyun & Dittmar, Robert F. & Gallant, A. Ronald & Gao, Bin, 2003. "Purebred or hybrid?: Reproducing the volatility in term structure dynamics," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 147-180.
    25. Duncan, George T, 1977. "A Matrix Measure of Multivariate Local Risk Aversion," Econometrica, Econometric Society, vol. 45(4), pages 895-903, May.
    26. Dong-Hyun Ahn & Robert F. Dittmar, 2002. "Quadratic Term Structure Models: Theory and Evidence," Review of Financial Studies, Society for Financial Studies, vol. 15(1), pages 243-288, March.
    27. Serge Darolles & Christian Gourieroux & Joann Jasiak, 2006. "Structural Laplace Transform and Compound Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(4), pages 477-503, July.
    28. Gourieroux, C. & Monfort, A. & Sufana, R., 2010. "International money and stock market contingent claims," Journal of International Money and Finance, Elsevier, vol. 29(8), pages 1727-1751, December.
    29. Karni, Edi, 1979. "On Multivariate Risk Aversion," Econometrica, Econometric Society, vol. 47(6), pages 1391-1401, November.
    30. Beaglehole, David & Tenney, Mark, 1992. "Corrections and additions to 'a nonlinear equilibrium model of the term structure of interest rates'," Journal of Financial Economics, Elsevier, vol. 32(3), pages 345-353, December.
    31. C. Gourieroux & A. Monfort & V. Polimenis, 2006. "Affine Models for Credit Risk Analysis," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(3), pages 494-530.
    32. Christian Gourieroux & Razvan Sufana, 2006. "A Classification of Two-Factor Affine Diffusion Term Structure Models," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(1), pages 31-52.
    33. David S. Bates, 2006. "Maximum Likelihood Estimation of Latent Affine Processes," Review of Financial Studies, Society for Financial Studies, vol. 19(3), pages 909-965.
    34. Li Chen & H. Vincent Poor, 2003. "Markovian Quadratic Term Structure Models For Risk-free And Defaultable Rates," Finance 0303008, University Library of Munich, Germany.
    35. Joann Jasiak & Christian Gourieroux, 2006. "Autoregressive gamma processes," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(2), pages 129-152.
    36. Constantinides, George M, 1992. "A Theory of the Nominal Term Structure of Interest Rates," Review of Financial Studies, Society for Financial Studies, vol. 5(4), pages 531-552.
    37. G.M. Constantinides & M. Harris & R. M. Stulz (ed.), 2003. "Handbook of the Economics of Finance," Handbook of the Economics of Finance, Elsevier, edition 1, volume 1, number 1.
    38. Ang, Andrew & Bekaert, Geert, 2002. "Regime Switches in Interest Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 163-182, April.
    39. José Fonseca & Martino Grasselli & Claudio Tebaldi, 2007. "Option pricing when correlations are stochastic: an analytical framework," Review of Derivatives Research, Springer, vol. 10(2), pages 151-180, May.
    40. Darrell Duffie & Rui Kan, 1996. "A Yield‐Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406, October.
    41. G.M. Constantinides & M. Harris & R. M. Stulz (ed.), 2003. "Handbook of the Economics of Finance," Handbook of the Economics of Finance, Elsevier, edition 1, volume 1, number 2.
    42. Gourieroux, C. & Jasiak, J. & Sufana, R., 2009. "The Wishart Autoregressive process of multivariate stochastic volatility," Journal of Econometrics, Elsevier, vol. 150(2), pages 167-181, June.
    43. Longstaff, Francis A & Schwartz, Eduardo S, 1992. "Interest Rate Volatility and the Term Structure: A Two-Factor General Equilibrium Model," Journal of Finance, American Finance Association, vol. 47(4), pages 1259-1282, September.
    44. Singleton, Kenneth J., 2001. "Estimation of affine asset pricing models using the empirical characteristic function," Journal of Econometrics, Elsevier, vol. 102(1), pages 111-141, May.
    45. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, vol. 53(2), pages 363-384, March.
    46. Li Chen & Damir Filipović & H. Vincent Poor, 2004. "Quadratic Term Structure Models For Risk‐Free And Defaultable Rates," Mathematical Finance, Wiley Blackwell, vol. 14(4), pages 515-536, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kwai S. Leung & Hon Y. Ng & Hoi Y. Wong, 2014. "Stochastic Skew in the Interest Rate Cap Market," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 34(12), pages 1146-1169, December.
    2. Deelstra, Griselda & Grasselli, Martino & Van Weverberg, Christopher, 2016. "The role of the dependence between mortality and interest rates when pricing Guaranteed Annuity Options," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 205-219.
    3. Dubecq, Simon & Monfort, Alain & Renne, Jean-Paul & Roussellet, Guillaume, 2016. "Credit and liquidity in interbank rates: A quadratic approach," Journal of Banking & Finance, Elsevier, vol. 68(C), pages 29-46.
