Swaption

<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">Swaption</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="#payer swaption">payer swaption</a><p class="word_list"> <a href="#receiver swaption">receiver swaption</a><p class="word_list"> <a href="#swaption">swaption</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="table5"> <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>A <b><a name="swaption">swaption</a></b> is an <a href="../articles/exchange_traded.htm">OTC</a> <a href="../articles/option.htm">option</a> on a <a href="../articles/swap.htm">swap</a>. Usually, the <a href="../articles/derivative_instrument.htm">underlying</a> swap is a <a href="../articles/interest_rate_swap.htm">vanilla interest rate swap</a>. Unless stated otherwise, that is how we will use the tem in this article. However, the term "swaption" might be used to refer to an option on any type of swap. </p> <p>In case you are wondering why anyone would want to buy a swaption, the answer is often that they don't want to. Frequently, they want to sell a swaption. Consider a <a href="../articles/corporation.htm">corporation</a> that has issued debt in the form of <a href="../articles/callable_bond.htm">callable bonds</a> paying a fixed semiannual interest rate. The corporation would like to swap the debt into <a href="../articles/floater.htm">floating</a> rate debt. The corporation enters into a <a href="../articles/interest_rate_swap.htm"> fixed-for-floating</a> swap with a derivatives dealer. To liquidate the call feature of the debt, it also sells the dealer a swaption. For derivatives dealers, clients often want to sell them swaptions while other clients want to buy <a href="../articles/cap.htm">caps</a> from them. The dealers then face the challenge of hedging the <a href="../articles/short_sale.htm">short</a> caps with the <a href="../articles/short_sale.htm">long</a> swaptions.</p> <p>Swaptions can be for <a href="../articles/option.htm">American</a>, <a href="../articles/option.htm">European</a> or <a href="../articles/option.htm">Bermudan</a> exercise. They can be <a href="../articles/physical%20settlement.htm">physically settled</a>, in which case an option is actually entered into upon exercise. They can also be <a href="../articles/physical%20settlement.htm">cash settled</a>, in which case the market value of the underlying swap changes hands upon exercise. </p> <p>To specify a swaption, we must indicate three things:</p> <p class="bullet"><img border="0" src="../images/bullet.gif" width="20" height="10">the <a href="../articles/option.htm">expiration date</a> of the option</p> <p class="bullet"><img border="0" src="../images/bullet.gif" width="20" height="10">the fixed rate on the underlying swap</p> <p class="bullet"><img border="0" src="../images/bullet.gif" width="20" height="10">the tenor (time to maturity at exercise of the option) of the swap.</p> <p>The purchaser of the swaption pays an up front <a href="../articles/time_value_and_intrinsic_value.htm">premium</a>. If she exercises, there is no <a href="../articles/option.htm">strike price</a> to pay. The two parties simply put on the prescribe swap. Note, however, the fixed rate specified for the swaption plays a role very similar to that of a strike price. The holder of the swaption will decide whether or not to exercise based on whether <a href="../articles/interest_rate_swap.htm">swap rates</a> rise above or fall below that fixed rate. For this reason, the fixed rate is often called the strike rate.</p> <table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="345" align="left" id="table6"> <tr> <td width="336"> <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>By symmetry, a <a href="../articles/option.htm">call</a> on a pay-fixed swap is the same thing as a <a href="../articles/option.htm">put</a> on a receive-fixed swap. Similarly, a call on a receive fixed swap is the same as a put on a pay fixed swap. For this reason, it is often more convenient to speak in terms of two basic forms of swaption:</p> <p class="bullet_line_space"><img border="0" src="../images/bullet.gif" width="20" height="10">A <b><a name="payer swaption">payer swaption</a></b> is a call on a pay-fixed swap—the swaption holder has the option to pay fixed on a swap.</p> <p class="bullet_line_space"><img border="0" src="../images/bullet.gif" width="20" height="10">A <b><a name="receiver swaption">receiver swaption</a></b> is a call on a receive fixed swap—the swaption holder has the option to receive fixed on a swap.</p> <p>Suppose a party purchases a 1x5 payer swaption struck at 5%. A year later, if the four-year swap rate is 6%, she will exercise the swaption and pay 5% fixed for <a href="../articles/libor.htm">Libor</a> flat on a four-year swap. If instead, the four-year swap rate is 4%, she will not exercise the swaption.</p> <p>Swaptions are priced using <a href="../articles/black_1976.htm">Black 76</a>. For this purpose, the underlier is treated as a <a href="../articles/forward.htm">forward</a> on a swap. </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%"> <p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/basis_swap.htm">basis swap</a> A floating-for-floating interest rate or currency swap.</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/callable_bond.htm">callable bond</a> </strong>A bond which allows the issuer to repurchase the bond for a specified price on certain dates prior to the bond's maturity.