Volatility clustering: Difference between revisions

Revision as of 03:08, 17 December 2009

Latest revision as of 00:03, 26 November 2023

(31 intermediate revisions by 20 users not shown)

Line 1:

In [[finance]], '''volatility clustering''' refers to the observation, first noted by [[Benoît Mandelbrot|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."<ref>Mandelbrot, B. B., [https://www.jstor.org/stable/2351623 The Variation of Certain Speculative Prices], The Journal of Business 36, No. 4, (1963), 394-419</ref> A quantitative manifestation of this fact is that, while returns themselves are uncorrelated, absolute returns <math>|r_{t}|</math> or their squares display a positive, significant and slowly decaying autocorrelation function: corr(|r{{sub|t}}|, |r{{sub|t+τ}} |) > 0 for τ ranging from a few minutes to several weeks. This empirical property has been documented in the 90's by [[Clive Granger|Granger]] and Ding (1993)<ref>Granger, C.W. J., Ding, Z. [https://www.jstor.org/stable/20076016 Some Properties of Absolute Return: An Alternative Measure of Risk ], Annales d'Économie et de Statistique, No. 40 (Oct. - Dec., 1995), pp. 67-91</ref> and Ding and [[Clive Granger|Granger]] (1996)<ref>Ding, Z., Granger, C.W.J. [https://doi.org/10.1016/0304-4076(95)01737-2 Modeling volatility persistence of speculative returns: A new approach], Journal of Econometrics), 1996, vol. 73, issue 1, 185-215</ref> among others; see also.<ref>{{cite conference|last1=Cont|first1=Rama|date=2007|editor1-last=Teyssière|editor1-first=Gilles|editor2-last=Kirman|editor2-first=Alan|title=Volatility Clustering in Financial Markets: Empirical Facts and Agent-Based Models|publisher=Springer|pages=289–309|doi=10.1007/978-3-540-34625-8_10|book-title=Long Memory in Economics}}</ref> Some studies point further to long-range dependence in volatility time series, see Ding, Granger and [[Robert F. Engle|Engle]] (1993)<ref>Zhuanxin Ding, Clive W.J. Granger, Robert F. Engle (1993)

{{Unreferenced stub|auto=yes|date=December 2009}}

[https://doi.org/10.1016/0927-5398(93)90006-D A long memory property of stock market returns and a new model], Journal of Empirical Finance,

In [[finance]], '''volatility clustering''' refers to the observation, as 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." A quantitative manifestation of this fact is that, while returns themselves are uncorrelated, absolute returns |rt| 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 a several weeks.

Volume 1, Issue 1, 1993, Pages 83-106</ref> and Barndorff-Nielsen and Shephard.<ref>{{cite encyclopedia |author= Ole E. Barndorff-Nielsen, Neil Shephard|chapter= Volatility|encyclopedia= Encyclopedia of Quantitative Finance|date= October 2010 |publisher= Wiley|editor-last= Cont|editor-first=Rama |doi=10.1002/9780470061602.eqf19019 |isbn= 9780470057568}}

</ref>

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 [[Derivative (finance)|derivatives]] pricing. The [[ARCH]] ([[Robert F. Engle|Engle]], 1982) and [[GARCH]] ([[Tim Bollerslev|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 widely-used 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 (finance)|volatility]] tends to revert to some mean rather than remaining constant or moving in [[monotonic]] fashion over time.

==See also==

*[[GARCH]]

*[[Stochastic volatility]]

==References==

{{Reflist}}

{{Volatility}}

{{DEFAULTSORT:Volatility Clustering}}

[[Category:Derivatives (finance)]]

[[Category:Technical analysis]]