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Fast maximum likelihood estimation of parameters for square root and Bessel processes

Author

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  • Fergusson Kevin

    (Economics, University of Melbourne, Melbourne, Australia)

Abstract

Explicit formulae for maximum likelihood estimates of the parameters of square root processes and Bessel processes and first and second order approximate sufficient statistics are supplied. Applications of the estimation formulae to simulated interest rate and index time series are supplied, demonstrating the accuracy of the approximations and the extreme speed-up in estimation time. This significantly improved run time for parameter estimation has many applications where ex-ante forecasts are required frequently and immediately, such as in hedging interest rate, index and volatility derivatives based on such models, as well as modelling credit risk, mortality rates, population size and voting behaviour.

Suggested Citation

  • 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.
    • Handle: RePEc:bpj:sndecm:v:25:y:2021:i:4:p:143-170:n:5
    DOI: 10.1515/snde-2019-0079
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    References listed on IDEAS

    as
    1. K. Fergusson & E. Platen, 2015. "Application Of Maximum Likelihood Estimation To Stochastic Short Rate Models," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 10(02), pages 1-26, December.
    2. 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.
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