Law of One Price

<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">Law of One Price</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="#law of one price">law of one price</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 class="body">The <b><a name="law of one price">law of one price</a></b> is a fundamental concept of finance theory. Consider two sets of future cash flows. These can be fixed (as in cash flows from <a href="../articles/treasury_bill.htm">Treasury bills</a>) and/or contingent (as in cash flows from <a href="../articles/option.htm">options</a>). Although they are identical, suppose the respective sets of cash flows are constructed differently—each achieved with different financial instruments. So long as those financial instruments do not differ with respect to factors such as tax treatment, <a href="../articles/liquidity.htm">liquidity</a>, <a href="../articles/credit_risk.htm">credit risk</a>, <a href="../articles/transaction_costs.htm">transaction costs</a>, etc., the two sets of cash flows must have the same <a href="../articles/valuation.htm">market value</a>. The law of one price states that there must be a single price that applies to both sets of cash flows in the market.</p> <p class="body"><a href="../articles/put_call_parity.htm">Put-call parity</a> illustrates the law of one price. A <a href="../articles/option.htm">call</a> option can be replicated with a static portfolio comprising</p> <p class="bullet"><img border="0" src="../images/bullet.gif" width="20" height="10">a <a href="../articles/option.htm">put</a> option, </p> <p class="bullet"><img border="0" src="../images/bullet.gif" width="20" height="10">a position in the <a href="../articles/derivative_instrument.htm">underlier</a>, and </p> <p class="bullet"><img border="0" src="../images/bullet.gif" width="20" height="10">cash. </p> <table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="345" align="left" id="table6"> <tr> <td width="336" height="10"><font size="2"> </font></td> <td width="9" height="10"></td> </tr> <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 class="body">Because of the law of one price, put-call parity requires that the call option and the replicating portfolio must have the same price.</p> <p class="body"><a href="../articles/interest_rate_parity.htm">Interest rate parity</a>, which plays an important role in the foreign exchange markets, is another example of the law of one price.</p> <p class="body">Any violation of the law of one price is an <a href="../articles/arbitrage.htm">arbitrage</a> opportunity. A common mistake traders make is to forget the caveat that the price discrepancy should not arise from factors such as tax treatment, liquidity or credit risk. They will put on what they perceive to be an arbitrage when in fact there is no violation of the law of one price.</p> <p class="body">The law of one price underlies the important <a href="../articles/option_pricing_theory.htm">financial engineering</a> concept of <a href="../articles/arbitrage_free_pricing.htm">arbitrage-free pricing</a>.</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/arbitrage.htm">arbitrage</a> <strong style="font-weight: 400"> A transaction which generates a risk-free profit</strong>.<p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><span class="verdana10"><strong style="font-weight: 400"><a href="../articles/arbitrage_free_model.htm">arbitrage-free model</a></strong></span><strong style="font-weight: 400"> A type of financial engineering model that generates prices that entail no arbitrage opportunities.</strong><p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/arbitrage_free_pricing.htm">arbitrage-free pricing</a> Pricing based upon arbitrage arguments.<p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/EMM.htm">fundamental theorem of asset pricing</a> A theorem that relates the existence of an equivalent martingale measure to the no-arbitrage condition and completeness of markets.<p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/interest_rate_parity.htm"><strong style="font-weight: 400">interest rate parity</strong></a><strong style="font-weight: 400"> An arbitrage condition that must hold between the spot interest rates of different currencies.</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> <p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><strong style="font-weight: 400"><a target="main" href="../articles/put_call_parity.htm">put-call parity</a> A relationship between the prices of European put and call options on the same underlier.</strong></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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Ross</b></td> </tr> <tr> <td width="10%"> <map name="FPMap423"> <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="#FPMap423" 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="FPMap356"> <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="#FPMap356" width="90" height="16"></td> <td width="10%" class="author">technical</td> <td width="70%">  </td> </tr> <tr> <td width="10%"> <p class="author">2004</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/ross_stephen_(2004).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_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 bgcolor="#FFFFCC" colspan="2"> <table border="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" cellpadding="6" id="table12"> <tr> <td width="100%" bgcolor="#FFFFFF"> <p align="center"><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 href="http://www.riskglossary.com/main/disclaimer.htm" target="_self"> 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, 2004</td> </tr> </table> </td> </tr> </table> </td> <td>  </td> </tr> </table> </div> </body>