Pricing Financial Instruments: the Finite Difference Method

<body stylesrc="../_private/template_title.htm" topmargin="10" leftmargin="10" bgcolor="#FFFFFF" link="#333366" vlink="#000000" alink="#000000"> <table border="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" cellpadding="0" id="table16"> <tr> <td width="780"> <div align="center"> <table border="0" cellpadding="5" cellspacing="0" height="206" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table17"> <tr> <td valign="top" align="right" height="198" width="1%"> <p align="left"> <img border="0" src="../images/book_tavella.gif" width="132" height="200"></td> <td valign="top" align="left" height="198"> <table border="0" cellspacing="1" style="border-collapse: collapse" bordercolor="#111111" cellpadding="0" id="table18"> <tr> <td colspan="3" width="0%"> <p class="book_title">Pricing Financial Instruments:<br> <strong><font face="Arial"><big> <span class="book_title_sub">The Finite Difference Method</span></big></font></strong></td> </tr> <tr> <td width="1%" class="book_details_tags" valign="top" height="16" align="left"> <img border="0" src="../images/blank_2x2.gif" width="2" height="2"><img border="0" src="../images/blank_2x2.gif" width="2" height="2"></td> <td width="52%" class="book_details_tags" valign="top" height="144" align="left" rowspan="9"> <map name="FPMap2"> <area href="../main/ratings.htm" shape="rect" coords="73, 0, 163, 33"> </map> <img border="0" src="../images_title/tavell32.gif" usemap="#FPMap2" width="192" height="175"></td> <td class="book_details" valign="top" height="16" align="left" width="50%"> </td> </tr> <tr> <td width="1%" class="book_details_tags" valign="top" height="16" align="left"> </td> <td class="book_details" valign="top" height="16" align="left" width="50%"> </td> </tr> <tr> <td width="1%" class="book_details_tags" valign="top" height="16" align="left"> </td> <td class="book_details" valign="top" height="16" align="left" width="50%"> </td> </tr> <tr> <td width="1%" class="book_details_tags" valign="top" height="16" align="left"> </td> <td class="book_details" valign="top" height="16" align="left" width="50%"> </td> </tr> <tr> <td width="1%" class="book_details_tags" valign="top" height="16" align="left"> </td> <td class="book_details" valign="top" height="16" align="left" width="50%"> </td> </tr> <tr> <td width="1%" class="book_details_tags" valign="top" height="16" align="left"> </td> <td class="book_details" valign="top" height="16" align="left" width="50%"> </td> </tr> <tr> <td width="1%" class="book_details_tags" valign="top" height="16" align="left"> </td> <td class="book_details" valign="top" height="16" align="left" width="50%"> </td> </tr> <tr> <td width="1%" class="book_details_tags" valign="top" height="16" align="left"> </td> <td class="book_details" height="32" align="center" width="50%" rowspan="2"> </td> </tr> <tr> <td width="1%" class="book_details_tags" valign="top" height="16" align="left"> </td> </tr> </table> </td> </tr> </table> <table border="0" cellpadding="10" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="468" id="table19"> <tr> <td> <script type="text/javascript"></script> <script type="text/javascript" src="http://pagead2.googlesyndication.com/pagead/show_ads.js"> </script> </td></tr> </table> </div> <table border="0" cellpadding="5" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table20"> <tr> <td width="48%" valign="top"> <p class="body">The finite difference method is a powerful tool for numerically solving partial differential equations. For valuing financial derivatives, it offers many advantages over trees and the Monte Carlo method. Its popularity has lagged behind those methods because it requires more specialized expertise. To meet this need, Tavella and Randall have produced an excellent monograph. Targeted to knowledgeable financial engineers, it assumes considerable knowledge of stochastic calculus and derivatives pricing theory.</p> <p class="body">Two opening chapters review familiar concepts of financial engineering: Ito's calculus, arbitrage pricing theory, etc. They discuss when a derivative can be modeled with a PDE and techniques, such as change of measure or dimension reduction, that make a problem more amenable to analysis by finite differences. </p> </td> <td width="52%" valign="top" class="body" rowspan="2"> <table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table21"> <tr> <td width="100%" bgcolor="#333366"> <p class="header_yellow" align="center">Contents</td> </tr> <tr> <td width="100%" class="explanatory_text"> <table border="1" cellpadding="0" cellspacing="5" style="border-collapse: collapse" bordercolor="#CCCCFF" bgcolor="#CCCCFF" width="100%" id="table22"> <tr> <td class="contents_expanded"> <p class="contents_compressed" style="line-height: 120%; margin-top: 7px; margin-bottom: 7px">1. Introduction 1 </p> <p class="contents_compressed" style="line-height: 120%; margin-top: 7px; margin-bottom: 7px">2. The Pricing Equations</p> <p class="contents_compressed" style="line-height: 120%; margin-top: 7px; margin-bottom: 7px">3. Analysis of Finite Difference Methods</p> <p class="contents_compressed" style="line-height: 120%; margin-top: 7px; margin-bottom: 7px">4. Special Issue</p> <p class="contents_compressed" style="line-height: 120%; margin-top: 7px; margin-bottom: 7px">5. Coordinate Transformations</p> <p class="contents_compressed" style="line-height: 120%; margin-top: 7px; margin-bottom: 7px">6. Numerical Examples</p> </td> </tr> </table> </td> </tr> </table> <table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="125" align="right" id="table23"> <tr> <td width="5" height="10"><font size="2"> </font></td> <td width="120" height="10"> <font size="2"> </font></td> </tr> <tr> <td width="5"> </td> <td width="120"> <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">Chapter 3 covers how to construct finite difference approximations. It focuses on stability issues and assesses distortions caused by discretization. Chapter 4 addresses practical issues related to jump models, path dependence, boundary conditions, etc. Chapter 5 covers coordinate transformations. The final chapter covers a number of valuable case studies.