Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Volatility Estimation Based on High-Frequency Data

  • Chapter
  • First Online:
Handbook of Computational Finance

Part of the book series: Springer Handbooks of Computational Statistics ((SHCS))

Abstract

With the availability of high-frequency data ex post daily (or lower frequency) nonparametric volatility measures have been developed, that are more precise than conventionally used volatility estimators, such as squared or absolute daily returns. The consistency of these estimators hinges on increasingly finer sampled high-frequency returns. In practice, however, the prices recorded at the very high frequency are contaminated by market microstructure noise. We provide a theoretical review and comparison of high-frequency based volatility estimators and the impact of different types of noise. In doing so we pay special focus on volatility estimators that explore different facets of high-frequency data, such as the price range, return quantiles or durations between specific levels of price changes.The various volatility estimators are applied to transaction and quotes data of the S&P500 E-mini and of one stock of Microsoft using different sampling frequencies and schemes. We further discuss potential sources of the market microstructure noise and test for its type and magnitude. Moreover, due to the volume of high-frequency financial data we focus also on computational aspects, such as data storage and retrieval.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  • Abadi, D. J., Madden, S. R., & Ferreira, M. (2006). Integrating compression and execution in column-oriented database systems. In Proceedings of the 2006 ACM SIGMOD International Conference on Management of Data (pp. 671–682).

    Google Scholar 

  • Abadi, D. J., Madden, S. R., & Hachem, N. (2008). Column-stores vs. row-stores: How different are they really? In Proceedings of the 2008 ACM SIGMOD International Conference on Management of Data (pp. 967–980).

    Google Scholar 

  • Aït-Sahalia, Y., Mykland, P. A., & Zhang, L. (2005). How often to sample a continuous-time process in the presence of market microstructure noise. Review of Financial Studies, 18, 351–416.

    Article  Google Scholar 

  • Aït-Sahalia, Y., Mykland, P. A., & Zhang, L. (2010). Ultra high frequency volatility estimation with dependent microstructure noise. Journal of Econometrics, 160(1), 2011, 160–175.

    Google Scholar 

  • Andersen, T. G., & Bollerslev, T. (1997). Intraday periodicity and volatility persistence in financial markets. Journal of Empirical Finance, 4, 115–158.

    Article  Google Scholar 

  • Andersen, T. G., & Bollerslev, T. (1998). Answering the skeptics: Yes, standard volatility models do provide accurate forecasts. International Economic Review, 39, 885–905.

    Article  Google Scholar 

  • Andersen, T. G., Bollerslev, T., Diebold, F. X., & Labys, P. (2000). Great realisations. Risk, 13, 105–108.

    Google Scholar 

  • Andersen, T. G., Bollerslev, T., Diebold, F. X., & Ebens, H. (2001). The distribution of realized stock return volatility. Journal of Financial Economics, 61, 43–76.

    Article  Google Scholar 

  • Andersen, T. G., Bollerslev, T., Diebold, F. X., & Labys, P. (2003). Modeling and forecasting realized volatility. Econometrica, 71, 579–625.

    Article  MathSciNet  MATH  Google Scholar 

  • Andersen, T. G., Bollerslev, T., & Diebold, F. X. (2007). Roughing it up: Including jump components in the measurement, modeling, and forecasting of return volatility. The Review of Economics and Statistics, 89, 701–720.

    Article  Google Scholar 

  • Andersen, T. G., Dobrev, D., & Schaumburg, E. (2009). Duration-based volatility estimation. Working Paper.

    Google Scholar 

  • Awartani, B., Corradi, V., & Distaso, W. (2009). Assessing market microstructure effects via realized volatility measures with an application to the dow jones industrial average stocks. Journal of Business & Economic Statistics, 27, 251–265.

    Article  MathSciNet  Google Scholar 

  • Barndorff-Nielsen, O. E., & Shephard, N. (2002a). Econometric analysis of realised volatility and its use in estimating stochastic volatility models. Journal of the Royal Statistical Society, Series B, 64, 253–280.

    Article  MathSciNet  MATH  Google Scholar 

  • Barndorff-Nielsen, O. E., & Shephard, N. (2002b). Estimating quadratic variation using realized variance. Journal of Applied Econometrics, 17(5), 457–477.

    Article  Google Scholar 

  • Barndorff-Nielsen, O. E., & Shephard, N. (2004). Power and bipower variation with stochastic volatility and jumps. Journal of Financial Econometrics, 2, 1–37.

