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A Nonlinear Filtering Approach To Volatility Estimation With A View Towards High Frequency Data

Author

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  • RÜDIGER FREY

    (Swiss Banking Institute, University of Zürich, Plattenstr 14, CH-8032 Zürich, Switzerland)

  • WOLFGANG J. RUNGGALDIER

    (Dipartimento di Matematica Pura ed Applicata, Universitá di Padova, Via Belzoni 7, I-35131-Padova, Italy)

Abstract

In this paper we consider a nonlinear filtering approach to the estimation of asset price volatility. We are particularly interested in models which are suitable for high frequency data. In order to describe some of the typical features of high frequency data we consider marked point process models for the asset price dynamics. Both jump-intensity and jump-size distribution of this marked point process depend on a hidden state variable which is closely related to asset price volatility. In our setup volatility estimation can therefore be viewed as a nonlinear filtering problem with marked point process observations. We develop efficient recursive methods to compute approximations to the conditional distribution of this state variable using the so-called reference probability approach to nonlinear filtering.

Suggested Citation

  • Rüdiger Frey & Wolfgang J. Runggaldier, 2001. "A Nonlinear Filtering Approach To Volatility Estimation With A View Towards High Frequency Data," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(02), pages 199-210.
    • Handle: RePEc:wsi:ijtafx:v:04:y:2001:i:02:n:s021902490100095x
    DOI: 10.1142/S021902490100095X
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    Citations

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    Cited by:

    1. Colaneri, Katia & Frey, Rüdiger, 2021. "Classical solutions of the backward PIDE for Markov modulated marked point processes and applications to CAT bonds," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 498-507.
    2. Eckhard Platen & Wolfgang Runggaldier, 2004. "A Benchmark Approach to Filtering in Finance," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(1), pages 79-105, March.
    3. Marco Minozzo & Silvia Centanni, 2012. "Monte Carlo likelihood inference for marked doubly stochastic Poisson processes with intensity driven by marked point processes," Working Papers 11/2012, University of Verona, Department of Economics.
    4. Eckhard Platen & Wolfgang Runggaldier, 2007. "A Benchmark Approach to Portfolio Optimization under Partial Information," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 14(1), pages 25-43, March.
    5. Gombani, Andrea & Jaschke, Stefan R. & Runggaldier, Wolfgang J., 2005. "A filtered no arbitrage model for term structures from noisy data," Stochastic Processes and their Applications, Elsevier, vol. 115(3), pages 381-400, March.
    6. Huyên Pham & Peter Tankov, 2008. "A Model Of Optimal Consumption Under Liquidity Risk With Random Trading Times," Mathematical Finance, Wiley Blackwell, vol. 18(4), pages 613-627, October.
    7. Ceci, Claudia & Colaneri, Katia & Cretarola, Alessandra, 2014. "A benchmark approach to risk-minimization under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 129-146.
    8. Kazufumi Fujimoto & Hideo Nagai & Wolfgang Runggaldier, 2014. "Expected Log-Utility Maximization Under Incomplete Information and with Cox-Process Observations," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 21(1), pages 35-66, March.
    9. Andrea Gombani & Wolfgang J. Runggaldier, 2001. "A Filtering Approach To Pricing In Multifactor Term Structure Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(02), pages 303-320.
    10. Jie Xiong & Yong Zeng, 2011. "A branching particle approximation to a filtering micromovement model of asset price," Statistical Inference for Stochastic Processes, Springer, vol. 14(2), pages 111-140, May.
    11. Avanzi, Benjamin & Wong, Bernard & Yang, Xinda, 2016. "A micro-level claim count model with overdispersion and reporting delays," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 1-14.
    12. Damian Camilla & Eksi Zehra & Frey Rüdiger, 2018. "EM algorithm for Markov chains observed via Gaussian noise and point process information: Theory and case studies," Statistics & Risk Modeling, De Gruyter, vol. 35(1-2), pages 51-72, January.
    13. Giorgia Callegaro & Giovanni Masi & Wolfgang Runggaldier, 2006. "Portfolio Optimization in Discontinuous Markets under Incomplete Information," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 13(4), pages 373-394, December.
    14. Claudia Ceci & Anna Gerardi, 2011. "Utility indifference valuation for jump risky assets," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 34(2), pages 85-120, November.
    15. Samuel N. Cohen & Robert J. Elliott, 2013. "Filters and smoothers for self-exciting Markov modulated counting processes," Papers 1311.6257, arXiv.org.
    16. Kyriakos Chourdakis, 2002. "Continuous Time Regime Switching Models and Applications in Estimating Processes with Stochastic Volatility and Jumps," Working Papers 464, Queen Mary University of London, School of Economics and Finance.
    17. Camilla Damian & Rudiger Frey, 2023. "Detecting Rough Volatility: A Filtering Approach," Papers 2302.12612, arXiv.org.
    18. Giorgia Callegaro & Claudia Ceci & Giorgio Ferrari, 2020. "Optimal reduction of public debt under partial observation of the economic growth," Finance and Stochastics, Springer, vol. 24(4), pages 1083-1132, October.

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