Volatility Clustering

<body onLoad="MM_checkPlugin('Shockwave Flash','','http://www.riskglossary.com/default_nofl.htm',false);return document.MM_returnValue" stylesrc="../_private/template.htm" bgcolor="#FFFFFF" link="#669933" vlink="#000000" alink="#000000"> <div align="left"> <table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table1"> <tr> <td width="740"> <table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" height="37" id="table2"> <tr> <td height="35" width="100%"> <table border="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" cellpadding="0" id="table3"> <tr> <td width="100%" align="left" valign="top"> <p class="header_gold">Volatility Clustering</td> <td width="45" align="right" valign="bottom"> <map name="FPMap6"> <area href="http://www.contingencyanalysis.com" shape="rect" coords="1, 0, 44, 11" target="_top"> </map> <img border="0" src="../images/home.gif" usemap="#FPMap6" width="45" height="12"></td> </tr> </table> </td> </tr> <tr> <td width="100%" bgcolor="#CC9966" height="2"> <img border="0" src="../images/blank_2x2.gif" width="2" height="2"></td> </tr> <tr> <td width="0%" valign="top" bgcolor="#FFFFCC"> <table border="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" cellpadding="0" cellspacing="1" id="table4"> <tr> <td width="0%" align="left" valign="top"> <p class="header2_black">Explained:<br> <img border="0" src="../images/blank_1x100.gif" width="100" height="1"></td> <td width="0%" align="left" valign="top"><p class="word_list"> <a href="#Volatility clustering">volatility clustering</a><br> <img border="0" src="../images/blank_1x160.gif" width="160" height="1"></td> <td width="100%" align="left" valign="top"><p class="word_list"> <br> <img border="0" src="../images/blank_1x160.gif" width="160" height="1"></td> </tr> </table> </td> </tr> </table> <table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="165" align="left" id="table5"> <tr> <td width="160">  </td> <td width="11"> </td> </tr> <tr> <td width="160"> <script type="text/javascript"></script> <script type="text/javascript" src="http://pagead2.googlesyndication.com/pagead/show_ads.js"> </script> </td> <td width="11"> </td> </tr> </table> <p class="body"><b><a name="Volatility clustering">Volatility clustering</a></b> is a property of most <a href="../articles/heteroskedasticity.htm"> heteroskedastic</a> <a href="../articles/time_series_stochastic_process.htm">stochastic processes</a> used in finance and economics. Heteroskedasticity, recall, is the property of time-varying (conditional or unconditional) <a href="../articles/standard_deviation.htm">variance</a> in a stochastic process. Volatility clustering is the property that there are periods of high and low (conditional or unconditional) variance. The <a href="../articles/volatility.htm">volatility</a> "clusters." This is illustrated in Exhibit 1. Its top graph is a realization of a heteroskedastic stochastic process without volatility clustering. Its volatility fluctuates, but it is independent from one time to the next. The second graph is a heterokedastic stochastic process with volatility clustering.</p> <div align="center"> <center> <table border="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="275" cellpadding="0" id="table6"> <tr> <td> <p class="exhibit_header"><span class="exhibit_header">Volatility Clustering</span><br> <span class="exhibit_subheader">Exhibit 1</span></td> </tr> <tr> <td bgcolor="#CC9966" height="2"> <img border="0" src="../images/blank_2x2.gif" width="2" height="2"></td> </tr> <tr> <td> <p style="margin-top: 6"> <img border="0" src="../images/ex1_ARCH_GARCH_a.gif" width="250" height="180"><br> <img border="0" src="../images/ex1_ARCH_GARCH_b.gif" width="250" height="180"></td> </tr> <tr> <td> <p class="exhibit_legend">Two time series are illustrated. The first does not exhibit volatility clustering. The second one does.</td> </tr> </table> </center> </div> <p class="body">Financial markets exhibit volatility clustering. They have periods of elevated volatility interspersed among more tranquil periods. Various stochastic processes are used to model volatility clustering, including <a href="../articles/ARCH_GARCH.htm">ARCH</a>, <a href="../articles/ARCH_GARCH.htm"> GARCH</a> and <a href="../articles/stochastic_volatility_model.htm">stochastic volatility</a> models.</p> <table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table7"> <tr> <td height="30" valign="bottom" colspan="2"> <p class="header2_black">Related Internal Links</td> </tr> <tr> <td colspan="2" bgcolor="#CC9966" height="2"> <img border="0" src="../images/blank_2x2.gif" width="2" height="2"></td> </tr> <tr> <td bgcolor="#FFFFCC" colspan="2"> <table border="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" cellpadding="6" id="table8"> <tr> <td width="100%"> <span style="font-family: Times New Roman; letter-spacing: -0.2pt"> <p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/ARCH_GARCH.htm">ARCH</a> A category of conditionally heteroskedastic stochastic processes.</p> <p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/heteroskedasticity.htm">heteroskedasticity</a> A condition where a stochastic process has non-constant second moments.</p> <p align="left" class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><strong style="font-weight: 400"><a href="../articles/kurtosis.htm">kurtosis</a> </strong>A parameter describing the peakedness and tails of a probability distribution.</p> <p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/stochastic_volatility_model.htm">stochastic volatility model</a> A category of conditionally heteroskedastic stochastic processes.</p> <p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><strong style="font-weight: 400"><a href="../articles/time_series_stochastic_process.htm">time series and stochastic processes</a> An introductory article.</strong></p> <p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><strong style="font-weight: 400"><a href="../articles/volatility.htm">volatility</a> A metric of  variability in a stochastic process.</strong></p> </span> <p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/volatility_skew.htm">volatility skew</a> A condition where implied volatilities vary by strike.</p> <span style="font-family: Times New Roman; 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