IDEAS home Printed from https://ideas.repec.org/a/now/fntfin/0500000032.html
   My bibliography  Save this article

Modeling the Term Structure of Interest Rates: A Review of the Literature

Author

Listed:
  • Gibson, Rajna
  • Lhabitant, Francois-Serge
  • Talay, Denis

Abstract

The last decades have seen the development of a profusion of theoretical models of the term structure of interest rates. The aim of this survey is to provide a comprehensive review of these continuous time modeling techniques of the term structure applicable to value and hedge default-free bonds and other interest rate derivatives. The originality of the survey lies in the fact that it provides a unifying framework in which most continuous-time term structure models can be nested and thus related to each other. Thus, we not only present the most important continuous-time term structure models in the literature but also provide a mathematically rigorous and unifying setting in which these models can be compared in terms of their similarities, distinguished in terms of their idiosyncratic features and in which their main contributions and limitations can easily be highlighted.

Suggested Citation

  • Gibson, Rajna & Lhabitant, Francois-Serge & Talay, Denis, 2010. "Modeling the Term Structure of Interest Rates: A Review of the Literature," Foundations and Trends(R) in Finance, now publishers, vol. 5(1–2), pages 1-156, December.
  • Handle: RePEc:now:fntfin:0500000032
    DOI: 10.1561/0500000032
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1561/0500000032
    Download Restriction: no

