In finance, volatility clustering refers to the observation, first noted by Mandelbrot (1963), that "large changes tend to be followed by large changes, of either sign, and small changes tend to be followed by small changes."[1] A quantitative manifestation of this fact is that, while returns themselves are uncorrelated, absolute returns or their squares display a positive, significant and slowly decaying autocorrelation function: corr(|rt|, |rt+τ |) > 0 for τ ranging from a few minutes to several weeks. This empirical property has been documented in the 90's by Granger and Ding (1993)[2] and Ding and Granger (1996)[3] among others; see also.[4] Some studies point further to long-range dependence in volatility time series, see Ding, Granger and Engle (1993)[5] and Barndorff-Nielsen and Shephard.[6]
Observations of this type in financial time series go against simple random walk models and have led to the use of GARCH models and mean-reverting stochastic volatility models in financial forecasting and derivatives pricing. The ARCH (Engle, 1982) and GARCH (Bollerslev, 1986) models aim to more accurately describe the phenomenon of volatility clustering and related effects such as kurtosis. The main idea behind these two models is that volatility is dependent upon past realizations of the asset process and related volatility process. This is a more precise formulation of the intuition that asset volatility tends to revert to some mean rather than remaining constant or moving in monotonic fashion over time.
^Mandelbrot, B. B., The Variation of Certain Speculative Prices, The Journal of Business 36, No. 4, (1963), 394-419
^Granger, C.W. J., Ding, Z. Some Properties of Absolute Return: An Alternative Measure of Risk , Annales d'Économie et de Statistique, No. 40 (Oct. - Dec., 1995), pp. 67-91
^Ding, Z., Granger, C.W.J. Modeling volatility persistence of speculative returns: A new approach, Journal of Econometrics), 1996, vol. 73, issue 1, 185-215
^Cont, Rama (2007). "Volatility Clustering in Financial Markets: Empirical Facts and Agent-Based Models". In Teyssière, Gilles; Kirman, Alan (eds.). Long Memory in Economics. Springer. pp. 289–309. doi:10.1007/978-3-540-34625-8_10.
^Zhuanxin Ding, Clive W.J. Granger, Robert F. Engle (1993) A long memory property of stock market returns and a new model, Journal of Empirical Finance, Volume 1, Issue 1, 1993, Pages 83-106
^Ole E. Barndorff-Nielsen, Neil Shephard (October 2010). "Volatility". In Cont, Rama (ed.). Encyclopedia of Quantitative Finance. Wiley. doi:10.1002/9780470061602.eqf19019. ISBN9780470057568.
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volatility, clustering, finance, volatility, clustering, refers, observation, first, noted, mandelbrot, 1963, that, large, changes, tend, followed, large, changes, either, sign, small, changes, tend, followed, small, changes, quantitative, manifestation, this,. In finance volatility clustering refers to the observation first noted by Mandelbrot 1963 that large changes tend to be followed by large changes of either sign and small changes tend to be followed by small changes 1 A quantitative manifestation of this fact is that while returns themselves are uncorrelated absolute returns r t displaystyle r t or their squares display a positive significant and slowly decaying autocorrelation function corr rt rt t gt 0 for t ranging from a few minutes to several weeks This empirical property has been documented in the 90 s by Granger and Ding 1993 2 and Ding and Granger 1996 3 among others see also 4 Some studies point further to long range dependence in volatility time series see Ding Granger and Engle 1993 5 and Barndorff Nielsen and Shephard 6 Observations of this type in financial time series go against simple random walk models and have led to the use of GARCH models and mean reverting stochastic volatility models in financial forecasting and derivatives pricing The ARCH Engle 1982 and GARCH Bollerslev 1986 models aim to more accurately describe the phenomenon of volatility clustering and related effects such as kurtosis The main idea behind these two models is that volatility is dependent upon past realizations of the asset process and related volatility process This is a more precise formulation of the intuition that asset volatility tends to revert to some mean rather than remaining constant or moving in monotonic fashion over time See also editGARCH Stochastic volatilityReferences edit Mandelbrot B B The Variation of Certain Speculative Prices The Journal of Business 36 No 4 1963 394 419 Granger C W J Ding Z Some Properties of Absolute Return An Alternative Measure of Risk Annales d Economie et de Statistique No 40 Oct Dec 1995 pp 67 91 Ding Z Granger C W J Modeling volatility persistence of speculative returns A new approach Journal of Econometrics 1996 vol 73 issue 1 185 215 Cont Rama 2007 Volatility Clustering in Financial Markets Empirical Facts and Agent Based Models In Teyssiere Gilles Kirman Alan eds Long Memory in Economics Springer pp 289 309 doi 10 1007 978 3 540 34625 8 10 Zhuanxin Ding Clive W J Granger Robert F Engle 1993 A long memory property of stock market returns and a new model Journal of Empirical Finance Volume 1 Issue 1 1993 Pages 83 106 Ole E Barndorff Nielsen Neil Shephard October 2010 Volatility In Cont Rama ed Encyclopedia of Quantitative Finance Wiley doi 10 1002 9780470061602 eqf19019 ISBN 9780470057568 nbsp This economics related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Volatility clustering amp oldid 1186864701, wikipedia, wiki, book, books, library,
