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High-Frequency and Model-Free Volatility Estimators

Author

Listed:
  • Robert Ślepaczuk

    (Faculty of Economic Sciences, University of Warsaw)

  • Grzegorz Zakrzewski

    (Deutsche Bank PBC S.A.)

Abstract
This paper focuses on volatility of financial markets, which is one of the most important issues in finance, especially with regard to modeling high-frequency data. Risk management, asset pricing and option valuation techniques are the areas where the concept of volatility estimators (consistent, unbiased and the most efficient) is of crucial concern. Our intention was to find the best estimator of true volatility taking into account the latest investigations in finance literature. Basing on the methodology presented in Parkinson (1980), Garman and Klass (1980), Rogers and Satchell (1991), Yang and Zhang (2000), Andersen et al. (1997, 1998, 1999a, 199b), Hansen and Lunde (2005, 2006b) and Martens (2007), we computed the various model-free volatility estimators and compared them with classical volatility estimator, most often used in financial models. In order to reveal the information set hidden in high-frequency data, we utilized the concept of realized volatility and realized range. Calculating our estimator, we carefully focused on Δ (the interval used in calculation), n (the memory of the process) and q (scaling factor for scaled estimators). Our results revealed that the appropriate selection of Δ and n plays a crucial role when we try to answer the question concerning the estimator efficiency, as well as its accuracy. Having nine estimators of volatility, we found that for optimal n (measured in days) and Δ (in minutes) we obtain the most efficient estimator. Our findings confirmed that the best estimator should include information contained not only in closing prices but in the price range as well (range estimators). What is more important, we focused on the properties of the formula itself, independently of the interval used, comparing the estimator with the same Δ, n and q parameter. We observed that the formula of volatility estimator is not as important as the process of selection of the optimal parameter n or Δ. Finally, we focused on the asymmetry between market turmoil and adjustments of volatility. Next, we put stress on the implications of our results for well-known financial models which utilize classical volatility estimator as the main input variable.

Suggested Citation

  • Robert Ślepaczuk & Grzegorz Zakrzewski, 2009. "High-Frequency and Model-Free Volatility Estimators," Working Papers 2009-13, Faculty of Economic Sciences, University of Warsaw.
    • Handle: RePEc:war:wpaper:2009-13
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    File URL: http://www.wne.uw.edu.pl/inf/wyd/WP/WNE_WP23.pdf
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    References listed on IDEAS

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    Cited by:

    1. Chuong Luong & Nikolai Dokuchaev, 2016. "Modeling Dependency Of Volatility On Sampling Frequency Via Delay Equations," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 11(02), pages 1-21, June.
    2. Svetlana Lapinova & Alexander Saichev & Maria Tarakanova, 2012. "Volatility estimation based on extremes of the bridge (in Russian)," Quantile, Quantile, issue 10, pages 73-90, December.
    3. Ahmad Sarlak & Zahra Talei, 2016. "Impact of High-Frequency Trading on the Stock Returns of Large and Small Companies in the Tehran Stock Exchange," International Journal of Economics and Finance, Canadian Center of Science and Education, vol. 8(4), pages 216-228, April.
    4. Ślepaczuk Robert & Sakowski Paweł & Zakrzewski Grzegorz, 2018. "Investment Strategies that Beat the Market. What Can We Squeeze from the Market?," Financial Internet Quarterly (formerly e-Finanse), Sciendo, vol. 14(4), pages 36-55, December.
    5. Ryszard Kokoszczyński & Paweł Sakowski & Robert Ślepaczuk, 2017. "Which Option Pricing Model Is the Best? HF Data for Nikkei 225 Index Options," Central European Economic Journal, Sciendo, vol. 4(51), pages 18-39, December.
    6. Neda Todorova, 2012. "Volatility estimators based on daily price ranges versus the realized range," Applied Financial Economics, Taylor & Francis Journals, vol. 22(3), pages 215-229, February.
    7. Ryszard Kokoszczyński & Natalia Nehrebecka & Paweł Sakowski & Paweł Strawiński & Robert Ślepaczuk, 2010. "Option Pricing Models with HF Data – a Comparative Study. The Properties of Black Model with Different Volatility Measures," Working Papers 2010-03, Faculty of Economic Sciences, University of Warsaw.
    8. Robert Ślepaczuk & Grzegorz Zakrzewski & Paweł Sakowski, 2012. "Investment strategies beating the market. What can we squeeze from the market?," Working Papers 2012-04, Faculty of Economic Sciences, University of Warsaw.

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    More about this item

    Keywords

    financial market volatility; high-frequency financial data; realized volatility and correlation; volatility forecasting; microstructure bias; the opening jump effect; the bid-ask bounce; autocovariance bias; daily patterns of volatility; emerging markets;
    All these keywords.

    JEL classification:

    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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