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T. R. (Tom) Hurd
(1956-2022)
Professor of
Mathematics
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Contact
Information:
Dr. T. R. Hurd, Professor of Mathematics McMaster University Hamilton, Ontario L8S 4K1 |
- 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. Recently I have been 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 few 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. In 2014, I gave the Nachdiplom lecture series at ETH in Zurich. This was a 24 lecture PhD level course entitled "Mathematics of Financial Systemic Risk":
The
economic crisis of 2007-08 was first and foremost a crisis of the financial
system, a particularly complex example of a complex adaptive system. This
course will take a three-stranded approach to understanding the scientific and
economic foundations for the transmission of dangerous shocks between financial
institutions, and determining conditions under which
these shocks can amplify into a network wide disruption. The first strand will
consider the structure and dynamics of banks, their balance sheets, and their interconnections.
The second strand will review and extend the general probability theory of
information cascades in random networks, and to determine the different ways a
financial crisis can be considered as a network cascade. The final strand will
develop analytical and simulation-based algorithms for large scale computation
of such idealized cascades. By the end of the course, we will have the means to
model and test financial networks to determine their susceptibility to systemic
collapse.
- Systemic Risk Analytics Lab In
partnership with Matheus Grasselli and Sebastian Jaimungal, we lead a Fields/CQAM
Laboratory devoted to developing analytical tools to study systemic
risk.
- Contagion! Systemic Risk in Financial
Networks
The title of this book, published by Springer Verlag in 2016, suggests that financial contagion is analogous to the spread of disease, and that damaging financial crises may be better understood by bringing to bear ideas that have been developed to understand the breakdown of other complex systems in our world. It also suggests that the aim of systemic risk management is similar to a primary aim of epidemiology, namely to identify situations when contagion danger is high, and then make targetted interventions to damp out the risk.
This book is intended to be two things, a timely summary of a growing body of systemic risk research as well as a unified mathematical framework for the primary channels that can transmit damaging shocks through financial systems. Much of its contents are new, not having appeared previously in published journals. It aims to serve as a coherent guide of equal interest to quantitative finance practitioners, financial regulators and a broad range of academics including economists, physicists, applied mathematicians and computer scientists.
- Teaching Interests
My primary role in the department is as Director of the M-Phimac Master in Financial Mathematics program. In recent years, my main interest is in teaching specialized courses in financial mathematics. I currently teach MFM 701 Foundations of Financial Mathematics, a course which serves as an introduction to modern financial security analysis and is a core course of M-Phimac. In the Winter 2019, I will teach MFM 712 Credit Risk Modeling.
- PhiMAC: the financial math lab at McMaster
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:
Master in Financial Mathematics at McMaster
M-Phimac is the name of our 12 month professional coursework master program offered by the Mathematics and Statistics Department at McMaster. It leads to the MFM (Master in Financial Mathematics ) degree. This program 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, followed by a 4 month "Major industrial project" during the summer months, you will be well prepared to go after one of many opportunities available in banking, insurance and the investment business.
- Published Research
Papers
1.
Zachary Feinstein and T.R. Hurd, "Contingent
Convertible Obligations and Financial Stability", January 2021
preprint at arxiv.org/abs/1909.09239,
32 pages.
2.
T.R. Hurd, "COVID-19: Analytics of contagion on
inhomogeneous random social networks", Infectious Disease Modelling, 6,
75-90, 2021.
3.
T. R. Hurd, "Bank Panics and Fire Sales, Insolvency
and Illiquidity", International Journal of Theoretical and Applied
Finance, 21:6, 2018.
4.
Eduardo Santos Diaz, Simon Haykin,
T.R. Hurd, "The Fifth-Degree Continuous-Discrete Cubature Kalman Filter
for Radar", IET Radar, Sonar & Navigation.
10.1049/iet-rsn.2018.5148. , 2018.
5.
P. Jevtic and T. R. Hurd. “The joint mortality of couples
in continuous time”, Insurance Mathematics and Economics, 75, 90-97, 2017.
6.
T. R. Hurd, James Gleeson, Sergey Melnik,
"A framework for analyzing contagion in banking networks",
PLOS ONE, 12, 1-20, DOI 10.1371/journal.pone.0170579, 2017.
