IDEAS home Printed from https://ideas.repec.org/p/yor/yorken/06-01.html
   My bibliography  Save this paper

Quadratic Term Structure Models in Discrete Time

Author

Abstract

This paper extends the results on quadratic term structure models in continuos time to the discrete time setting. The continuos time setting can be seen as a special case of the discrete time one. Recursive closed form solutions for zero coupon bonds are provided even in the presence of multiple correlated underlying factors. Pricing bond options requires simple integration. Model parameters may well be time dependent without scuppering such tractability. Model estimation does not require a restrictive choice of the market price of risk. The model can also be used for pricing credit risk and is particularly useful when the factors are or depend on periodically released macroeconomic data or corporate financial reports.

Suggested Citation

  • Marco Realdon, 2006. "Quadratic Term Structure Models in Discrete Time," Discussion Papers 06/01, Department of Economics, University of York.
    • Handle: RePEc:yor:yorken:06/01
    as

    Download full text from publisher

    File URL: https://www.york.ac.uk/media/economics/documents/discussionpapers/2006/0601.pdf
    File Function: Main text
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Duffee, Gregory R, 1999. "Estimating the Price of Default Risk," The Review of Financial Studies, Society for Financial Studies, vol. 12(1), pages 197-226.
    3. Francis A. Longstaff & Sanjay Mithal & Eric Neis, 2005. "Corporate Yield Spreads: Default Risk or Liquidity? New Evidence from the Credit Default Swap Market," Journal of Finance, American Finance Association, vol. 60(5), pages 2213-2253, October.
    4. Ang, Andrew & Bekaert, Geert, 2002. "Short rate nonlinearities and regime switches," Journal of Economic Dynamics and Control, Elsevier, vol. 26(7-8), pages 1243-1274, July.
    5. Christian Gourieroux & Alain Monfort & Vassilis Polimenis, 2002. "Affine Term Structure Models," Working Papers 2002-49, Center for Research in Economics and Statistics.
    6. 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..
    7. Duffie, Darrell & Singleton, Kenneth J, 1999. "Modeling Term Structures of Defaultable Bonds," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 687-720.
    8. Qiang Dai & Kenneth Singleton, 2003. "Term Structure Dynamics in Theory and Reality," The Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 631-678, July.
    9. Dong-Hyun Ahn & Robert F. Dittmar, 2002. "Quadratic Term Structure Models: Theory and Evidence," The Review of Financial Studies, Society for Financial Studies, vol. 15(1), pages 243-288, March.
    10. Christian Gourieroux & Razvan Sufana, 2003. "Whishart Quadratic Term Structure Models," Working Papers 2003-50, Center for Research in Economics and Statistics.
    11. Constantinides, George M, 1992. "A Theory of the Nominal Term Structure of Interest Rates," The Review of Financial Studies, Society for Financial Studies, vol. 5(4), pages 531-552.
    12. 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.
    13. Sun, Licheng, 2005. "Regime shifts in interest rate volatility," Journal of Empirical Finance, Elsevier, vol. 12(3), pages 418-434, June.
    14. 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.
    15. Ang, Andrew & Piazzesi, Monika, 2003. "A no-arbitrage vector autoregression of term structure dynamics with macroeconomic and latent variables," Journal of Monetary Economics, Elsevier, vol. 50(4), pages 745-787, May.
    16. Edwin J. Elton & Martin J. Gruber & Deepak Agrawal & Christopher Mann, 2001. "Explaining the Rate Spread on Corporate Bonds," Journal of Finance, American Finance Association, vol. 56(1), pages 247-277, February.
    17. 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.
    18. repec:bla:jfinan:v:59:y:2004:i:1:p:227-260 is not listed on IDEAS
    19. Li Chen & H. Vincent Poor, 2003. "Markovian Quadratic Term Structure Models For Risk-free And Defaultable Rates," Finance 0303008, University Library of Munich, Germany.
    20. Jan Ericsson & Joel Reneby, 2005. "Estimating Structural Bond Pricing Models," The Journal of Business, University of Chicago Press, vol. 78(2), pages 707-735, March.
    21. Darrell Duffie & Rui Kan, 1996. "A Yield‐Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406, October.
    22. Sun, Tong-sheng, 1992. "Real and Nominal Interest Rates: A Discrete-Time Model and Its Continuous-Time Limit," The Review of Financial Studies, Society for Financial Studies, vol. 5(4), pages 581-611.
    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. Chung, Tsz-Kin & Hui, Cho-Hoi & Li, Ka-Fai, 2017. "Term-structure modelling at the zero lower bound: Implications for estimating the forward term premium," Finance Research Letters, Elsevier, vol. 21(C), pages 100-106.
    2. Marcello Pericoli & Marco Taboga, 2022. "Nearly Exact Bayesian Estimation of Non-linear No-Arbitrage Term-Structure Models [Pricing the Term Structure with Linear Regressions]," Journal of Financial Econometrics, Oxford University Press, vol. 20(5), pages 807-838.
    3. Andreasen, Martin M. & Christensen, Bent Jesper, 2015. "The SR approach: A new estimation procedure for non-linear and non-Gaussian dynamic term structure models," Journal of Econometrics, Elsevier, vol. 184(2), pages 420-451.
    4. Marco Realdon, 2006. "Equity Valuation Under Stochastic Interest Rates," Discussion Papers 06/12, Department of Economics, University of York.
    5. Bruno Feunou & Jean-Sébastien Fontaine & Anh Le & Christian Lundblad, 2022. "Tractable Term Structure Models," Management Science, INFORMS, vol. 68(11), pages 8411-8429, November.
    6. Campbell, John Y. & Sunderam, Adi & Viceira, Luis M., 2017. "Inflation Bets or Deflation Hedges? The Changing Risks of Nominal Bonds," Critical Finance Review, now publishers, vol. 6(2), pages 263-301, September.
    7. Andreasen, Martin M & Meldrum, Andrew, 2015. "Dynamic term structure models: the best way to enforce the zero lower bound in the United States," Bank of England working papers 550, Bank of England.
    8. Anne Lundgaard Hansen, 2018. "Volatility-Induced Stationarity and Error-Correction in Macro-Finance Term Structure Modeling," Discussion Papers 18-12, University of Copenhagen. Department of Economics.
    9. Hansen, Anne Lundgaard, 2021. "Modeling persistent interest rates with double-autoregressive processes," Journal of Banking & Finance, Elsevier, vol. 133(C).
    10. Martin M. Andreasen & Andrew C. Meldrum, 2018. "A Shadow Rate or a Quadratic Policy Rule? The Best Way to Enforce the Zero Lower Bound in the United States," Finance and Economics Discussion Series 2018-056, Board of Governors of the Federal Reserve System (U.S.).
    11. Andreasen, Martin & Meldrum, Andrew, 2013. "Likelihood inference in non-linear term structure models: the importance of the lower bound," Bank of England working papers 481, Bank of England.
    12. Realdon, Marco, 2016. "Tests of non linear Gaussian term structure models," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 44(C), pages 128-147.

