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Application of Maximum Likelihood Estimation to Stochastic Short Rate Models

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Abstract

The application of maximum likelihood estimation is not well studied for stochastic short rate models because of the cumbersome detail of this approach. We investigate the applicability of maximum likelihood estimation to stochastic short rate models. We restrict our consideration to three important short rate models, namely the Vasicek, Cox-Ingersoll-Ross and 3/2 short rate models, each having a closed-form formula for the transition density function. The parameters of the three interest rate models are fitted to US cash rates and are found to be consistent with market assessments.

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  • Kevin Fergusson & Eckhard Platen, 2015. "Application of Maximum Likelihood Estimation to Stochastic Short Rate Models," Research Paper Series 361, Quantitative Finance Research Centre, University of Technology, Sydney.
  • Handle: RePEc:uts:rpaper:361
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    1. 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: Theory Of Valuation, chapter 5, pages 129-164 World Scientific Publishing Co. Pte. Ltd..
    2. Sirimon Treepongkaruna, 2003. "Quasi-maximum likelihood estimates of Kiwi short-term interest rate," Applied Economics Letters, Taylor & Francis Journals, vol. 10(15), pages 937-942.
    3. 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.
    4. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    5. Jun Yu & Peter C. B. Phillips, 2001. "A Gaussian approach for continuous time models of the short-term interest rate," Econometrics Journal, Royal Economic Society, vol. 4(2), pages 1-3.
    6. Chapman, David A & Long, John B, Jr & Pearson, Neil D, 1999. "Using Proxies for the Short Rate: When Are Three Months Like an Instant?," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 763-806.
    7. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    8. Eckhard Platen, 1999. "A short term interest rate model," Finance and Stochastics, Springer, vol. 3(2), pages 215-225.
    9. 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.
    10. Faff, Robert & Gray, Philip, 2006. "On the estimation and comparison of short-rate models using the generalised method of moments," Journal of Banking & Finance, Elsevier, vol. 30(11), pages 3131-3146, November.
    11. Ahn, Dong-Hyun & Gao, Bin, 1999. "A Parametric Nonlinear Model of Term Structure Dynamics," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 721-762.
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    Cited by:

    1. Luca Vincenzo Ballestra & Graziella Pacelli & Davide Radi, 2016. "A Note On Fergusson And Platen: “Application Of Maximum Likelihood Estimation To Stochastic Short Rate Models”," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 11(04), pages 1-7, December.
    2. repec:taf:applec:v:49:y:2017:i:56:p:5662-5672 is not listed on IDEAS
    3. Chambers, MJ & McCrorie, JR & Thornton, MA, 2017. "Continuous Time Modelling Based on an Exact Discrete Time Representation," Economics Discussion Papers 20497, University of Essex, Department of Economics.
    4. repec:wsi:afexxx:v:14:y:2019:i:01:n:s2010495219500027 is not listed on IDEAS
    5. repec:wsi:afexxx:v:12:y:2017:i:01:n:s2010495217500051 is not listed on IDEAS
    6. repec:taf:gnstxx:v:29:y:2017:i:4:p:731-743 is not listed on IDEAS
    7. Kevin Fergusson & Eckhard Platen, 2017. "Less-Expensive Valuation of Long Term Annuities Linked to Mortality, Cash and Equity," Papers 1711.02808, arXiv.org.

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    Keywords

    Stochastic short rate; maximum likelihood estimation; Vasicek model; Cox-Ingersoll-Ross model; 3/2 model;

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