Greeks

<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="table2"> <tr> <td width="740"> <table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" height="37" id="table3"> <tr> <td height="35" width="100%"> <table border="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" cellpadding="0" id="table4"> <tr> <td width="100%" align="left" valign="top"> <p class="header_gold">Greeks</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="table5"> <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="#Greeks">Greeks</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" style="border-collapse: collapse" bordercolor="#111111" width="310" align="right" id="table6"> <tr> <td align="right" width="9" height="14"></td> <td width="300" height="14"> <font size="2"> </font><font size="4"> </font></td> </tr> <tr> <td align="right" width="9"> </td> <td width="300"> <script type="text/javascript"></script> <script type="text/javascript" src="http://pagead2.googlesyndication.com/pagead/show_ads.js"> </script>  </td> </tr> </table> <p class="body"><strong style="font-weight: 400">The </strong><strong> <a name="Greeks">Greeks</a></strong><strong style="font-weight: 400"> are a <a href="../articles/set.htm">set</a> of factor sensitivities used extensively by traders to quantify the exposures of portfolios that contain </strong> <a href="../articles/option.htm"> <strong style="font-weight: 400">options</strong></a><strong style="font-weight: 400">. Each measures how the portfolio's <a href="../articles/valuation.htm">market value</a> should respond to a change in some variable—an <a href="../articles/derivative_instrument.htm">underlier</a>, <a href="../articles/volatility.htm">implied volatility</a>, interest rate or time. There are five Greeks:</strong></p> <p class="bullet" style="margin-top: 6; margin-bottom: 6"> <img border="0" src="../images/bullet.gif" width="20" height="10"><strong style="font-weight: 400"><a href="../articles/delta_and_gamma.htm">delta</a> measures first order (linear) sensitivity to an underlier;</strong></p> <p class="bullet" style="margin-top: 6; margin-bottom: 6"> <img border="0" src="../images/bullet.gif" width="20" height="10"><strong style="font-weight: 400"><a href="../articles/delta_and_gamma.htm">gamma</a> measures second order (quadratic) sensitivity to an underlier;</strong></p> <p class="bullet" style="margin-top: 6; margin-bottom: 6"> <img border="0" src="../images/bullet.gif" width="20" height="10"><strong style="font-weight: 400"><a href="../articles/vega.htm">vega</a> measures first order (linear) sensitivity to the implied volatility of an underlier;</strong></p> <p class="bullet" style="margin-top: 6; margin-bottom: 6"> <img border="0" src="../images/bullet.gif" width="20" height="10"><strong style="font-weight: 400"><a href="../articles/theta.htm">theta</a> measures first order (linear) sensitivity to the passage of time;</strong></p> <p class="bullet" style="margin-top: 6; margin-bottom: 6"> <img border="0" src="../images/bullet.gif" width="20" height="10"><strong style="font-weight: 400"><a href="../articles/rho.htm">rho</a> measures first order (linear) sensitivity to an applicable interest rate.</strong></p> <table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="135" align="left" id="table7"> <tr> <td width="125" height="6"> <font style="font-size: 6pt"> </font></td> <td width="10" height="6"></td> </tr> <tr> <td width="125"> <script type="text/javascript"></script> <script type="text/javascript" src="http://pagead2.googlesyndication.com/pagead/show_ads.js"> </script>  </td> <td width="10"> </td> </tr> </table> <p class="body"><strong style="font-weight: 400">They are called the Greeks because four out of the five are named after letters of the Greek alphabet. Vega is the exception. For reasons unknown, it is named after the brightest star in the constellation Lyra. At times, vega has been called kappa, but the name vega is now well established.</strong></p> <p class="body"><strong style="font-weight: 400">Four of the five are <a href="../articles/risk_metric_and_risk_measure.htm">risk metrics</a>. Theta is not because the passage of time in certain—it entails no risk. Theta is akin to the accrual of interest on a <a href="../articles/coupon_bond.htm">bond</a>.</strong></p> <p class="body"><strong style="font-weight: 400">The Greeks are defined as first—and in the case of gamma, second—partial derivatives. See articles on each (linked above) for more information.</strong></p> <table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table8"> <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="table9"> <tr> <td width="100%"> <p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/delta_and_gamma.htm">delta and gamma</a> Factor sensitivities measuring a portfolio's first and second order (linear and quadratic) sensitivity to the value of an underlier.</p> <p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/derivative_instrument.htm">derivative instrument</a> An instrument which derives its value from the value of other financial instruments. Article includes a list of vanilla and exotic derivatives.</p> <p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/risk_management.htm">financial risk management</a> Practices by which a firm optimizes the manner in which it takes financial risk.<p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/market_risk.htm">market risk</a> Exposure to the uncertain market value of a portfolio.</p> <p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/option_pricing_theory.htm">option pricing theory</a> The body of financial theory used by financial engineers to value options and other derivative instruments.</p> <p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/options_spread.htm">option spreads</a> Positions combining one or more options in a single underlier.</p> <p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/put_call_parity.htm">p</a><a href="../articles/put_call_parity.htm" target="main">ut-call parity</a> A formula that relates the price of a put to the price of a corresponding call.