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Stylised facts of financial time series and hidden Markov models in continuous time

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  • Peter Nystrup
  • Henrik Madsen
  • Erik Lindstr�m

Abstract

Hidden Markov models are often applied in quantitative finance to capture the stylised facts of financial returns. They are usually discrete-time models and the number of states rarely exceeds two because of the quadratic increase in the number of parameters with the number of states. This paper presents an extension to continuous time where it is possible to increase the number of states with a linear rather than quadratic growth in the number of parameters. The possibility of increasing the number of states leads to a better fit to both the distributional and temporal properties of daily returns.

Suggested Citation

  • Peter Nystrup & Henrik Madsen & Erik Lindstr�m, 2015. "Stylised facts of financial time series and hidden Markov models in continuous time," Quantitative Finance, Taylor & Francis Journals, vol. 15(9), pages 1531-1541, September.
    • Handle: RePEc:taf:quantf:v:15:y:2015:i:9:p:1531-1541
    DOI: 10.1080/14697688.2015.1004801
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    References listed on IDEAS

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    1. Malmsten, Hans & Teräsvirta, Timo, 2004. "Stylized Facts of Financial Time Series and Three Popular Models of Volatility," SSE/EFI Working Paper Series in Economics and Finance 563, Stockholm School of Economics, revised 03 Sep 2004.
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    Cited by:

    1. Yu, Xing & Li, Yanyan & Lu, Junli & Shen, Xilin, 2023. "Futures hedging in crude oil markets: A trade-off between risk and return," Resources Policy, Elsevier, vol. 80(C).
    2. Anindya Goswami & Kedar Nath Mukherjee & Irvine Homi Patalwala & Sanjay N. S, 2022. "Regime recovery using implied volatility in Markov modulated market model," Papers 2201.10304, arXiv.org, revised Mar 2022.
    3. Peter Nystrup & Henrik Madsen & Erik Lindström, 2018. "Dynamic portfolio optimization across hidden market regimes," Quantitative Finance, Taylor & Francis Journals, vol. 18(1), pages 83-95, January.
    4. Valeriy Zakamulin, 2023. "Not all bull and bear markets are alike: insights from a five-state hidden semi-Markov model," Risk Management, Palgrave Macmillan, vol. 25(1), pages 1-25, March.
    5. Elizabeth Fons & Paula Dawson & Jeffrey Yau & Xiao-jun Zeng & John Keane, 2019. "A novel dynamic asset allocation system using Feature Saliency Hidden Markov models for smart beta investing," Papers 1902.10849, arXiv.org.
    6. Peter Nystrup & Stephen Boyd & Erik Lindström & Henrik Madsen, 2019. "Multi-period portfolio selection with drawdown control," Annals of Operations Research, Springer, vol. 282(1), pages 245-271, November.
    7. Ioannis Anagnostou & Drona Kandhai, 2019. "Risk Factor Evolution for Counterparty Credit Risk under a Hidden Markov Model," Risks, MDPI, vol. 7(2), pages 1-22, June.
    8. Guglielmo D'Amico & Filippo Petroni, 2020. "A micro-to-macro approach to returns, volumes and waiting times," Papers 2007.06262, arXiv.org.

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