    Article  Google Scholar 

  • Barndorff-Nielsen, O. E., Shephard, N., & Winkel, M. (2006). Limit theorems for multipower variation in the presence of jumps. Stochastic Processes and their Applications, 116, 796–806.

    Article  MathSciNet  MATH  Google Scholar 

  • Barndorff-Nielsen, O. E., Hansen, P. R., Lunde, A., & Shephard, N. (2008). Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise. Econometrica, 76, 1481–1536.

    Article  MathSciNet  MATH  Google Scholar 

  • Barndorff-Nielsen, O. E., Hansen, P. R., Lunde, A., & Shephard, N. (2009). Realized kernels in practice: Trades and quotes. Econometrics Journal, 12, C1–C32.

    Article  MathSciNet  MATH  Google Scholar 

  • Barndorff-Nielsen, O. E., Hansen, P. R., Lunde, A., & Shephard, N. (2010). Subsampled realised kernels. Journal of Econometrics, 160(1), 2011, 204–219.

    Google Scholar 

  • Boncz, P. A. (2002). Monet: A Next-Generation DBMS Kernel for Query-Intensive Applications. PhD thesis, Universiteit van Amsterdam: Netherlands.

    Google Scholar 

  • Brownlees, C. T., & Gallo, G. M. (2006). Financial econometric analysis at ultra-high frequency: Data handling concerns. Computational Statistics & Data Analysis, 51, 2232–2245.

    Article  MathSciNet  MATH  Google Scholar 

  • Cho, C., & Frees, F. (1988). Estimating the volatility of discrete stock prices. Journal of Finance, 43, 451–466.

    Article  Google Scholar 

  • Christensen, K., & Podolskij, M. (2007). Realized range-based estimation of integrated variance. Journal of Econometrics, 141, 323–349.

    Article  MathSciNet  Google Scholar 

  • Christensen, K., Podolskij, M.. & Vetter, M. (2009a). Bias-correcting the realized range-based variance in the presence of market microstructure noise. Finance and Stochastics, 13, 239–268.

    Article  MathSciNet  MATH  Google Scholar 

  • Christensen, K., Oomen, R., & Podolskij, M. (2009b). Realised quantile-based estimation of the integrated variance. Working Paper.

    Google Scholar 

  • Curci, G., & Corsi, F. (2006). A discrete sine transform approach for realized volatility measurement. Working Paper.

    Google Scholar 

  • Dacorogna, M. M., Müller, U. A., Nagler, R. J., Olsen, R. B., & Puctet, O. V. (1993). A geographical model for the daily and weekly seasonal volatility in the foreign exchange market. Journal of International Money and Finance, 12, 413–438.

    Article  Google Scholar 

  • David, H. A. (1970). Order statistics. New York: Wiley.

    MATH  Google Scholar 

  • Eraker, B., Johannes, M., & Polson, N. (2003). The impact of jumps in volatility and returns. Journal of Finance, 58, 1269–1300.

    Article  Google Scholar 

  • Feller, W. (1951). The asymptotic distribution of the range of sums of independent random variables. The Annals of Mathematical Statistics, 22, 427–432.

    Article  MathSciNet  MATH  Google Scholar 

  • Garman, M. B., & Klass, M. J. (1980). On the estimation of security price volatilities from historical data. Journal of Business, 53, 67–78.

    Article  Google Scholar 

  • Gouriéroux, C., & Jasiak, J. (2001). Financial Econometrics: Problems, Models, and Methods. Princeton, NJ: Princeton University Press.

    MATH  Google Scholar 

  • Griffin, J. E., & Oomen, R. C. A. (2010). Covariance measurement in the presence of non-synchronous trading and market microstructure noise. Journal of Econometrics, 160(1), 2011, 58–68.

    Google Scholar 

  • Hansen, P. R., & Lunde, A. (2006). Realized variance and market microstructure noise. Journal of Business & Economic Statistics, 24(2), 127–161.

    Article  MathSciNet  Google Scholar 

  • Hasbrouck, J. (2007). Empirical market microstructure: The institutions, economics, and econometrics of securities trading. UK: Oxford University Press

    Google Scholar 

  • Huang, X., & Tauchen, G. (2005). The relative contribution of jumps to total price variance. Journal of Financial Econometrics, 3(4), 456–499.

    Article  Google Scholar 

  • Klößner, S. (2009). Estimating volatility using intradaily highs and lows. Working Paper.

    Google Scholar 

  • Lee, C. M. C., & Ready, M. J. (1991). Inferring trade direction from intraday data. Journal of Finance, 46, 733–746.

