ÿþ<!doctype html public "-//w3c//dtd html 4.0 transitional//en"> <html> <head> <meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> <meta name="GENERATOR" content="Mozilla/4.5 (Macintosh; U; PPC) [Netscape]"> <title>Tom Hurd's Homepage Information</title> </head> <body BACKGROUND="2n.jpg"> <TABLE CELLSPACING=0 BORDER=0 CELLPADDING=7 WIDTH=740> <TR><TD WIDTH="25%" VALIGN="TOP" HEIGHT=120> <P><A NAME="top"></A><iMG SRC="maclogopms.gif" WIDTH=200 HEIGHT=108></TD> <TD WIDTH="75%" VALIGN="TOP" HEIGHT=120> <B><FONT FACE="arial" SIZE=7>T. R. (Tom) Hurd<BR> </B></FONT><H1> Professor of Mathematics</H1></TD> </TR> </TABLE> <hr> <TABLE CELLSPACING=0 BORDER=0 CELLPADDING=7 WIDTH=740> <TR><TD WIDTH="29%" VALIGN="TOP" HEIGHT=120> <img src="HurdPicture.jpg" WIDTH=180 HEIGHT=180 ></td> <td WIDTH="71%" VALIGN="TOP" HEIGHT=120> <h2>Contact Information:</h2> <pre> Dr. T. R. Hurd, Professor of Mathematics <a href = "http://www.math.mcmaster.ca">Department of Mathematics and Statistics</a> <a href = "http://dailynews.mcmaster.ca/">McMaster University</a> <a href = "http://www.city.hamilton.on.ca/">Hamilton</a>, Ontario L8S 4K1 Canada <em>Office:</em> Hamilton Hall 416 <em>Phone:</em> (905) 525-9140 extension 27304 <em>FAX:</em> (905) 522-0935 <em>E-mail:</em> hurdt at mcmaster dot ca</a> </pre> </td> </table> <hr> <ul> <li><font size=+1>Research Interests</font size></a> <br><br> Since 1998 my research programme has been concentrated in the rapidly developing field of <a href="finmath.html">financial mathematics</a>. Prior to this I worked primarily in <a href="mathphys.html"> mathematical physics</a>. Financial crises such as the 2007/08 global meltdown lead to insolvency or default of firms, and in turn such firm defaults create further market distress that compounds the crisis. Understanding capital structure of firms and the links joining them is thus a critical area of concern to society. In accounting, a firm's balance sheet records book values of A (assets), D (debt) and E (equity) on a quarterly basis. Mathematical Finance takes a market perspective that sees the firm and all the securities that trade on it in terms of prices observed in the liquid capital markets. Market values reflect but do not equal book values, and are updated continuously not just 4 times a year. The two strands of this proposal are to develop market models of capital structure and default risk at the one-firm and system-wide levels. Traditional firm models focus on the randomness of A while treating D as non-random, and view securities such as credit default swaps as derivatives on A. A new "hybrid" approach takes A and D as joint stochastic processes and treats both credit and equity securities as derivatives on A and D, enabling trading and hedging between credit and equity markets. The first strand of this proposal is to address the central question about hybrid models: "How well can the collective of all observed market securities written on a firm be understood as derivatives on the unobserved processes A and D?" Financial systemic risk is defined as the risk that insolvency of some banks triggers further bank defaults. Such "domino events" are transmitted through links representing interbank loans that are identifiable in banks' balance sheets. Modeling financial networks and their systemic risk is both of strategic importance for society and an important applied mathematics problem. My second strand is to investigate how capital structure and default risk for banks intertwine with random network theory and to address the primary question "Which structural aspects of a financial network most affect systemic risk?" In a nutshell, my research aims to extend the range of Mathematical Finance to give a practical market-based understanding of firms and their links.