    File URL: https://libkey.io/10.1561/0500000032?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Brennan, Michael J. & Schwartz, Eduardo S., 1982. "An Equilibrium Model of Bond Pricing and a Test of Market Efficiency," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 17(3), pages 301-329, September.
    2. 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.
    3. R. Bhar & C. Chiarella, 1997. "Transformation of Heath?Jarrow?Morton models to Markovian systems," The European Journal of Finance, Taylor & Francis Journals, vol. 3(1), pages 1-26, March.
    4. Buser, Stephen A & Hendershott, Patric H & Sanders, Anthony B, 1990. "Determinants of the Value of Call Options of Default-Free Bonds," The Journal of Business, University of Chicago Press, vol. 63(1), pages 33-50, January.
    5. Pierluigi Balduzzi & Sanjiv Ranjan Das & Silverio Foresi, 1998. "The Central Tendency: A Second Factor In Bond Yields," The Review of Economics and Statistics, MIT Press, vol. 80(1), pages 62-72, February.
    6. W. Schachermayer, 1994. "Martingale Measures For Discrete‐Time Processes With Infinite Horizon," Mathematical Finance, Wiley Blackwell, vol. 4(1), pages 25-55, January.
    7. 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.
    8. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    9. Arturo Kohatsu & Roger Pettersson, 2002. "Variance reduction methods for simulation of densities on Wiener space," Economics Working Papers 597, Department of Economics and Business, Universitat Pompeu Fabra.
    10. Longstaff, Francis A., 1990. "The valuation of options on yields," Journal of Financial Economics, Elsevier, vol. 26(1), pages 97-121, July.
    11. Ramaswamy, Krishna & Sundaresan, Suresh M., 1986. "The valuation of floating-rate instruments : Theory and evidence," Journal of Financial Economics, Elsevier, vol. 17(2), pages 251-272, December.
    12. Courtadon, Georges, 1982. "The Pricing of Options on Default-Free Bonds," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 17(1), pages 75-100, March.
    13. Andrew Carverhill, 1994. "When Is The Short Rate Markovian?," Mathematical Finance, Wiley Blackwell, vol. 4(4), pages 305-312, October.
    14. Ho, Thomas S Y & Lee, Sang-bin, 1986. "Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-1029, December.
    15. 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.
    16. Back, Kerry & Pliska, Stanley R., 1991. "On the fundamental theorem of asset pricing with an infinite state space," Journal of Mathematical Economics, Elsevier, vol. 20(1), pages 1-18.
    17. Chan, K C, et al, 1992. "An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-1227, July.
    18. Markus Leippold & Liuren Wu, 1999. "The Potential Approach to Bond and Currency Pricing," Finance 9903004, University Library of Munich, Germany.
    19. Jeffrey, Andrew, 1995. "Single Factor Heath-Jarrow-Morton Term Structure Models Based on Markov Spot Interest Rate Dynamics," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 30(4), pages 619-642, December.
    20. Freddy Delbaen, 1992. "Representing Martingale Measures When Asset Prices Are Continuous And Bounded," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 107-130, April.
    21. 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.
    22. Mireille Bossy & Rajna Gibson & Francois-Serge Lhabitant & Nathalie Pistre & Denis Talay, 2006. "Model misspecification analysis for bond options and Markovian hedging strategies," Review of Derivatives Research, Springer, vol. 9(2), pages 109-135, September.
    23. Brennan, Michael J. & Schwartz, Eduardo S., 1977. "Savings bonds, retractable bonds and callable bonds," Journal of Financial Economics, Elsevier, vol. 5(1), pages 67-88, August.
    24. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    25. Hull, John & White, Alan, 1993. "One-Factor Interest-Rate Models and the Valuation of Interest-Rate Derivative Securities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(2), pages 235-254, June.
    26. Dunn, Kenneth B & McConnell, John J, 1981. "Valuation of GNMA Mortgage-Backed Securities," Journal of Finance, American Finance Association, vol. 36(3), pages 599-616, June.
    27. Rendleman, Richard J. & Bartter, Brit J., 1980. "The Pricing of Options on Debt Securities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 15(1), pages 11-24, March.
    28. Andrew Mark Jeffrey, 1995. "Single Factor Heath-Jarrow-Morton Term Structure Models Based on Markov Spot Interest Rate Dynamics," Yale School of Management Working Papers ysm46, Yale School of Management.
    29. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    30. Schaefer, Stephen M & Schwartz, Eduardo S, 1987. "Time-Dependent Variance and the Pricing of Bond Options," Journal of Finance, American Finance Association, vol. 42(5), pages 1113-1128, December.
    31. Darrell Duffie & Rui Kan, 1996. "A Yield‐Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406, October.
    32. Nicole El Karoui & Helyette Geman & Vincent Lacoste, 2000. "On the role of state variables in interest rates models," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 16(3), pages 197-217, July.
    33. Kreps, David M., 1981. "Arbitrage and equilibrium in economies with infinitely many commodities," Journal of Mathematical Economics, Elsevier, vol. 8(1), pages 15-35, March.
    34. Jamshidian, Farshid, 1989. " An Exact Bond Option Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 205-209, March.
    35. Pham, Huyen & Touzi, Nizar, 1999. "The fundamental theorem of asset pricing with cone constraints," Journal of Mathematical Economics, Elsevier, vol. 31(2), pages 265-279, March.
    36. 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.