</p> <p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/rho.htm">rho</a> Factor sensitivity measuring a portfolio's first order (linear) sensitivity to the risk-free rate.</p> <p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/scenario_analysis.htm">scenario analysis</a> Formalized "what if" analysis typically performed as a part of asset-liability management or corporate risk management.</p> <p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/theta.htm">theta</a> Factor sensitivity measuring a portfolio's first order (linear) sensitivity to the passage of time.</p> <p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/value_at_risk.htm">value-at-risk</a> A category of market risk measures.<p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/vega.htm">vega</a> Factor sensitivity measuring a portfolio's first order (linear) sensitivity to the implied volatility of an underlier.</p> </td> </tr> </table> </td> </tr> <tr> <td height="30" valign="bottom" colspan="2"> <p class="header2_black">Sponsored 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" width="75"> <img border="0" src="../images/ad_side_banner_1.jpg" width="103" height="285"></td> <td bgcolor="#FFFFCC" width="99%"> <script type="text/javascript"></script> <script type="text/javascript" src="http://pagead2.googlesyndication.com/pagead/show_ads.js"> </script>  </td> </tr> <tr> <td height="30" valign="bottom" colspan="2"> <p class="header2_black">Related Books</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="table10"> <tr> <td width="100%"> <p class="explanatory_text">Natenberg (<a target="_blank" href="http://www.riskbook.com/link/natenberg_s_(1994).htm">1994</a>) and Taleb (<a target="_blank" href="http://www.riskbook.com/link/taleb_n_(1996).htm">1996</a>) discuss the Greeks in the context of trading. Natenberg is introductory. Taleb is a sophisticated book for professional derivatives traders.</p> <table border="0" cellpadding="4" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table11"> <tr> <td width="100" align="left" valign="top"> <map name="FPMap579"> <area target="_blank" href="http://www.riskbook.com/link/natenberg_s_(1994).htm" shape="rect" coords="0, 0, 82, 124"> </map> <img border="0" src="../images/book_natenberg_s_(1994)_125.gif" usemap="#FPMap579" width="83" height="125"></td> <td align="left" valign="top"> <table border="0" cellpadding="1" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table12"> <tr> <td width="90%" colspan="3"> <p class="title"> <a target="_blank" href="http://www.riskbook.com/link/natenberg_s_(1994).htm"> Option Volatility & Pricing</a></td> </tr> <tr> <td colspan="3"> <p class="author"><b>Sheldon Natenberg</b></td> </tr> <tr> <td width="10%"><map name="FPMap580"> <area target="_blank" href="http://www.riskbook.com/main/ratings.htm" shape="rect" coords="0, 0, 89, 15"> </map> <img border="0" src="../images/star_5.gif" usemap="#FPMap580" width="90" height="16"></td> <td width="10%" class="author">quality</td> <td width="70%"> <p class="author"> </td> </tr> <tr> <td width="10%"><map name="FPMap581"> <area target="_blank" href="http://www.riskbook.com/main/ratings.htm" shape="rect" coords="0, 0, 89, 15"> </map> <img border="0" src="../images/tech_2.gif" usemap="#FPMap581" width="90" height="16"></td> <td width="10%" class="author">technical</td> <td width="70%">  </td> </tr> <tr> <td width="10%"> <p class="author">1994</td> <td width="10%"> </td> <td width="70%"> <p align="center"><map name="FPMap582"> <area target="_blank" coords="0, 0, 145, 19" shape="rect" href="http://www.riskbook.com/link/natenberg_s_(1994).htm"> </map> <img border="0" src="../images/pointer_review.gif" usemap="#FPMap582" width="146" height="20"></td> </tr> </table> </td> </tr> </table> <table border="0" cellpadding="4" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table13"> <tr> <td width="100" align="left" valign="top"> <map name="FPMap583"> <area target="_blank" href="http://www.riskbook.com/link/taleb_n_(1996).htm" shape="rect" coords="0, 0, 87, 124"> </map> <img border="0" src="../images/book_taleb_n_(1996)_125.gif" usemap="#FPMap583" width="88" height="125"></td> <td align="left" valign="top"> <table border="0" cellpadding="1" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table14"> <tr> <td width="90%" colspan="3"> <p class="title"> <a target="_blank" href="http://www.riskbook.com/link/taleb_n_(1996).htm"> Dynamic Hedging</a></td> </tr> <tr> <td colspan="3"> <p class="author"><b>Nassim Taleb</b></td> </tr> <tr> <td width="10%"> <map name="FPMap422"> <area target="_blank" href="http://www.riskbook.com/main/ratings.htm" shape="rect" coords="0, 0, 89, 15"></map> <img border="0" src="../images/star_6.gif" usemap="#FPMap422" width="90" height="16"></td> <td width="10%" class="author">quality</td> <td width="70%"> <p class="author"> </td> </tr> <tr> <td width="10%"> <map name="FPMap397"> <area target="_blank" href="http://www.riskbook.com/main/ratings.htm" shape="rect" coords="0, 0, 89, 15"> </map><img border="0" src="../images/tech_3.gif" usemap="#FPMap397" width="90" height="16"></td> <td width="10%" class="author">technical</td> <td width="70%">  </td> </tr> <tr> <td width="10%"> <p class="author">1996</td> <td width="10%"> </td> <td width="70%"> <p align="center"><map name="FPMap366"> <area target="_blank" coords="0, 0, 145, 19" shape="rect" href="http://www.riskbook.com/link/taleb_n_(1996).htm"> </map> <img border="0" src="../images/pointer_review.gif" usemap="#FPMap366" width="146" height="20"></td> </tr> </table> </td> </tr> </table> </td> </tr> </table> </td> </tr> <tr> <td height="30" valign="bottom" colspan="2"> <p class="header2_black">Sponsored 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" width="75"> <img border="0" src="../images/ad_side_banner_3.jpg" width="103" height="285"></td> <td bgcolor="#FFFFCC" width="99%">  <p class="ad_legend" style="margin-left: 0; 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