Volatility and Correlation: In the Pricing of Equity, Foreign Exchange and Interest Rate Options

<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="table2"> <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="table3"> <tr> <td valign="top" align="right" height="198" width="1%"> <p align="left"> <img border="0" src="../images/book_rebonato_(2004).gif" width="137" height="200"></td> <td valign="top" align="left" height="198"> <table border="0" cellspacing="1" style="border-collapse: collapse" bordercolor="#111111" cellpadding="0" id="table4"> <tr> <td colspan="3" width="0%"> <p class="book_title">Volatility and Correlations<br> <font size="3">The Perfect Hedger and the Fox </font></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/rebona75.gif" usemap="#FPMap2" width="208" height="158"></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="table5"> <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="table6"> <tr> <td width="50%" valign="top"> <p class="body_expanded">This is a sophisticated text on the modeling of volatility and correlation surfaces for derivatives pricing and hedging. Drawing on the latest literature, Rebonato discusses the modeling of smiles, mean reversion and correlation. The material is theoretical, but Rebonato's informal hands-on style will appeal to practitioners. </p> <p class="body_expanded">There are various models that support volatility smiles, including:</p> <p class="bullet"><img border="0" src="../images/bullet.gif" width="20" height="10">Stochastic volatility models,<p class="bullet"> <img border="0" src="../images/bullet.gif" width="20" height="10">Jump-diffusion models,<p class="bullet"> <img border="0" src="../images/bullet.gif" width="20" height="10">GARCH volatility models.<p class="body_expanded">The author takes us on a tour of the most useful models. There is an extensive discussion of the Derman and Kani implementation of restricted stochastic volatility models, as well as related techniques. There is a chapter on closed-form solutions based upon parametric models of a risk-neutral density. Another chapter covers mixed jump-diffusion processes. This includes a discussion of the work of Britten-Jones and Neuberger, which extends option pricing theory to incomplete markets. The last three chapters of the book focus on fixed-income topics, primarily in a Brace, Gatarek, Musiela framework. </p> <p class="body_expanded">What is nice about this book is the tremendous amount of cutting-edge material covered. Reading the book will make you want to head to the library to find the original articles. I especially like the practical context in which the theoretical material is presented. Throughout the book, there are examples and case studies on pricing and hedging derivatives in the real world. These bring the book to life. <b>[Review based on the first edition.]</b></p> </td> <td width="50%" valign="top" class="body" rowspan="2"> <table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table7"> <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="table8"> <tr> <td class="contents_expanded"> <p class="contents_compressed" style="margin-top: 9; margin-bottom: 9"><b>I Foundations</b></p> <p class="contents_compressed" style="margin-top: 9; margin-bottom: 9">1. Theory and practice of option modelling</p> <p class="contents_compressed" style="margin-top: 9; margin-bottom: 9">2. Option replication</p> <p class="contents_compressed" style="margin-top: 9; margin-bottom: 9">3. The building blocks</p> <p class="contents_compressed" style="margin-top: 9; margin-bottom: 9">4. Variance and mean reversion in the real and the risk-adjusted worlds</p> <p class="contents_compressed" style="margin-top: 9; margin-bottom: 9">5. Instantaneous and terminal correlation</p> <p class="contents_compressed" style="margin-top: 9; margin-bottom: 9"><b>II Smiles - equity and FX</b></p> <p class="contents_compressed" style="margin-top: 9; margin-bottom: 9">6. Pricing options in the presence of smiles</p> <p class="contents_compressed" style="margin-top: 9; margin-bottom: 9">7. Empirical facts about smiles</p> <p class="contents_compressed" style="margin-top: 9; margin-bottom: 9">8. General features of smile-modelling approaches</p> <p class="contents_compressed" style="margin-top: 9; margin-bottom: 9">9. The input data : fitting an exogenous smile surface</p> <p