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.