7.
T. R. Hurd, Davide Cellai, Sergey Melnik, Quentin Shao, "Double Cascade Model of
Financial Crises", International Journal of Theoretical and Applied
Finance (IJTAF), 19:5, 1-27, 2016. Download pdf file
8.
T. R. Hurd, "The Construction and Properties of
Assortative Configuration Graphs", in "Recent Progress and Modern
Challenges in Applied Mathematics, Modeling and Computational Science",
Fields Institute Communications, ed. Roderick Melnik,
Springer-Verlag Berlin, 2016. Download pdf file
9.
Yacine Aït-Sahalia, T. R. Hurd, Portfolio Choice in Markets
with Contagion", Journal of Financial Econometrics, 14, 1-28, 2015.
Download pdf file
10. T. R. Hurd,
James Gleeson "On Watts' Cascade Model with Random Link Weights", Journal
of Complex Networks, 1, 25-43, 2013.
Download pdf file
11. 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
Download pdf file
12. 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
Download pdf file
13. 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
Download pdf file
14. 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.
Download pdf file
15. T. R. Hurd, Zhuowei Zhou "A Fourier transform method for spread
option pricing”, SIAM Journal of Financial Mathematics, 1, 142-157,
2009.
Download pdf file
16. T. R. Hurd “Credit
Risk Modelling using time-changed Brownian motion”, Int. J. Theor. App. Fin. 12, 1213–1230, 2009.
Download pdf file
17. 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.
Download pdf file
18. T. R. Hurd "Saddlepoint approximations in portfolio credit risk",
in Encyclopedia of Quantitative Finance, ed. R. Cont,
Wiley-UK, 7 pages, 2008.
Download pdf file
19. 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.
Download pdf file
20. T. R. Hurd,
A. Kuznetsov "Explicit formulas for Laplace
transforms of stochastic integrals", Markov Processes and Related
Fields, 14, 277-290, 2008.
Download pdf file
21. T. R. Hurd,
A. Kuznetsov "Affine Markov chain models of multifirm credit migration", Journal of Credit
Risk 3, 3-29, 2007.
Download pdf file
22. M. R. Grasselli, T. R. Hurd "Indifference pricing and
hedging for volatility derivatives", Applied Mathematical Finance 14,
303-317, 2007.
Download pdf file
23. Jingping Yang, T. R.
Hurd, Xuping Zhang "Saddlepoint
approximation method for pricing CDOs", Journal of Computational
Finance 10, 1-20, 2006.
Download pdf file
24. T. R. Hurd "A
note on log-optimal portfolios in exponential Levy markets",
Statistics and Decisions, 22, pp. 225-236, 2004
Download pdf file
25. M. R. Grasselli, T. R. Hurd "Weiner chaos and the
Cox-Ingersoll-Ross model", Proc. R. Soc. A, 461, pp. 459-479,
2004
Download pdf file
26. T. Choulli, T. R. Hurd "The role of Hellinger
processes in mathematical finance", Entropy 3, pp. 152-163, 2001
Download pdf file
27. 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
Download ps file ; pdf file
- Research Working Papers
1.
T. R. Hurd, Zhuowei Zhou "Two-factor
capital structure models for equity and credit”, working paper, October
2011
Download pdf file
2.
T. R. Hurd, Zhuowei Zhou "Structural
credit risk using time-changed Brownian motions: a tale of two models”,
working paper, September 2011
Download pdf file
3.
J. Abad, T. R. Hurd "Error bounds for Monte Carlo
based portfolio optimization", working paper, February 2004
Download pdf file
4.
M. R. Grasselli, T. R. Hurd "A
Monte Carlo method for exponential hedging of contingent claims",
working paper, November 2002
Download ps file; pdf file
5.
T. Choulli, T. R. Hurd "The
portfolio selection problem via Hellinger processes", working paper,
October 2001
Download pdf file
6.
T. R. Hurd "Pricing formulas, model error and
hedging derivative portfolios", working paper, August 2001
Download pdf file
- Applied Math at McMaster
Applied math is thriving at McMaster. Come and visit the website of the McMaster Applied Math Research Group
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