IDEAS home Printed from https://ideas.repec.org/a/vrs/eaiada/v25y2021i3p42-71n4.html
   My bibliography  Save this article

Equilibrium Short-Rate Models Vs No-Arbitrage Models: Literature Review and Computational Examples

Author

Listed:
  • Josheski Dushko

    (Business Administration, University Goce Delchev, Stip, Macedonia)

  • Apostolov Mico

    (Business Administration, University Goce Delchev, Stip, Macedonia)

Abstract

In this paper equilibrium short-rate models are compared against no-arbitrage short-rate models. This article is composed of the introduction to this literature and a review, followed by numerical examples of one-factor short-rate models; the Cox-Ingersoll-Ross (CIR) model and the Vasicek model. No-arbitrage models were presented through the Hull-White (HW) model, the Binomial lattice model for bond pricing and interest rate modelling, the Black-Karasinski (BK) model, and the Heath-Jarrow-Morton (HJM) model. The results prove that no single interest rate model exists that can be used for all purposes. These models were compared in terms of volatility, mean reversion process and convergence. The end results confirm the dependence of volatility on the level rate as a determinant of the predictive success of these models.

Suggested Citation

  • 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.
    • Handle: RePEc:vrs:eaiada:v:25:y:2021:i:3:p:42-71:n:4
    DOI: 10.15611/eada.2021.3.03
    as

