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Change Point Detection and Estimation of the Two-Sided Jumps of Asset Returns Using a Modified Kalman Filter

Author

Listed:
  • Ourania Theodosiadou

    (Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece)

  • Sotiris Skaperas

    (Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece)

  • George Tsaklidis

    (Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece)

Abstract

In the first part of the paper, the positive and negative jumps of NASDAQ daily (log-) returns and three of its stocks are estimated based on the methodology presented by Theodosiadou et al. 2016, where jumps are assumed to be hidden random variables. For that reason, the use of stochastic state space models in discrete time is adopted. The daily return is expressed as the difference between the two-sided jumps under noise inclusion, and the recursive Kalman filter algorithm is used in order to estimate them. Since the estimated jumps have to be non-negative, the associated pdf truncation method, according to the non-negativity constraints, is applied. In order to overcome the resulting underestimation of the empirical time series, a scaling procedure follows the stage of truncation. In the second part of the paper, a nonparametric change point analysis concerning the (variance–) covariance is applied to the NASDAQ return time series, as well as to the estimated bivariate jump time series derived after the scaling procedure and to each jump component separately. A similar change point analysis is applied to the three other stocks of the NASDAQ index.

Suggested Citation

  • Ourania Theodosiadou & Sotiris Skaperas & George Tsaklidis, 2017. "Change Point Detection and Estimation of the Two-Sided Jumps of Asset Returns Using a Modified Kalman Filter," Risks, MDPI, vol. 5(1), pages 1-14, March.
    • Handle: RePEc:gam:jrisks:v:5:y:2017:i:1:p:15-:d:92028
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    References listed on IDEAS

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    1. Ole E. Barndorff-Nielsen & Neil Shephard, 2006. "Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation," Journal of Financial Econometrics, Oxford University Press, vol. 4(1), pages 1-30.
    2. Pan, Jun, 2002. "The jump-risk premia implicit in options: evidence from an integrated time-series study," Journal of Financial Economics, Elsevier, vol. 63(1), pages 3-50, January.
    3. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    4. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
    5. Ole E. Barndorff-Nielsen, 2004. "Power and Bipower Variation with Stochastic Volatility and Jumps," Journal of Financial Econometrics, Oxford University Press, vol. 2(1), pages 1-37.
    6. Tobias Berens & Dominik Wied & Daniel Ziggel, 2014. "Automated Portfolio Optimization Based on a New Test for Structural Breaks," Acta Universitatis Danubius. OEconomica, Danubius University of Galati, issue 2(2), pages 243-264, April.
    7. repec:bla:jfinan:v:59:y:2004:i:3:p:1367-1404 is not listed on IDEAS
    8. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    9. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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    Cited by:

    1. Ourania Theodosiadou & George Tsaklidis, 2021. "State Space Modeling with Non-Negativity Constraints Using Quadratic Forms," Mathematics, MDPI, vol. 9(16), pages 1-13, August.

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