    37. Farshid Jamshidian, 1996. "Bond, futures and option evaluation in the quadratic interest rate model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 3(2), pages 93-115.
    38. Miltersen, Kristian R & Sandmann, Klaus & Sondermann, Dieter, 1997. "Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates," Journal of Finance, American Finance Association, vol. 52(1), pages 409-430, March.
    39. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
    40. Schaefer, Stephen M. & Schwartz, Eduardo S., 1984. "A Two-Factor Model of the Term Structure: An Approximate Analytical Solution," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 19(4), pages 413-424, December.
    41. Dothan, L. Uri, 1978. "On the term structure of interest rates," Journal of Financial Economics, Elsevier, vol. 6(1), pages 59-69, March.
    42. Alan Brace & Dariusz G¸atarek & Marek Musiela, 1997. "The Market Model of Interest Rate Dynamics," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 127-155, April.
    43. Richard, Scott F., 1978. "An arbitrage model of the term structure of interest rates," Journal of Financial Economics, Elsevier, vol. 6(1), pages 33-57, March.
    44. Ball, Clifford A. & Torous, Walter N., 1983. "Bond Price Dynamics and Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 18(4), pages 517-531, December.
    45. Pearson, Neil D & Sun, Tong-Sheng, 1994. "Exploiting the Conditional Density in Estimating the Term Structure: An Application to the Cox, Ingersoll, and Ross Model," Journal of Finance, American Finance Association, vol. 49(4), pages 1279-1304, September.
    46. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    47. Peter Ritchken & L. Sankarasubramanian, 1995. "Volatility Structures Of Forward Rates And The Dynamics Of The Term Structure1," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 55-72, January.
    48. Langetieg, Terence C, 1980. "A Multivariate Model of the Term Structure," Journal of Finance, American Finance Association, vol. 35(1), pages 71-97, March.
    49. Brennan, Michael J. & Schwartz, Eduardo S., 1979. "A continuous time approach to the pricing of bonds," Journal of Banking & Finance, Elsevier, vol. 3(2), pages 133-155, July.
    50. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    51. Marsh, Terry A & Rosenfeld, Eric R, 1983. "Stochastic Processes for Interest Rates and Equilibrium Bond Prices," Journal of Finance, American Finance Association, vol. 38(2), pages 635-646, May.
    52. Li Chen & H. Vincent Poor, 2003. "Markovian Quadratic Term Structure Models For Risk-free And Defaultable Rates," Finance 0303008, University Library of Munich, Germany.
    53. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1980. "An Analysis of Variable Rate Loan Contracts," Journal of Finance, American Finance Association, vol. 35(2), pages 389-403, May.
    54. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    55. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    56. Michael J. Brennan and Eduardo S. Schwartz., 1979. "A Continuous-Time Approach to the Pricing of Bonds," Research Program in Finance Working Papers 85, University of California at Berkeley.
    57. 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.
    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. Lassaâd Mbarek & Hardik A. Marfatia & Sonja Juko, 2018. "Time-varying Response of Treasury Yields to Monetary Policy Shocks: Evidence from the Tunisian Bond Market," Working Papers 1243, Economic Research Forum, revised 23 Oct 2018.
    2. Fendel, Ralf & Neumann, Christian, 2021. "Tail risk in the European sovereign bond market during the financial crises: Detecting the influence of the European Central Bank," Global Finance Journal, Elsevier, vol. 50(C).
    3. Lucas Marc Fuhrer & Basil Guggenheim & Matthias Jüttner, 2019. "A survey-based estimation of the Swiss franc forward term premium," Swiss Journal of Economics and Statistics, Springer;Swiss Society of Economics and Statistics, vol. 155(1), pages 1-18, December.
    4. Bernardo D'Auria & Jos'e Antonio Salmer'on, 2017. "Valuing the anticipative information on the stochastic short interest rates," Papers 1711.03642, arXiv.org, revised Nov 2021.
    5. Udbodh Bhandari & Tilak Jaisi & Niranjan Devkota & Dipendra Karki & Dipak Bahadur Adhikari & Udaya Raj Paudel & Seeprata Parajuli, 2021. "Retail Loan Under Interest Rate Fluctuation in Nepal: Costumers Interest, Challenges and Managerial Solutions," Journal of Asian Business Strategy, Asian Economic and Social Society, vol. 11(1), pages 46-54, June.
    6. Radu Tunaru, 2015. "Model Risk in Financial Markets:From Financial Engineering to Risk Management," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 9524, January.
    7. Berdin, Elia, 2016. "Interest rate risk, longevity risk and the solvency of life insurers," ICIR Working Paper Series 23/16, Goethe University Frankfurt, International Center for Insurance Regulation (ICIR).
    8. D'Auria, Bernardo & García Martí, Dolores & Salmeron Garrido, Jose Antonio, 2017. "Optimal portfolio with insider information on the stochastic interest rate," DES - Working Papers. Statistics and Econometrics. WS 25819, Universidad Carlos III de Madrid. Departamento de Estadística.
    9. Christophe Michel & Victor Reutenauer & Denis Talay & Etienne Tanré, 2016. "Liquidity costs: a new numerical methodology and an empirical study," Post-Print hal-01098096, HAL.
    10. Tunaru, Diana, 2017. "Gaussian estimation and forecasting of the U.K. yield curve with multi-factor continuous-time models," International Review of Financial Analysis, Elsevier, vol. 52(C), pages 119-129.
    11. Alan De Genaro & Marco Avellaneda, 2018. "Pricing Interest Rate Derivatives Under Monetary Changes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(06), pages 1-28, September.