class="contents_compressed" style="margin-top: 9; margin-bottom: 9">10. Quadratic variation and smiles</p> <p class="contents_compressed" style="margin-top: 9; margin-bottom: 9">11. Local-volatility models : the Derman-and-Kani approach</p> <p class="contents_compressed" style="margin-top: 9; margin-bottom: 9">12. Extracting the local volatility from option prices</p> <p class="contents_compressed" style="margin-top: 9; margin-bottom: 9">13. Stochastic-volatility processes</p> <p class="contents_compressed" style="margin-top: 9; margin-bottom: 9">14. Jump-diffusion processes</p> <p class="contents_compressed" style="margin-top: 9; margin-bottom: 9">15. Variance-gamma</p> <p class="contents_compressed" style="margin-top: 9; margin-bottom: 9">16. Displaced diffusions and generalizations</p> <p class="contents_compressed" style="margin-top: 9; margin-bottom: 9">17. No-arbitrage restrictions on the dynamics of smile surfaces</p> <p class="contents_compressed" style="margin-top: 9; margin-bottom: 9"><b>III Interest rates - deterministic volatilities</b></p> <p class="contents_compressed" style="margin-top: 9; margin-bottom: 9">18. Mean reversion in interest-rate models</p> <p class="contents_compressed" style="margin-top: 9; margin-bottom: 9">19. Volatility and correlation in the LIBOR market model</p> <p class="contents_compressed" style="margin-top: 9; margin-bottom: 9">20. Calibration strategies for the LIBOR market model</p> <p class="contents_compressed" style="margin-top: 9; margin-bottom: 9">21. Specifying the instantaneous volatility of forward rates</p> <p class="contents_compressed" style="margin-top: 9; margin-bottom: 9">22. Specifying the instantaneous correlation among forward rates</p> <p class="contents_compressed" style="margin-top: 9; margin-bottom: 9"><b>IV Interest rates - smiles</b></p> <p class="contents_compressed" style="margin-top: 9; margin-bottom: 9">23. How to model interest-rate smiles</p> <p class="contents_compressed" style="margin-top: 9; margin-bottom: 9">24. (CEV) processes in the context of the LMM</p> <p class="contents_compressed" style="margin-top: 9; margin-bottom: 9">25. Stochastic-volatility extensions of the LMM</p> <p class="contents_compressed" style="margin-top: 9; margin-bottom: 9">26. The dynamics of the swaption matrix</p> <p class="contents_compressed" style="margin-top: 9; margin-bottom: 9">27. Stochastic-volatility extension of the LMM : two-regime instantaneous volatility</td> </tr> </table> </td> </tr> </table> <p class="body" align="center"> </p> </td> </tr> <tr> <td width="50%" valign="bottom"> <table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table9"> <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" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" cellpadding="0" id="table10"> <tr> <td width="100%" bgcolor="#FFFFFF"> <table border="0" cellpadding="10" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table11"> <tr> <td width="50%" bgcolor="#FFFFCC" align="center"> <table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" bgcolor="#FFFFCC" id="table12"> <tr> <td> <p class="body" style="margin-bottom: 6"><b><font color="#333366" size="3">For related books, see sections:</font></b></p> <p class="bullet_line_space"> <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"><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"><img border="0" src="../images/bullet.gif" width="20" height="10"><a target="_top" href="../link_topic/financial_engineering_modeling_volatility.htm">Financial Engineering - Modeling Volatility</a></p> <p class="bullet_line_space"><img border="0" src="../images/bullet.gif" width="20" height="10"><a target="_top" href="../link_topic/math_stochastic_calculus.htm">Mathematics - Stochastic Calculus</a><p class="bullet_line_space"> <img border="0" src="../images/bullet.gif" width="20" height="10"><a target="_top" href="../link_topic/finance_financial_econometrics.htm">Finance - Financial Econometrics</a><p class="bullet_line_space"> <img border="0" src="../images/bullet.gif" width="20" height="10"><a target="_top" href="../link_topic/math_time_series.htm">Mathematics - Time Series Analysis</a></td> </tr> </table> </td> <td width="50%" bgcolor="#CCCCFF" align="left" valign="top"> <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> </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; 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