Office: Hamilton Hall 416 Phone: (905) 525-9140 extension 27304 FAX: (905) 522-0935 E-mail: hurdt at mcmaster dot ca
Research Interests
Since 1998 my research programme has been concentrated in the
rapidly developing field of financial
mathematics. Prior to this I worked primarily in mathematical physics. 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?"
Applying balance sheet modelling to the interbank network leads
immediately to the problem of financial systemic risk,
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. I am
Principal Investigator of a major research project entitled Financial Systemic Risk:
a Network Science Approach sponsored by the Global Risk
Institute (GRI). In the past couple of years, have
given minicourses on Systemic Risk at a number of research
institutions: IMPA in Rio, the 11th
Winter school on Mathematical Finance in the Netherlands,
and MACSI at the University
of Limerick.
I supervise PhiMAC,
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!
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 brochure.
Mprime
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 Mprime
website.
Published Research Papers
T. R. Hurd, James Gleeson "On Watts' Cascade Model
with Random Link Weights", to appear in Journal of
Complex Networks, 2013.
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James Gleeson, T. R. Hurd, Sergey Melnik, Adam Hackett "Systemic
risk
in banking networks without Monte Carlo simulation",
to appear in "Advances in Network Analysis and its
Applications", Mathematics in Industry series, ed. E.
Kranakis, Springer Verlag, Berlin Heidelberg New York, 2011
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M. Grasselli, T. R. Hurd “The Fields Institute
Thematic Program on Quantitative Finance: Foundations and
Applications January to June, 2010” Quantitative
Finance, 11, 21 - 29, 2011
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Chuang Yi, A. Tchernitser, T. R. Hurd "Randomized
structural models of credit spreads", Quantitative
Finance, 2010,
http://www.informaworld.com/10.1080/14697688.2010.507213.
DOI: 10.1080/14697688.2010.507213
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Ienkaran Arasaratnam, Simon Haykin, T. R. Hurd "Cubature
Filtering for Continuous-Discrete Systems: Theory with an
Application to Tracking", IEEE Transactions on Signal
Processing, 2010, 29 pages.
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T. R. Hurd, Zhuowei Zhou "A Fourier transform method
for spread option pricing”, SIAM Journal of Financial
Mathematics, 1, 142-157, 2009.
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T. R. Hurd “Credit Risk Modelling using time-changed
Brownian motion”, Int. J. Theor. App. Fin. 12,
1213–1230, 2009.
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T. R. Hurd, A. Kuznetsov "On the first passage time
for Brownian motion subordinated by a Levy process",
Journal of Applied Probability 46.1, 181-198, 2009.
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T. R. Hurd "Saddlepoint approximations in portfolio
credit risk", in Encyclopedia of Quantitative Finance,
ed. R. Cont, Wiley-UK, 7 pages, 2008.
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Y. Ait-Sahalia, J. Cacho-Diaz, T. Hurd "Portfolio
Choice with Jumps: A Closed Form Solution" , Annals
of Applied Probability,19.2, 277-290, 2008.
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T. R. Hurd, A. Kuznetsov "Explicit formulas for
Laplace transforms of stochastic integrals", Markov
Processes and Related Fields, 14, 277-290, 2008.
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T. R. Hurd, A. Kuznetsov "Affine Markov chain models
of multifirm credit migration", Journal of Credit Risk
3, 3-29, 2007.
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M. R. Grasselli, T. R. Hurd "Indifference pricing and
hedging for volatility derivatives", Applied
Mathematical Finance 14, 303-317, 2007.
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Jingping Yang, T. R. Hurd, Xuping Zhang "Saddlepoint
approximation method for pricing CDOs", Journal of
Computational Finance 10, 1-20, 2006.
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T. R. Hurd "A note on log-optimal portfolios in
exponential Levy markets", Statistics and Decisions, 22,
pp. 225-236, 2004
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M. R. Grasselli, T. R. Hurd "Weiner chaos and the
Cox-Ingersoll-Ross model", Proc. R. Soc. A, 461,
pp. 459-479, 2004
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T. Choulli, T. R. Hurd "The role of Hellinger
processes in mathematical finance", Entropy 3,
pp. 152-163, 2001
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J. Boland, T.R. Hurd, M. Pivato, L. Seco "Measures of
dependence for multivariate Levy distributions",
Proceedings of the Conference on Disordered and Complex
Systems, edited by P. Sollich et al, American Institute of
Physics, 2001
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Research Working Papers
Yacine Aït-Sahalia, T. R. Hurd, Portfolio Choice in Markets with Contagion",
working paper, September 2012.
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file
T. R. Hurd, Zhuowei Zhou "Two-factor capital structure
models for equity and credit”, working paper, October
2011
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T. R. Hurd, James Gleeson "A framework for analyzing
contagion in banking networks", working paper, October
2011
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T. R. Hurd, Zhuowei Zhou "Structural credit risk using
time-changed Brownian motions: a tale of two models”,
working paper, September 2011
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J. Abad, T. R. Hurd "Error bounds for Monte Carlo
based portfolio optimization", working paper, February
2004
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M. R. Grasselli, T. R. Hurd "A Monte Carlo method for
exponential hedging of contingent claims", working
paper, November 2002
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T. Choulli, T. R. Hurd "The portfolio selection
problem via Hellinger processes", working paper,
October 2001
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T. R. Hurd "Pricing formulas, model error and hedging
derivative portfolios", working paper, August 2001
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