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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. 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.
    2. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
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    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?," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 763-806.
    7. 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..
    8. 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.
    9. Eckhard Platen, 1999. "A short term interest rate model," Finance and Stochastics, Springer, vol. 3(2), pages 215-225.
    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," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 721-762.
    12. 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.
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    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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).
    8. 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.
    9. 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.
    10. 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.
    11. 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.
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    Keywords

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