    4. Monfort, Alain & Pegoraro, Fulvio, 2012. "Asset pricing with Second-Order Esscher Transforms," Journal of Banking & Finance, Elsevier, vol. 36(6), pages 1678-1687.
    5. Da Fonseca, José & Gnoatto, Alessandro & Grasselli, Martino, 2013. "A flexible matrix Libor model with smiles," Journal of Economic Dynamics and Control, Elsevier, vol. 37(4), pages 774-793.
    6. Chiarella, Carl & Da Fonseca, José & Grasselli, Martino, 2014. "Pricing range notes within Wishart affine models," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 193-203.
    7. Monfort, Alain & Renne, Jean-Paul & Roussellet, Guillaume, 2015. "A Quadratic Kalman Filter," Journal of Econometrics, Elsevier, vol. 187(1), pages 43-56.
    8. Alfonsi, Aurélien & Kebaier, Ahmed & Rey, Clément, 2016. "Maximum likelihood estimation for Wishart processes," Stochastic Processes and their Applications, Elsevier, vol. 126(11), pages 3243-3282.
    9. Takamizawa, Hideyuki & 高見澤, 秀幸, 2015. "Impact of No-arbitrage on Interest Rate Dynamics," Working Paper Series G-1-5, Hitotsubashi University Center for Financial Research.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. repec:wyi:journl:002109 is not listed on IDEAS
    2. Qiang Dai & Kenneth Singleton, 2003. "Term Structure Dynamics in Theory and Reality," Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 631-678, July.
    3. Alain Monfort & Fulvio Pegoraro, 2007. "Switching VARMA Term Structure Models - Extended Version," Working Papers 2007-19, Center for Research in Economics and Statistics.
    4. Jiang, George & Yan, Shu, 2009. "Linear-quadratic term structure models - Toward the understanding of jumps in interest rates," Journal of Banking & Finance, Elsevier, vol. 33(3), pages 473-485, March.
    5. H. Bertholon & A. Monfort & F. Pegoraro, 2008. "Econometric Asset Pricing Modelling," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 6(4), pages 407-458, Fall.
    6. Peter Feldhütter & Christian Heyerdahl-Larsen & Philipp Illeditsch, 2018. "Risk Premia and Volatilities in a Nonlinear Term Structure Model [Quadratic term structure models: theory and evidence]," Review of Finance, European Finance Association, vol. 22(1), pages 337-380.
    7. Realdon, Marco, 2009. ""Extended Black" term structure models," International Review of Financial Analysis, Elsevier, vol. 18(5), pages 232-238, December.
    8. Chiarella, Carl & Hsiao, Chih-Ying & Tô, Thuy-Duong, 2016. "Stochastic correlation and risk premia in term structure models," Journal of Empirical Finance, Elsevier, vol. 37(C), pages 59-78.
    9. Lioui, Abraham & Poncet, Patrice, 2004. "General equilibrium real and nominal interest rates," Journal of Banking & Finance, Elsevier, vol. 28(7), pages 1569-1595, July.
    10. Duffee, Gregory R., 2013. "Bond Pricing and the Macroeconomy," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 907-967, Elsevier.
    11. Likuan Qin & Vadim Linetsky, 2014. "Positive Eigenfunctions of Markovian Pricing Operators: Hansen-Scheinkman Factorization, Ross Recovery and Long-Term Pricing," Papers 1411.3075, arXiv.org, revised Sep 2015.
    12. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    13. Driessen, Joost & Melenberg, Bertrand & Nijman, Theo, 2005. "Testing affine term structure models in case of transaction costs," Journal of Econometrics, Elsevier, vol. 126(1), pages 201-232, May.
    14. Gourieroux, C. & Monfort, A. & Sufana, R., 2010. "International money and stock market contingent claims," Journal of International Money and Finance, Elsevier, vol. 29(8), pages 1727-1751, December.
    15. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    16. Dai, Qiang & Singleton, Kenneth J., 2003. "Fixed-income pricing," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 20, pages 1207-1246, Elsevier.
    17. Inci, Ahmet Can, 2007. "US-Swiss term structures and exchange rate dynamics," Global Finance Journal, Elsevier, vol. 18(2), pages 270-288.
    18. Peng Cheng & Olivier Scaillet, 2002. "Linear-Quadratic Jump-Diffusion Modeling with Application to Stochastic Volatility," FAME Research Paper Series rp67, International Center for Financial Asset Management and Engineering.
    19. Perignon, Christophe & Smith, Daniel R., 2007. "Yield-factor volatility models," Journal of Banking & Finance, Elsevier, vol. 31(10), pages 3125-3144, October.
    20. Realdon, Marco, 2006. "Quadratic term structure models in discrete time," Finance Research Letters, Elsevier, vol. 3(4), pages 277-289, December.
    21. Dong Heon Kim, 2004. "Nonlinearity in the Term Structure," Econometric Society 2004 Far Eastern Meetings 440, Econometric Society.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:dyncon:v:35:y:2011:i:6:p:815-824. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jedc .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.