</p> <p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/currency_swap.htm">currency swap</a> A swap for the exchange of cash flow streams in two different currencies.<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 that derives value from the value of some commodity, energy, or other financial instrument.</strong><p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/fixed_income_term_structure.htm">fixed income term structure</a> Refers collectively to a spot curve, forward curve, discount curve, yield curve or any other curve that describes the time value of money.<p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/floater.htm">floater</a> A fixed income instrument whose coupon fluctuates with some designated reference rate.</p> <p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/forward_rate_agreement.htm">forward rate agreement</a> A cash-settled forward contract on a short-term loan.<p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/cap.htm"><strong style="font-weight: 400">interest rate cap</strong></a><strong style="font-weight: 400"> A derivative instrument which is linked to interest rates.</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/interest_rate_spreads.htm">interest rate spreads</a> Spreads between interest rates.</strong><p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/interest_rate_swap.htm">interest rate swap</a> A swap under which both cash flow streams are in the same currency and are defined as cash flow streams that might be associated with some fixed income obligation. <p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/swap.htm">swap</a> An OTC derivative under which two counterparties exchange two cash flow streams.</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_2.jpg" width="103" height="285"></td> <td bgcolor="#FFFFCC" width="99%">  <p class="ad_legend" style="margin-left: 0; 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For a comprehensive treatment, see Das (<a target="_blank" href="http://www.riskbook.com/link/das_satyajit_(2003).htm">2003</a>).</p> <span style="font-family: Times New Roman; letter-spacing: -0.2pt"> <table border="0" cellpadding="4" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table10"> <tr> <td width="100" align="left" valign="top"> <map name="FPMap476"> <area target="_blank" href="http://www.riskbook.com/link/james_and_webber_(2000).htm" shape="rect" coords="0, 0, 82, 124"> </map> <img border="0" src="../images/book_james_125.gif" usemap="#FPMap476" 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="table11"> <tr> <td width="90%" colspan="3"> <p class="title"> <a target="_blank" href="http://www.riskbook.com/link/james_and_webber_(2000).htm"> Interest Rate Modelling</a></td> </tr> <tr> <td colspan="3"> <p class="author"><b>Jessica James and Nick Webber</b></td> </tr> <tr> <td width="10%"> <map name="FPMap477"> <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="#FPMap477" 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="FPMap478"> <area target="_blank" href="http://www.riskbook.com/main/ratings.htm" shape="rect" coords="0, 1, 89, 15"> </map><img border="0" src="../images/tech_4.gif" usemap="#FPMap478" width="90" height="16"></td> <td width="10%" class="author">technical</td> <td width="70%">  </td> </tr> <tr> <td width="10%"> <p class="author">2000</td> <td width="10%"> </td> <td width="70%"> <p align="center"><map name="FPMap479"> <area target="_blank" coords="0, 0, 145, 19" shape="rect" href="http://www.riskbook.com/link/james_and_webber_(2000).htm"> </map> <img border="0" src="../images/pointer_review.gif" usemap="#FPMap479" 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="table12"> <tr> <td width="100" align="left" valign="top"> <map name="FPMap591"> <area target="_blank" href="http://www.riskbook.com/link/das_satyajit_(2003).htm" shape="rect" coords="0, 0, 84, 124"> </map> <img border="0" src="../images/book_das_satyajit_(2003)_125.gif" usemap="#FPMap591" width="85" height="125"></td> <td align="left" valign="top"> <table border="0" cellpadding="1" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table13"> <tr> <td width="90%" colspan="3"> <p class="title"> <a target="_blank" href="http://www.riskbook.com/link/das_satyajit_(2003).htm"> Swaps/Financial Derivatives</a></td> </tr> <tr> <td colspan="3"> <p class="author"><b>Satyajit Das</b></td> </tr> <tr> <td width="10%"> <p 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style="border-collapse: collapse" bordercolor="#111111" width="100%" cellpadding="6" id="table14"> <tr> <td width="100%"> <p class="explanatory_text"> <img border="0" src="../images/bullet_bullhorn_narrow.gif" align="left" width="27" height="22"><b><a target="_top" href="http://www.riskarchive.com/link_thread/01-2/00000c02.htm">Swaption duration - student</a></b> <i>07 Mar 2001<br> </i>Analytic formula for the duration of a swaption.</td> </tr> </table> </td> </tr> <tr> <td bgcolor="#FFFFCC" colspan="2"> <table border="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" cellpadding="6" id="table15"> <tr> <td width="100%" bgcolor="#FFFFFF"> <p align="center" style="margin-top: 18"><map name="FPMap365"> <area target="_top" href="http://www.riskglossary.com" shape="rect" coords="0, 0, 164, 102"> </map><img border="0" src="../images/logo.jpg" usemap="#FPMap365" width="165" height="103"></p> <p align="center"><span class="verdana10"> <a 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