    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. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    2. 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.
    3. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742, November.
    4. 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.
    5. repec:dau:papers:123456789/5374 is not listed on IDEAS
    6. 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.
    7. Constantin Mellios, 2001. "Valuation of Interest Rate Options in a Two-Factor Model of the Term Structure of Interest Rate," Working Papers 2001-1, Laboratoire Orléanais de Gestion - université d'Orléans.
    8. Carl Chiarella & Xue-Zhong He & Christina Sklibosios Nikitopoulos, 2015. "Derivative Security Pricing," Dynamic Modeling and Econometrics in Economics and Finance, Springer, edition 127, number 978-3-662-45906-5, December.
    9. Zongwu Cai & Yongmiao Hong, 2013. "Some Recent Developments in Nonparametric Finance," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    10. Casassus, Jaime & Collin-Dufresne, Pierre & Goldstein, Bob, 2005. "Unspanned stochastic volatility and fixed income derivatives pricing," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2723-2749, November.
    11. Boero, G. & Torricelli, C., 1996. "A comparative evaluation of alternative models of the term structure of interest rates," European Journal of Operational Research, Elsevier, vol. 93(1), pages 205-223, August.
    12. repec:wyi:journl:002108 is not listed on IDEAS
    13. repec:wyi:journl:002109 is not listed on IDEAS
    14. Josheski Dushko & Apostolov Mico, 2021. "Equilibrium Short-Rate Models Vs No-Arbitrage Models: Literature Review and Computational Examples," Econometrics. Advances in Applied Data Analysis, Sciendo, vol. 25(3), pages 42-71, September.
    15. Vetzal, Kenneth R., 1997. "Stochastic volatility, movements in short term interest rates, and bond option values," Journal of Banking & Finance, Elsevier, vol. 21(2), pages 169-196, February.
    16. Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 69-96, November.
    17. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    18. Cai, Zongwu & Hong, Yongmiao, 2003. "Nonparametric Methods in Continuous-Time Finance: A Selective Review," SFB 373 Discussion Papers 2003,15, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    19. repec:uts:finphd:40 is not listed on IDEAS
    20. Giuseppe Arbia & Michele Di Marcantonio, 2015. "Forecasting Interest Rates Using Geostatistical Techniques," Econometrics, MDPI, vol. 3(4), pages 1-28, November.
    21. Sercu, P., 1991. "Bond options and bond portfolio insurance," Insurance: Mathematics and Economics, Elsevier, vol. 10(3), pages 203-230, December.
    22. Kevin John Fergusson, 2018. "Less-Expensive Pricing and Hedging of Extreme-Maturity Interest Rate Derivatives and Equity Index Options Under the Real-World Measure," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 3-2018.
    23. Jiang, George J., 1997. "A generalized one-factor term structure model and pricing of interest rate derivative securities," Research Report 97A34, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    24. Mondher Bellalah, 2009. "Derivatives, Risk Management & Value," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 7175, January.

    More about this item

    Keywords

    Term structure; Interest rates; Continuous-time models; Finance; Financial econometrics; Macroeconomics; Financial Markets and Institutions; Mathematical Finance;
    All these keywords.

    JEL classification:

    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

    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:now:fntfin:0500000032. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: http://www.nowpublishers.com/ .

    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: Alet Heezemans (email available below). General contact details of provider: http://www.nowpublishers.com/ .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.