</li> <br><br><li><font size=+1>Teaching Interests</font size> <br><br> In recent years, my primary interest is in teaching specialized courses in financial mathematics. In September 2011 I will be teaching Math 771 Mathematics of Finance, a course which serves as an introduction to modern financial security analysis and is a core course of our M-Phimac coursework MSc in Financial Mathematics. In January 2012, I will teach Math 774 The Mathematics of Credit Risk and Math 1AA03 Calculus II. </li> <br><br><li><font size=+1>PhiMAC: the financial math lab at McMaster</font size> <br> <br> I supervise <a href="http://www.math.mcmaster.ca/phimac">PhiMAC</a>, a group of researchers in the Mathematics Department at McMaster who share a common interest in computational finance. We encourage interest from prospective graduate students and researchers from around the world. Have a look at our website!</li> <br><br><li><font size=+1>M-PhiMAC: Master's in Financial Mathematics at McMaster</font size> <br> <br> M-Phimac, the coursework M.Sc. program offered by the Mathematics and Statistics Department at McMaster, is for the student who wants a fast track to a finance industry career in the areas of risk management, derivative securities analysis and portfolio design. After completing eight specialized grad courses in eight months, plus a number of optional training activities, you will be well prepared to go after one of many opportunities available in banking, insurance and the investment business. Have a look at our <a href="M-Phimac_brochure_2010.pdf">brochure</a>.</li> <br><br> <li><font size=+1>Mprime</font size> <br> <br> Mprime, the only Network of Centres of Excellence for the mathematical sciences, brings together academia, industry and the public sector to develop cutting edge mathematical tools vital to our knowledge-based economy. I am a core investigator of an Mprime initiative titled "Modelling Trading and Risk in the Market", involving researchers at University of Calgary, University of Toronto, University of Western Ontario, University of British Columbia and McMaster University. The general theme of our work is to develop mathematical tools for measurement and management of financial risk. For a detailed description of our Mprime project and others see the <a href="http://www.apmaths.uwo.ca/~mdavison/research/mtrm/index.htm">Mprime website</a>.</li> <br><br> <li><font size=+1>Published Research Papers</font size></a> <br><br> <ol> <li>James Gleeson, T. R. Hurd, Sergey Melnik, Adam Hackett <i>"Systemic risk in banking networks without Monte Carlo simulation"</i>, to appear in "Advances in Network Analysis and its Applications", Mathematics in Industry series, ed. E. Kranakis, Springer Verlag, Berlin Heidelberg New York, 2011 <br>Download <a href="NetworkPaperISpringer_v2.pdf">pdf file</a> </li> <br> <li> M. Grasselli, T. R. Hurd <i>  The Fields Institute Thematic Program on Quantitative Finance: Foundations and Applications January to June, 2010 </i> Quantitative Finance, 11, 21 - 29, 2011 <br> Download <a href="report_QF.doc">pdf file</a></li> <br> <li> Chuang Yi, A. Tchernitser, T. R. Hurd <i>"Randomized structural models of credit spreads"</i>, Quantitative Finance, 2010, http://www.informaworld.com/10.1080/14697688.2010.507213. DOI: 10.1080/14697688.2010.507213 <br> Download <a href="YiTcherHurd08.pdf">pdf file</a></li> <br> <li> Ienkaran Arasaratnam, Simon Haykin, T. R. Hurd <i>"Cubature Filtering for Continuous-Discrete Systems: Theory with an Application to Tracking"</i>, IEEE Transactions on Signal Processing, 2010, 29 pages. <br> Download <a href="ArasHayKHurd2010.pdf">pdf file</a></li> <br> <li>T. R. Hurd, Zhuowei Zhou <i>"A Fourier transform method for spread option pricing </i>, SIAM Journal of Financial Mathematics, <b>1</b>, 142-157, 2009. <br> Download <a href="HurdZhouSpreadoptionsSIAM.pdf">pdf file</a></li> <br> <li>T. R. Hurd <i> Credit Risk Modelling using time-changed Brownian motion </i>, Int. J. Theor. App. Fin. <b>12</b>, 1213 1230, 2009. <br> Download <a href="IJTAF_1208_P1213.pdf">pdf file</a></li> <br> <li>T. R. Hurd, A. Kuznetsov <i>"On the first passage time for Brownian motion subordinated by a Levy process"</i>, Journal of Applied Probability <b>46.1</b>, 181-198, 2009. <br> Download <a href="HurdKuznetsovFirstPassage.pdf">pdf file</a></li> <br> <li>T. R. Hurd <i>"Saddlepoint approximations in portfolio credit risk"</i>, in Encyclopedia of Quantitative Finance, ed. R. Cont, Wiley-UK, 7 pages, 2008.