- Derivatives and Credit Contagion in Interconnected
Networks
by S. Heise and R. Kühn,
Eur. Phys. J. B 85, 115 (2012) (New expanded version, 31 Jan 2012) DOI 10.1140/epjb/e2012-20740-0
also available at http://arxiv.org/abs/1202.3025
The importance of adequately modeling credit risk has once again been highlighted in the recent financial crisis. Defaults tend to cluster around times of economic stress due to poor macro-economic conditions, but also by directly triggering each other through contagion. Although credit default swaps have radically altered the dynamics of contagion for more than a decade, models quantifying their impact on systemic risk are still missing. Here, we examine contagion through credit default swaps in a stylized economic network of corporates and financial institutions. We analyse such a system using a stochastic setting, which allows us to exploit limit theorems to exactly solve the contagion dynamics for the entire system. Our analysis shows that, by creating additional contagion channels, CDS can actually lead to greater instability of the entire network in times of economic stress. This is particularly pronounced when CDS are used by banks to expand their loan books (arguing that CDS would offload the additional risks from their balance sheets). Thus, even with complete hedging through CDS, a significant loan book expansion can lead to considerably enhanced probabilities for the occurrence of very large losses and very high default rates in the system. Our approach adds a new dimension to research on credit contagion, and could feed into a rational underpinning of an improved regulatory framework for credit derivatives.
- A Solvable Model for Distribution
Networks on Random Graphs
by D. Nasiev, J. van Mourik and R. Kühn,
Phys. Rev. E 76, 041120 (2007)
We propose a simple model that captures the salient properties of distribution
networks, and study the possible occurrence of black-outs, i.e. sudden failings
of large portions of such networks. The model is defined on a random graph of
finite connectivity. The nodes of the graph represent hubs of the network,
while the edges of the graph represent the links of the distribution network.
Both, the nodes and the edges carry dynamical two state variables representing
the functioning or dysfunctional state of the node or link in question. We
describe a dynamical process in which the breakdown of a link or node is
triggered when the level of maintenance it receives falls below a given
threshold. This form of dynamics can lead to situations of catastrophic
breakdown, if levels of maintenance are themselves dependent on the functioning
of the net, once maintenance levels locally fall below a critical threshold due
to fluctuations. We formulate conditions under which such systems can be
analysed in terms of thermodynamic equilibrium techniques, and under these
conditions derive a phase diagram characterising the collective behaviour of the
system, given its model parameters. The phase diagram is confirmed
qualitatively and quantitatively by simulations on explicit realisations of the
graph, thus confirming the validity of our approach.
- Credit Contagion and Credit Risk
by J.P.L. Hatchett and R. Kühn,
Quantitative Finance 9, 373-382 (2009)
(pdf)
We study a simple, solvable model that allows us to investigate
effects of credit contagion on the default probability of individual
firms, in both portfolios of firms and on an economy wide scale.
While the effect of interactions may be small in typical (most
probable) scenarios they are magnified, due to feedback, by
situations of economic stress, which in turn leads to fatter tails
in loss distributions of large loan portfolios.
- Phase Transitions in Operational
Risk
by K. Anand and R Kühn
Phys. Rev. E 75, 016111 (2007) (pdf)
In this paper we explore the functional correlation approach to
operational risk. We consider networks with heterogeneous a-priori
conditional and unconditional failure probability. In the limit of
sparse connectivity, self-consistent expressions for the dynamical
evolution of order parameters are obtained. Under equilibrium
conditions, expressions for the stationary states are also obtained.
The consequences of the analytical theory developed are analyzed using
phase diagrams. We find co-existence of operational and non-operational
phases, much as in liquid-gas systems. Such systems are susceptible to
discontinuous phase transitions from the operational to non-operational
phase via catastrophic breakdown. We find this feature to be robust
against variation of the microscopic modelling assumptions.
- Effects of Economic Interactions
on Credit Risk
by J.P.L. Hatchett and R. Kühn, J.
