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Moment based regression algorithms for drift and volatility estimation in continuous-time Markov switching models

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  • Robert J. Elliott
  • Vikram Krishnamurthy
  • Jörn Sass

Abstract

We consider a continuous time Markov switching model (MSM) which is widely used in mathematical finance. The aim is to estimate the parameters given observations in discrete time. Since there is no finite dimensional filter for estimating the underlying state of the MSM, it is not possible to compute numerically the maximum likelihood parameter estimate via the well known expectation maximization (EM) algorithm. Therefore in this paper, we propose a method of moments based parameter estimator. The moments of the observed process are computed explicitly as a function of the time discretization interval of the discrete time observation process. We then propose two algorithms for parameter estimation of the MSM. The first algorithm is based on a least-squares fit to the exact moments over different time lags, while the second algorithm is based on estimating the coefficients of the expansion (with respect to time) of the moments. Extensive numerical results comparing the algorithm with the EM algorithm for the discretized model are presented. Copyright © 2008 The Authors. Journal compilation © Royal Economic Society 2008

Suggested Citation

  • Robert J. Elliott & Vikram Krishnamurthy & Jörn Sass, 2008. "Moment based regression algorithms for drift and volatility estimation in continuous-time Markov switching models," Econometrics Journal, Royal Economic Society, vol. 11(2), pages 244-270, July.
    • Handle: RePEc:ect:emjrnl:v:11:y:2008:i:2:p:244-270
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    Citations

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    Cited by:

    1. Markus Hahn & Sylvia Frühwirth-Schnatter & Jörn Sass, 2009. "Estimating models based on Markov jump processes given fragmented observation series," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 93(4), pages 403-425, December.
    2. Krishnamurthy, Vikram & Leoff, Elisabeth & Sass, Jörn, 2018. "Filterbased stochastic volatility in continuous-time hidden Markov models," Econometrics and Statistics, Elsevier, vol. 6(C), pages 1-21.
    3. Bäuerle Nicole & Gilitschenski Igor & Hanebeck Uwe, 2015. "Exact and approximate hidden Markov chain filters based on discrete observations," Statistics & Risk Modeling, De Gruyter, vol. 32(3-4), pages 159-176, December.
    4. Ma, Jingtang & Li, Wenyuan & Zheng, Harry, 2017. "Dual control Monte-Carlo method for tight bounds of value function in regime switching utility maximization," European Journal of Operational Research, Elsevier, vol. 262(3), pages 851-862.
    5. Nicole Bauerle & Igor Gilitschenski & Uwe D. Hanebeck, 2014. "Exact and Approximate Hidden Markov Chain Filters Based on Discrete Observations," Papers 1411.0849, arXiv.org, revised Dec 2014.
    6. Elisabeth Leoff & Leonie Ruderer & Jörn Sass, 2022. "Signal-to-noise matrix and model reduction in continuous-time hidden Markov models," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(2), pages 327-359, April.
    7. Lux, Thomas, 2013. "Exact solutions for the transient densities of continuous-time Markov switching models: With an application to the poisson multifractal model," Kiel Working Papers 1871, Kiel Institute for the World Economy (IfW Kiel).
    8. Vikram Krishnamurthy & Elisabeth Leoff & Jorn Sass, 2016. "Filterbased Stochastic Volatility in Continuous-Time Hidden Markov Models," Papers 1602.05323, arXiv.org.

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