Barrier Option

<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">Barrier Option</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="#barrier option">barrier option</a><p class="word_list"> <a href="#knock-in">knock-in option</a><p class="word_list"> <a href="#knockout">knockout option</a><p class="word_list"> <a href="#reverse barrier options">reverse barrier option</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="left" id="table5"> <tr> <td width="300" height="14"><font size="2"> </font><font size="4"> </font></td> <td width="9" height="14"></td> </tr> <tr> <td width="300"> <script type="text/javascript"></script> <script type="text/javascript" src="http://pagead2.googlesyndication.com/pagead/show_ads.js"> </script>  </td> <td width="9"> </td> </tr> </table> <p class="body"><strong style="font-weight: 400">A </strong><strong> <a name="barrier option">barrier option</a></strong><strong style="font-weight: 400"> is a path dependent <a href="../articles/option.htm">option</a> that has one of two features: </strong></p> <ol> <li> <p class="bullet"><strong style="font-weight: 400">A </strong><strong> <a name="knockout">knockout</a></strong><strong style="font-weight: 400"> feature causes the option to immediately terminate if the <a href="../articles/derivative_instrument.htm">underlier</a> reaches a specified barrier level, or </strong></p> </li> <li> <p class="bullet"><strong style="font-weight: 400">A </strong><strong> <a name="knock-in">knock-in</a></strong><strong style="font-weight: 400"> feature causes the option to become effective only if the underlier first reaches a specified barrier level.</strong></p> </li> </ol> <p class="body">Premiums are paid in advance. Due to the contingent nature of the option, they tend to be lower than for a corresponding vanilla option.</p> <p class="body"><strong style="font-weight: 400">Consider a knock-in call option with a strike price of EUR 100 and a knock-in barrier at EUR 110. Suppose the option was purchased when the underlier was at EUR 90. If the option expired with the underlier at EUR 103, but the underlier never reached the barrier level of EUR 110 during the life of the option, the option would expire worthless. On the other hand, if the underlier first rose to the EUR 110 barrier, this would cause the option to knock-in. It would then be worth EUR 3 when it expired with the underlier at EUR103. This is illustrated in Exhibit 1:</strong></p> <div align="center"> <center> <table border="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="400" cellpadding="0" id="table6"> <tr> <td> <p class="exhibit_header"><span class="exhibit_header">Example: Up-And-In Barrier Call Option</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> <img border="0" src="../images/ex1_barrier_option.gif" width="400" height="152"></td> </tr> <tr> <td> <p class="exhibit_legend">An up-and-in barrier call option expires worthless unless the underlier value hits the barrier at some time during the life of the option.</td> </tr> </table> </center> </div> <table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="345" align="right" id="table7"> <tr> <td align="right" width="9" height="10"></td> <td width="336" height="10"> <font size="2"> </font></td> </tr> <tr> <td align="right" width="9"> </td> <td width="336"> <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 particular option in this example is known as an "up-and-in" option because the underlier must first go "up" to the barrier before the option knocks "in." </strong></p> <p class="body"><strong style="font-weight: 400">In all, there are eight flavors of barrier options comprising European puts or calls having barriers that are: </strong></p> <p class="bullet"><img border="0" src="../images/bullet.gif" width="20" height="10"><strong style="font-weight: 400">up-and-in,</strong></p> <p class="bullet"><img border="0" src="../images/bullet.gif" width="20" height="10"><strong style="font-weight: 400">down-and-in,</strong></p> <p class="bullet"><img border="0" src="../images/bullet.gif" width="20" height="10"><strong style="font-weight: 400">up-and-out, or</strong></p> <p class="bullet"><img border="0" src="../images/bullet.gif" width="20" height="10"><strong style="font-weight: 400">down-and-out.</strong></p> <p class="body">Of the eight, four either knock-in or knockout when they are in-the-money. These are called <b><a name="reverse barrier options"> reverse barrier options</a></b>. They can pose significant hedging challenges for the issuer.</p> <p class="body">Alternative structures include multiple barriers or barriers incorporated into other types of derivatives. For example, <a href="../articles/binary_option.htm">binary options</a> can be structured with barriers.