    Article  Google Scholar 

  • Mancini, C. (2009). Non-parametric threshold estimation for models with stochastic diffusion coefficient and jumps. Scandinavian Journal of Statistics, 36, 270–296.

    Article  MathSciNet  MATH  Google Scholar 

  • Martens, M., & van Dijk, D. (2007). Measuring volatility with the realized range. Journal of Econometrics, 138, 181–207.

    Article  MathSciNet  Google Scholar 

  • McAleer, M., & Medeiros, M. (2008). Realized volatilty: A review. Econometric Reviews, 26, 10–45.

    Article  MathSciNet  Google Scholar 

  • Mosteller, F. (1946). On some useful “inefficient” statistics. The Annals of Mathematical Statistics, 17, 377–408.

    Article  MathSciNet  MATH  Google Scholar 

  • Oomen, R. C. (2006). Properties of realized variance under alternative sampling schemes. Journal of Business & Economic Statistics, 24(2), 219–237.

    Article  MathSciNet  Google Scholar 

  • Parkinson, M. (1980). The extreme value method for estimating the variance of the rate of return. Journal of Business, 53, 61–65.

    Article  Google Scholar 

  • Podolskij, M., & Vetter, M. (2009). Estimation of volatility functionals in the simultaneous presence of microstructure noise and jumps. Bernoulli, 15, 634–658.

    Article  MathSciNet  MATH  Google Scholar 

  • Roll, R. (1984). A simple implicit measure of the effective bid-ask spread in an efficient market. Journal of Finance, 39, 1127–1139.

    Article  Google Scholar 

  • Stonebraker, M., Abadi, D., Batkin, A., Chen, X., Cherniack, M., Ferreiraa, M., Lau, E., Lin, A., Madden, S., ONeil, E., ONeil, P., Rasin, A., Tran, N., & Zdonik, S. (2005). C-Store: A column-oriented DBMS. In Proceedings of the 31st International Conference on Very Large Data Bases (pp. 553–564). NY: ACM.

    Google Scholar 

  • Vetter, M. (2010). Limit theorems for bipower variation of semimartingales. Stochastic Processes and their Applications, 120, 22–38.

    Article  MathSciNet  MATH  Google Scholar 

  • Wasserfallen, W., & Zimmermann, H. (1985). The behavior of intra-daily exchange rates. Journal of Banking and Finance, 9, 55–72.

    Article  Google Scholar 

  • Zhang, L. (2006). Efficient estimation of stochastic volatility using noisy observations: A multi-scale approach. Bernoulli, 12, 1019–1043.

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang, L., Mykland, P. A., & Aït-Sahalia, Y. (2005). A tale of two time scales: Determining integrated volatility with noisy high-frequency data. Journal of the American Statistical Association, 100, 1394–1411.

    Article  MathSciNet  MATH  Google Scholar 

  • Zhou, B. (1996). High-frequency data and volatility in foreign-exchange rates. Journal of Business & Economic Statistics, 14, 45–52.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Economics, University of Bonn, Adenauerallee 24-42, 53113, Bonn, Germany

    Christian Pigorsch

  2. Department of Economics, University of Mannheim, L7, 3-5, 68131, Mannheim, Germany

    Uta Pigorsch

  3. Business School of the University of Mannheim, L5, 5, 68131, Mannheim, Germany

    Ivaylo Popov

Authors
  1. Christian Pigorsch
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Uta Pigorsch
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ivaylo Popov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Uta Pigorsch .

Editor information

Editors and Affiliations

  1. , Risk Management Institute, National University of Singapore, 21 Heng Mui Keng Terrace, Level 4, Singapore, 119613, Singapore

    Jin-Chuan Duan

  2. L.v.Bortkiewicz Chair of Statistics, C.A.S.E. Centre f. Appl. Stat. & Econ., Humboldt-Universität zu Berlin, Unter den Linden 6, Berlin, 10099, Germany

    Wolfgang Karl Härdle

  3. , Department of Computational and Data Sci, George Mason University, University Drive 4400, Fairfax, 22030, Virginia, USA

    James E. Gentle

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Pigorsch, C., Pigorsch, U., Popov, I. (2012). Volatility Estimation Based on High-Frequency Data. In: Duan, JC., Härdle, W., Gentle, J. (eds) Handbook of Computational Finance. Springer Handbooks of Computational Statistics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17254-0_13

Download citation

Publish with us

Policies and ethics

Search

Navigation