Phys. A 39 2231-2251
(2006)
(pdf)
We study a credit risk model which captures effects of economic
interactions on a firm's default probability. Economic interactions are
represented as a functionally defined graph, and the existence of both
cooperative, and competitive, business relations is taken into account.
We provide an analytic solution of the model in a limit where the
number of business relations of each company is large, but the overall
fraction of the economy with which a given company interacts may be
small. While the effects of economic interactions are relatively weak
in typical (most probable) scenarios, they are pronounced in situations
of economic stress, and thus lead to a substantial fattening of the
tails of loss distributions in large loan portfolios. This manifests
itself in a pronounced enhancement of the Value at Risk computed for
interacting economies in comparison with their non-interacting
counterparts.
- Intermittency in an Interacting Generalization of the
Geometric Brownian Motion Model
by R. Kühn and P. Neu,
J. Phys A 41, 324015 (2008) (pdf)
We propose a minimal interacting generalisation of the geometric Brownian
motion model, which turns out to be formally equivalent to a model describing
the dynamics of networks of analogue neurons. For suficiently strong
interactions, such systems may have many meta-stable states. Transitions
between meta-stable states are associated with macroscopic reorganisations
of the system, which can be triggered by random external forcing. Such a
system will exhibit intermittent dynamics within a large part of its parameter
space. We propose market dynamics as a possible application of this model, in
which case random external forcing would correspond to arrival of important
information. The emergence of a model of interacting prices of the type
considered here can be argued to follow naturally from a general argument
based on integrating out all non-price degrees of freedom from the dynamics
of a hypothetical complete description of economic dependencies.
- Adequate Capital and Stress Testing for Operational Risks
by R. Kühn and P. Neu,
reprint (pdf),
in: Operational Risk Modelling and Analysis: Theory and Practice,
M. Cruz (Editor), (Risk Waters Group, 2004), pp 273 - 289
We describe how the notion of sequential correlations naturally
leads to the quantification of operational risk. Our main point
is that functional dependencies between mutually supportive
processes give rise to non-trivial temporal correlations, which
can lead to the occurrence of collective risk events in the form
of bursts and avalanches of process failures, and crashes of
process networks. We show how the adequate capital for
operational risk can be calculated via a stochastic dynamics
defined on a topological network of interacting processes. One
of the main virtues of the present model is the suitability for
capital allocation and stress testing of operational risks.
- Credit Risk Enhancement in a Network of Interdependent Firms
by P. Neu and R. Kühn,
Physica A 342, 639-655 (2004) (pdf)
We propose a dynamical model to study the impact of sequential
defaults in a network of economically interdependent firms on the loss
distribution for bank loan portfolios. Exploring the analogy to a lattice
gas model from physics, correlations between sequential defaults are modeled
as due to functionally defined, heterogeneous couplings between mutually
dependent business partners. In our model functional dependencies result
in an enhancement of credit risk and a reduced granularity of the loan
portfolio. We find that corporate dependencies may result in additional
extreme losses in the loan portfolio. In particular - depending on the
relationship between the firms - collective phenomena such as bursts and
avalanches of defaults can be observed in the model. In this context,
traditional credit risk models are inadequate because they underestimate
the required equity capital. Furthermore, our model setting is particularly
applicable for doing stress analyses of credit risk in loan portfolios.
- Functional correlation approach to operational risk in
banking organizations
by R. Kühn and P. Neu, Physica
A 322 650-666 (2003) (pdf).
A Value-at-Risk-based model is proposed to compute the adequate
equity capital necessary to cover potential losses due to operational
risks, such as human and system process failures, in banking
organizations. Exploring the analogy to a lattice gas model from
physics, correlations between sequential failures are modeled by as
functionally defined, heterogeneous couplings
between mutually supportive processes. In contrast to traditional risk
models
for market and credit risk, where correlations are described as
equal-time-correlations by a covariance matrix, the dynamics of the
model shows collective phenomena such as bursts and avalanches of
process failures.
12 PhD positions across Europe within the new European Marie Curie training network