</p> <p class="body">I highly recommend this book for practicing financial engineers. Prior familiarity with finite difference methods, as might be obtained from Wilmott, Dewynne and Howison (<a href="../titles/wilmott_et_al_(1997).htm">2000</a>) or Seydel (<a href="../titles/seydel_r_(2002).htm">2002</a>), will be valuable. </p> <p class="body_expanded" align="center" style="margin-bottom: 6px"> </p> </td> </tr> <tr> <td width="48%" valign="bottom"> <table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table24"> <tr> <td width="100%"> <script type="text/javascript"></script> <script type="text/javascript" src="http://pagead2.googlesyndication.com/pagead/show_ads.js"> </script> </td></tr> </table> </td> </tr> </table> <table border="0" cellpadding="10" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table25"> <tr> <td width="50%" bgcolor="#FFFFCC" align="center"> <table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" bgcolor="#FFFFCC" id="table26"> <tr> <td> <p class="body" style="margin-bottom: 6; margin-left:10"><b><font color="#333366" size="3">For related books, see sections:</font></b></p> <p class="bullet_line_space" style="margin-left: 10"> <img border="0" src="../images/bullet.gif" width="20" height="10"><a target="_top" href="../link_topic/financial_engineering_intermediate.htm">Financial Engineering - Intermediate Theory</a></p> <p class="bullet_line_space" style="margin-left: 10"> <img border="0" src="../images/bullet.gif" width="20" height="10"><a target="_top" href="../link_topic/financial_engineering_theory.htm">Financial Engineering - Advanced Theory</a></p> <p class="bullet_line_space" style="margin-left: 10"> <img border="0" src="../images/bullet.gif" width="20" height="10"><a target="_top" href="../link_topic/financial_engineering_numerical_methods.htm">Financial Engineering - Numerical Methods</a></p> <p class="bullet" style="margin-top: 5; margin-bottom: 5; margin-left:10"> <img border="0" src="../images/bullet.gif" width="20" height="10"><a target="_top" href="../link_topic/math_financial_math.htm">Math - Financial Math</a></p> <p class="bullet" style="margin-top: 5; margin-bottom: 5; margin-left:10"> <img border="0" src="../images/bullet.gif" width="20" height="10"><a target="_top" href="../link_topic/math_software.htm">Math - Analytic Software</a></td> </tr> </table> </td> </tr> </table> </td> <td>  </td> </tr> </table>  <table border="0" style="border-collapse: collapse" width="100%" cellpadding="0" id="table1" bgcolor="#FFFFFF"> <tr> <td colspan="2" height="12"> <p style="margin-top: 0"> </td> </tr> <tr> <td align="right"> <p align="left" style="margin-bottom: 2px"> <a target="_top" href="http://www.riskexpertise.com/link/advertising.htm"> <font size="1" color="#000000" face="Arial">Ads by Contingency Analysis.</font></a></td> <td align="left"> <p align="right" style="margin-bottom: 2px"> <a target="_top" href="http://www.riskexpertise.com/link/advertising.htm"> <font size="1" color="#000000" face="Arial">Advertise on this site.</font></a></td> </tr> <tr> <td align="center" colspan="2">  <iframe src="http://servedbyadbutler.com/adserve/;ID=147917;size=300x250;setID=93136;type=iframe" allowtransparency="true" background-color="transparent" style="margin: 0px; padding: 0px; border-width: 0px" width="300" height="250" frameborder="0" marginwidth="0" marginheight="0" scrolling="no"> <![if lt IE 4]> <script src="http://servedbyadbutler.com/adserve/;ID=147917;size=300x250;setID=93136;type=js" type="text/javascript"> </script> <noscript> <a href="http://servedbyadbutler.com/go2/;ID=147917;size=300x250;setID=93136"> <img src="http://servedbyadbutler.com/adserve/;ID=147917;size=300x250;setID=93136;type=img" border="0" height="250" width="300" alt=""></a> </noscript><![endif]> </iframe>   </td> </tr> </table> <p align="center" style="margin-top: 20"> <map name="FPMap0_I1"> <area href="http://www.riskbook.com" shape="rect" coords="0, 0, 184, 29" target="_top"></map> <img border="0" src="../images/open_book_riskbook.gif" usemap="#FPMap0_I1" width="185" height="30"></p> <p class="a" align="center"><font face="Arial" size="2"><a href="../main/disclaimer.htm">disclaimer</a></font></p> <p class="a" align="center"><span class="verdana10">website:</span> <a target="_top" href="http://www.contingencyanalysis.com"> <font size="2" face="Arial">http://www.contingencyanalysis.com</font></a><br> <span class="verdana10">books direct link:</span> <a target="_top" href="http://www.riskbook.com"><font size="2" face="Arial">http://www.riskbook.com</font></a><br> copyright <font face="Times New Roman">©</font> Contingency Analysis, 1996 - current</p> <p class="a" 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_book_white.gif" usemap="#FPMap1_I1" width="241" height="89"></p>  </body>