<br> Download <a href="SaddlepointApproximations2.pdf">pdf file</a></li> <br> <li> Y. Ait-Sahalia, J. Cacho-Diaz, T. Hurd <i> "Portfolio Choice with Jumps: A Closed Form Solution" </i>, Annals of Applied Probability,<b>19.2</b>, 277-290, 2008. <br> Download <a href="portjump.pdf">pdf file</a></li> <br> <li>T. R. Hurd, A. Kuznetsov <i>"Explicit formulas for Laplace transforms of stochastic integrals"</i>, Markov Processes and Related Fields, <b>14</b>, 277-290, 2008. <br> Download <a href="StochIntHurdKuzn.pdf">pdf file</a></li> <br> <li>T. R. Hurd, A. Kuznetsov <i>"Affine Markov chain models of multifirm credit migration"</i>, Journal of Credit Risk <b>3</b>, 3-29, 2007. <br> Download <a href="AMCpaperHurdKuzn.pdf">pdf file</a></li> <br> <li>M. R. Grasselli, T. R. Hurd <i>"Indifference pricing and hedging for volatility derivatives"</i>, Applied Mathematical Finance <b>14</b>, 303-317, 2007. <br> Download <a href="IndifferenceGrasHurd.pdf">pdf file</a></li> <br> <li> Jingping Yang, T. R. Hurd, Xuping Zhang <i>"Saddlepoint approximation method for pricing CDOs"</i>, Journal of Computational Finance <b>10</b>, 1-20, 2006. <br> Download <a href="SaddlepointCDOfinal.pdf">pdf file</a></li> <br> <li>T. R. Hurd <i>"A note on log-optimal portfolios in exponential Levy markets"</i>, Statistics and Decisions, <b>22</b>, pp. 225-236, 2004 <br> Download <a href="Utilitynote.pdf">pdf file</a></li> <br> <li>M. R. Grasselli, T. R. Hurd <i>"Weiner chaos and the Cox-Ingersoll-Ross model"</i>, Proc. R. Soc. A, <b> 461</b>, pp. 459-479, 2004 <br> Download <a href="newchaos.pdf">pdf file</a></li> <br> <li>T. Choulli, T. R. Hurd <i>"The role of Hellinger processes in mathematical finance"</i>, Entropy <b> 3</b>, pp. 152-163, 2001 <br>Download <a href="entropyfinal.pdf">pdf file</a></li> <br> <li>J. Boland, T.R. Hurd, M. Pivato, L. Seco <i>"Measures of dependence for multivariate Levy distributions"</i>, Proceedings of the Conference on Disordered and Complex Systems, edited by P. Sollich et al, American Institute of Physics, 2001 <br>Download <a href="levy.ps">ps file</a> ; <a href="finallevyshort.pdf">pdf file</a></li> <br> </ol> <li><font size=+1> Research Working Papers</font size></a> <br><br> <ol> <li>T. R. Hurd, Zhuowei Zhou <i>"Two-factor capital structure models for equity and credit </i>, working paper, October 2011 <br> Download <a href="HurdZhouCreditEquity.pdf">pdf file</a></li> <br> <li>T. R. Hurd, James Gleeson <i>"A framework for analyzing contagion in banking networks"</i>, working paper, October 2011 <br>Download <a href="HurdGleesonContagion.pdf">pdf file</a></li> <br> <li>T. R. Hurd, Zhuowei Zhou <i>"Structural credit risk using time-changed Brownian motions: a tale of two models </i>, working paper, September 2011 <br> Download <a href="HurdZhuoTCBMSIAMrevised.pdf">pdf file</a></li> <br> <li>J. Abad, T. R. Hurd <i>"Error bounds for Monte Carlo based portfolio optimization"</i>, working paper, February 2004 <br>Download <a href="HurdAbad.pdf">pdf file</a></li> <br> <li>M. R. Grasselli, T. R. Hurd <i>"A Monte Carlo method for exponential hedging of contingent claims"</i>, working paper, November 2002 <br>Download <a href="monte.ps">ps file</a>; <a href="monte.pdf">pdf file</a></li> <br> <li>T. Choulli, T. R. Hurd <i>"The portfolio selection problem via Hellinger processes"</i>, working paper, October 2001 <br>Download <a href="hurd,tom-utility.pdf">pdf file</a></li> <br> <li>T. R. Hurd <i>"Pricing formulas, model error and hedging derivative portfolios"</i>, working paper, August 2001 <br>Download <a href="hedging.pdf">pdf file</a></li> <br> </ol> <li> <font size=+1>Applied Math at McMaster</font size><br><br> Applied math is thriving at McMaster. Come and visit the website of the <a href="http://www.math.mcmaster.ca/research/area.php?area_id=3/">McMaster Applied Math Research Group</a></li> <hr> <ul> <li><a href = "http://www.math.mcmaster.ca/people/"> Directory of Personal Home Pages</a> for the Department of Mathematics and Statistics </li> <li><a href = "http://www.math.mcmaster.ca/"> Department of Mathematics and Statistics Home Page</a> </li> <li> <a href = "http://dailynews.mcmaster.ca/"> McMaster University Home Page</a> <hr> <!<a href="http://cgi3.fxweb.com/v2-openstat.cgi?userid=M52869&password2=public"> <! Webtracker </A> <address> last updated&nbsp; 17/10/2011</address> </body> </html>