    Download full text from publisher

    File URL: https://doi.org/10.15611/eada.2021.3.03
    Download Restriction: no
    File URL: https://libkey.io/10.15611/eada.2021.3.03?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. Frederic S. Mishkin, 1978. "Efficient-Markets Theory: Implications for Monetary Policy," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 9(3), pages 707-752.
    2. 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.
    3. Pesando, James E, 1979. "On the Random Walk Characteristics of Short- and Long-Term Interest Rates in an Efficient Market," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 11(4), pages 457-466, November.
    4. Heath, David & Jarrow, Robert & Morton, Andrew, 1990. "Bond Pricing and the Term Structure of Interest Rates: A Discrete Time Approximation," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(4), pages 419-440, December.
    5. 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..
    6. 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..
    7. Yoosef Maghsoodi, 1996. "Solution Of The Extended Cir Term Structure And Bond Option Valuation," Mathematical Finance, Wiley Blackwell, vol. 6(1), pages 89-109, January.
    8. 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.
    9. 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.
    10. 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.
    11. Longstaff, Francis A., 1992. "Multiple equilibria and term structure models," Journal of Financial Economics, Elsevier, vol. 32(3), pages 333-344, December.
    12. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    13. Turan G. Bali, 1999. "An empirical comparison of continuous time models of the short term interest rate," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 19(7), pages 777-797, October.
    14. 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.
    15. Andersen, Torben G. & Lund, Jesper, 1997. "Estimating continuous-time stochastic volatility models of the short-term interest rate," Journal of Econometrics, Elsevier, vol. 77(2), pages 343-377, April.
    16. 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..
    17. Poterba, James M. & Summers, Lawrence H., 1988. "Mean reversion in stock prices : Evidence and Implications," Journal of Financial Economics, Elsevier, vol. 22(1), pages 27-59, October.
    18. Li, Anlong & Ritchken, Peter & Sankarasubramanian, L, 1995. "Lattice Models for Pricing American Interest Rate Claims," Journal of Finance, American Finance Association, vol. 50(2), pages 719-737, June.
    19. Fama, Eugene F., 1984. "Term premiums in bond returns," Journal of Financial Economics, Elsevier, vol. 13(4), pages 529-546, December.
    20. Sirimon Treepongkaruna & Stephen Gray, 2003. "On the robustness of short–term interest rate models," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 43(1), pages 87-121, March.
    21. Dothan, L. Uri, 1978. "On the term structure of interest rates," Journal of Financial Economics, Elsevier, vol. 6(1), pages 59-69, March.
    22. 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.
    23. 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.
    24. 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.
    25. 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.
    26. Ho, Thomas S. Y. & Lee, Sang Bin, 2004. "The Oxford Guide to Financial Modeling: Applications for Capital Markets, Corporate Finance, Risk Management and Financial Institutions," OUP Catalogue, Oxford University Press, number 9780195169621.
    27. 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.
    28. 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.
    29. Ahn, Dong-Hyun & Gao, Bin, 1999. "A Parametric Nonlinear Model of Term Structure Dynamics," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 721-762.
    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. Indu Rani & Chandan Kumar Verma, 2024. "Analyzing Short-Rate Models for Efficient Bond Option Pricing: A Review," SN Operations Research Forum, Springer, vol. 5(3), pages 1-26, 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. 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.
    2. repec:wyi:journl:002108 is not listed on IDEAS
    3. 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.
    4. Fergusson, Kevin, 2020. "Less-Expensive Valuation And Reserving Of Long-Dated Variable Annuities When Interest Rates And Mortality Rates Are Stochastic," ASTIN Bulletin, Cambridge University Press, vol. 50(2), pages 381-417, May.
    5. repec:uts:finphd:40 is not listed on IDEAS
    6. 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, January-A.
    7. 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.
    8. 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.
    9. 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.
    10. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    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. 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.
    13. Franco Parisi, 1998. "Tasas de Interés Nominal de Corto Plazo en Chile: Una Comparación Empírica de sus Modelos," Latin American Journal of Economics-formerly Cuadernos de Economía, Instituto de Economía. Pontificia Universidad Católica de Chile., vol. 35(105), pages 161-182.
    14. Antonio Mele, 2003. "Fundamental Properties of Bond Prices in Models of the Short-Term Rate," The Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 679-716, July.
    15. Giuseppe Arbia & Michele Di Marcantonio, 2015. "Forecasting Interest Rates Using Geostatistical Techniques," Econometrics, MDPI, vol. 3(4), pages 1-28, November.
    16. repec:wyi:journl:002109 is not listed on IDEAS
    17. 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, May.
    18. Broze, Laurence & Scaillet, Olivier & Zakoian, Jean-Michel, 1995. "Testing for continuous-time models of the short-term interest rate," Journal of Empirical Finance, Elsevier, vol. 2(3), pages 199-223, September.
    19. repec:dau:papers:123456789/5374 is not listed on IDEAS
    20. 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).
    21. Dennis Kristensen, 2004. "A Semiparametric Single-Factor Model of the Term Structure," FMG Discussion Papers dp501, Financial Markets Group.
    22. Jin-Chuan Duan & Kris Jacobs, 2001. "Short and Long Memory in Equilibrium Interest Rate Dynamics," CIRANO Working Papers 2001s-22, CIRANO.
    23. Duan, Jin-Chuan & Jacobs, Kris, 2008. "Is long memory necessary? An empirical investigation of nonnegative interest rate processes," Journal of Empirical Finance, Elsevier, vol. 15(3), pages 567-581, June.
    24. Arismendi-Zambrano, Juan & Belitsky, Vladimir & Sobreiro, Vinicius Amorim & Kimura, Herbert, 2022. "The implications of dependence, tail dependence, and bounds’ measures for counterparty credit risk pricing," Journal of Financial Stability, Elsevier, vol. 58(C).

    More about this item

    Keywords

    equilibrium models; one factor short-rate models; no-arbitrage models; Vasicek model; Hull-White (HW) model; Black-Karasinski (BK) model; Heath-Jarrow-Morton (HJM) model; Cox-Ingersoll-Ross (CIR) model;
    All these keywords.

    JEL classification:

    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • E47 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Forecasting and Simulation: Models and Applications

    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:vrs:eaiada:v:25:y:2021:i:3:p:42-71:n:4. 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: Peter Golla (email available below). General contact details of provider: https://www.sciendo.com .

    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.