    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. Marco Realdon, 2007. "Extended-Gaussian Term Structure Models and Credit Risk Applications," Discussion Papers 07/27, Department of Economics, University of York.
    2. repec:wyi:journl:002109 is not listed on IDEAS
    3. Qiang Dai & Kenneth Singleton, 2003. "Term Structure Dynamics in Theory and Reality," The Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 631-678, July.
    4. 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.
    5. 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.
    6. 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.
    7. Realdon, Marco, 2009. ""Extended Black" term structure models," International Review of Financial Analysis, Elsevier, vol. 18(5), pages 232-238, December.
    8. 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.
    9. Alain Monfort & Fulvio Pegoraro, 2007. "Switching VARMA Term Structure Models - Extended Version," Working Papers 2007-19, Center for Research in Economics and Statistics.
    10. 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.
    11. 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.
    12. 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.
    13. Inci, Ahmet Can, 2007. "US-Swiss term structures and exchange rate dynamics," Global Finance Journal, Elsevier, vol. 18(2), pages 270-288.
    14. Perignon, Christophe & Smith, Daniel R., 2007. "Yield-factor volatility models," Journal of Banking & Finance, Elsevier, vol. 31(10), pages 3125-3144, October.
    15. Enlin Pan & Liuren Wu, 2006. "Taking Positive Interest Rates Seriously," World Scientific Book Chapters, in: Cheng-Few Lee (ed.), Advances In Quantitative Analysis Of Finance And Accounting, chapter 14, pages 327-356, World Scientific Publishing Co. Pte. Ltd..
    16. Gourieroux, C. & Monfort, A., 2008. "Quadratic stochastic intensity and prospective mortality tables," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 174-184, August.
    17. Samson Assefa, 2007. "Pricing Swaptions and Credit Default Swaptions in the Quadratic Gaussian Factor Model," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 3-2007, January-A.
    18. 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.
    19. 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.
    20. Leunglung Chan & Eckhard Platen, 2016. "Pricing of long dated equity-linked life insurance contracts," Published Paper Series 2016-5, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    21. Filipović, Damir & Gourier, Elise & Mancini, Loriano, 2016. "Quadratic variance swap models," Journal of Financial Economics, Elsevier, vol. 119(1), pages 44-68.

    More about this item

    Keywords

    Quadratic term structure model; discrete time; bond valuation; recursive solution; bond option;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:yor:yorken:06/01. 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: Paul Hodgson (email available below). General contact details of provider: https://edirc.repec.org/data/deyoruk.html .

    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.