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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: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    2. Eckhard Platen, 1999. "A short term interest rate model," Finance and Stochastics, Springer, vol. 3(2), pages 215-225.
    3. 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.
    4. 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.
    5. 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.
    6. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    7. 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.
    8. 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.
    9. Jun Yu & Peter C.B. Phillips, 2001. "Gaussian Estimation of Continuous Time Models of the Short Term Interest Rate," Cowles Foundation Discussion Papers 1309, Cowles Foundation for Research in Economics, Yale University.
    10. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    11. 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.
    12. 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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    1. Davide Radi & Vu Phuong Hoang & Gabriele Torri & Hana Dvořáčková, 2021. "A revised version of the Cathcart & El-Jahel model and its application to CDS market," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(2), pages 669-705, December.
    2. 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.
    3. Fergusson Kevin, 2021. "Fast maximum likelihood estimation of parameters for square root and Bessel processes," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 25(4), pages 143-170, September.
    4. Kevin Fergusson & Eckhard Platen, 2017. "Less-Expensive Valuation of Long Term Annuities Linked to Mortality, Cash and Equity," Papers 1711.02808, arXiv.org.
    5. Aigner, Philipp, 2023. "Identifying scenarios for the own risk and solvency assessment of insurance companies," ICIR Working Paper Series 48/23, Goethe University Frankfurt, International Center for Insurance Regulation (ICIR).
    6. Cheng Cai & Tiziano De Angelis & Jan Palczewski, 2021. "The American put with finite-time maturity and stochastic interest rate," Papers 2104.08502, arXiv.org, revised Feb 2024.
    7. Luca Vincenzo Ballestra & Graziella Pacelli & Davide Radi, 2017. "Valuing investment projects under interest rate risk: empirical evidence from European firms," Applied Economics, Taylor & Francis Journals, vol. 49(56), pages 5662-5672, December.
    8. 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.
    9. Qinwen Zhu & Hui Liu & Chengfeng Sun, 2019. "Edgeworth Expansion For The Distribution Of The Maximum Likelihood Estimate In The Vasicek Model," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 1-26, March.
    10. Song, Xiaodong & Johnson, Paul & Duck, Peter, 2021. "A novel combination of Mycielski–Markov, regime switching and jump diffusion models for solar energy," Applied Energy, Elsevier, vol. 301(C).
    11. K. Fergusson, 2017. "Asymptotics Of Bond Yields And Volatilities For Extended Vasicek Models Under The Real-World Measure," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 12(01), pages 1-33, March.
    12. Frederico Pinheiro & Onofre Alves Simões, 2023. "An ‘Eiopean’ Tool to Project Post Retirement Income in Portuguese Defined Contribution Pension Schemes," Working Papers REM 2023/0288, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.
    13. Kevin Fergusson, 2020. "Forecasting inflation using univariate continuous‐time stochastic models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(1), pages 37-46, January.
    14. Nikolai Dokuchaev, 2017. "A pathwise inference method for the parameters of diffusion terms," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(4), pages 731-743, October.
    15. Kladívko, Kamil & Rusý, Tomáš, 2023. "Maximum likelihood estimation of the Hull–White model," Journal of Empirical Finance, Elsevier, vol. 70(C), pages 227-247.
    16. Cheng Cai & Tiziano De Angelis & Jan Palczewski, 2022. "The American put with finite‐time maturity and stochastic interest rate," Mathematical Finance, Wiley Blackwell, vol. 32(4), pages 1170-1213, October.
    17. 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.

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    Keywords

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