</p> <p class="body">Merton priced a down-and-out call option in his seminal (<a href="#Merton">1973</a>) paper. The classic paper providing analytic pricing formulas for barriers is Reiner and Rubinstein (<a href="#Reiner">1991</a>). See Haug (<a target="_blank" href="http://www.riskbook.com/link/haug_e_(1997).htm">1997</a>) for an alternative treatment of the same formulas. A shortcoming of analytic formulas is their use of a single implied volatility. Because barrier options are path-dependent, it is desirable to model a term structure of implied volatilities. See Taleb (<a target="_blank" href="http://www.riskbook.com/link/taleb_n_(1996).htm">1996</a>).</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"><strong style="font-weight: 400"><a href="../articles/asian_option.htm">Asian option</a> An option whose expiration value depends on the average value of an underlier over a specified period.</strong><p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/binary_option.htm"><strong style="font-weight: 400">binary option</strong></a><strong style="font-weight: 400"> A type of option which features a discontinuous expiration value.</strong><p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/derivative_instrument.htm"><strong style="font-weight: 400">derivative instrument</strong></a><strong style="font-weight: 400"> An instrument which derives its value from the value of other financial instruments. Article includes a list of vanilla and exotic derivatives.</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/lookback_option.htm">lookback option</a> </strong> <strong style="FONT-WEIGHT: 400">A path dependent option whose payoff depends upon the maximum or minimum underlier value achieved during the entire life of the option.</strong><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/option_pricing_theory.htm">option pricing theory</a> The body of financial theory used by financial engineers to value options and other derivative instruments.</strong><p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/path_dependence.htm">path dependence</a> A property of certain exotic options whose terminal value depends upon the path taken by the underlier during the life of the option.</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%">  <p class="ad_legend" style="margin-left: 0; margin-bottom:2"> <a target="_top" href="http://www.riskexpertise.com/link/advertising.htm"> <font color="#000000">Ads by Contingency Analysis</font></a></p> <p style="margin-top: 0; margin-bottom: 0"> <iframe src="http://servedbyadbutler.com/adserve/;ID=147917;size=336x265;setID=82436;type=iframe" style="margin: 0px; padding: 0px; border-width: 0px" width="336" height="265" frameborder="0" marginwidth="0" marginheight="0" scrolling="no" name="I1"> <![if lt IE 4]> <script src="http://servedbyadbutler.com/adserve/;ID=147917;size=336x265;setID=82436;type=js" type="text/javascript"> </script> <noscript> <a href="http://servedbyadbutler.com/go2/;ID=147917;size=336x265;setID=82436"> <img src="http://servedbyadbutler.com/adserve.ibs/;ID=147917;size=336x265;setID=82436;type=img" border="0" height="265" width="336" alt=""></a> </noscript><![endif]></iframe>   </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">Haug (<a target="_blank" href="http://www.riskbook.com/link/haug_e_(1997).htm">1997</a>) and Bryis et al (<a target="_blank" href="http://www.riskbook.com/link/briys_et_al_(1998).htm">1998</a>) describes classic pricing methodologies. 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src="../images/bullet_paper_glossary.gif" width="21" height="15"><a name="Merton">Merton</a>, Robert C. (1973). Theory of rational option pricing, <i>Bell Journal of Economics and Management Science</i>, 4 (1), 141-183. Available in Merton (<a target="_blank" href="http://www.riskbook.com/link/merton_r_(1992).htm">1990</a>).</p> <p class="explanatory_text"> <img border="0" src="../images/bullet_paper_glossary.gif" width="21" height="15"><a name="Reiner">Reiner</a>, Eric and Mark Rubenstein (1991). Breaking down the barriers, <i>Risk</i>, 4 (8), 28-35.</td> </tr> </table> </td> </tr> </table>  <p align="center"><map name="FPMap0_I1"> <area target="_top" href="http://www.riskglossary.com" shape="rect" coords="0, 0, 164, 102"> </map><img border="0" src="../images/logo.jpg" usemap="#FPMap0_I1" width="165" height="103"></p> <p align="center"><span class="verdana10"> <a href="http://www.riskglossary.com/main/disclaimer.htm">Disclaimer</a></span></p> <p align="center">website: <span class="verdana10"> <a target="_top" href="http://www.contingencyanalysis.com">http://www.contingencyanalysis.com</a></span><br> glossary direct link: <span class="verdana10"> <a target="_top" href="http://www.riskglossary.com">http://www.riskglossary.com</a></span><br> copyright © Contingency Analysis, 1996 - current</p> <p align="center"><map name="FPMap1_I1"> <area target="_top" href="http://www.contingencyanalysis.com" shape="rect" coords="0, 0, 240, 88"> </map><img border="0" src="../images/logo_glossary_white.gif" usemap="#FPMap1_I1" width="241" height="89"></p> </td> <td>  </td> </tr> </table> </div> </body>