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An online estimation scheme for a Hull–White model with HMM-driven parameters

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Abstract

This paper considers the implementation of a mean-reverting interest rate model with Markov-modulated parameters. Hidden Markov model filtering techniques in Elliott (1994, Automatica, 30:1399–1408) and Elliott et al. (1995, Hidden Markov Models: Estimation and Control. Springer, New York) are employed to obtain optimal estimates of the model parameters via recursive filters of auxiliary quantities of the observation process. Algorithms are developed and implemented on a financial dataset of 30-day Canadian Treasury bill yields. We also provide standard errors for the model parameter estimates. Our analysis shows that within the dataset and period studied, a model with two regimes is sufficient to describe the interest rate dynamics on the basis of very small prediction errors and the Akaike information criterion.

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Authors and Affiliations

  1. CARISMA School of Information Systems, Computing and Mathematics, Brunel University, Uxbridge, Middlesex, UB8 3PH, UK

    Christina Erlwein

  2. Department of Statistical and Actuarial Sciences, University of Western Ontario, 2nd Floor Western Science Centre, London, ON, Canada, N6A 5B7

    Rogemar Mamon

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  1. Christina Erlwein
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  2. Rogemar Mamon
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Correspondence to Rogemar Mamon.

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Erlwein, C., Mamon, R. An online estimation scheme for a Hull–White model with HMM-driven parameters. Stat Methods Appl 18, 87–107 (2009). https://doi.org/10.1007/s10260-007-0082-4

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