45 research outputs found
Statistical mechanics of complex economies
In the pursuit of ever increasing efficiency and growth, our economies have
evolved to remarkable degrees of complexity, with nested production processes
feeding each other in order to create products of greater sophistication from
less sophisticated ones, down to raw materials. The engine of such an expansion
have been competitive markets that, according to General Equilibrium Theory
(GET), achieve efficient allocations under specific conditions. We study large
random economies within the GET framework, as templates of complex economies,
and we find that a non-trivial phase transition occurs: the economy freezes in
a state where all production processes collapse when either the number of
primary goods or the number of available technologies fall below a critical
threshold. As in other examples of phase transitions in large random systems,
this is an unintended consequence of the growth in complexity. Our findings
suggest that the Industrial Revolution can be regarded as a sharp transition
between different phases, but also imply that well developed economies can
collapse if too many intermediate goods are introduced.Comment: 30 pages, 10 figure
DebtRank: A microscopic foundation for shock propagation
The DebtRank algorithm has been increasingly investigated as a method to
estimate the impact of shocks in financial networks, as it overcomes the
limitations of the traditional default-cascade approaches. Here we formulate a
dynamical "microscopic" theory of instability for financial networks by
iterating balance sheet identities of individual banks and by assuming a simple
rule for the transfer of shocks from borrowers to lenders. By doing so, we
generalise the DebtRank formulation, both providing an interpretation of the
effective dynamics in terms of basic accounting principles and preventing the
underestimation of losses on certain network topologies. Depending on the
structure of the interbank leverage matrix the dynamics is either stable, in
which case the asymptotic state can be computed analytically, or unstable,
meaning that at least one bank will default. We apply this framework to a
dataset of the top listed European banks in the period 2008 - 2013. We find
that network effects can generate an amplification of exogenous shocks of a
factor ranging between three (in normal periods) and six (during the crisis)
when we stress the system with a 0.5% shock on external (i.e. non-interbank)
assets for all banks.Comment: 10 pages, 2 figure
Emergence of giant strongly connected components in continuum disk-spin percolation
We propose a continuum model of percolation in two dimensions for overlapping disks with spin. In this model the existence of bonds is determined by the distance between the centers of the disks, and by the scalar product of the (randomly) directed spin with the direction of the vector connecting the centers of neighboring disks. The direction of a single spin is controlled by a "temperature", representing the amount of polarization of the spins in the direction of an external field. Our model is inspired by biological neuronal networks and aims to characterize their topological properties when axonal guidance plays a major role. We numerically study the phase diagram of the model observing the emergence of a giant strongly connected component, representing the portion of neurons that are causally connected. We provide strong evidence that the critical exponents depend on the temperature
Lost in Diversification
As financial instruments grow in complexity more and more information is
neglected by risk optimization practices. This brings down a curtain of opacity
on the origination of risk, that has been one of the main culprits in the
2007-2008 global financial crisis. We discuss how the loss of transparency may
be quantified in bits, using information theoretic concepts. We find that {\em
i)} financial transformations imply large information losses, {\em ii)}
portfolios are more information sensitive than individual stocks only if
fundamental analysis is sufficiently informative on the co-movement of assets,
that {\em iii)} securitisation, in the relevant range of parameters, yields
assets that are less information sensitive than the original stocks and that
{\em iv)} when diversification (or securitisation) is at its best (i.e. when
assets are uncorrelated) information losses are maximal. We also address the
issue of whether pricing schemes can be introduced to deal with information
losses. This is relevant for the transmission of incentives to gather
information on the risk origination side. Within a simple mean variance scheme,
we find that market incentives are not generally sufficient to make information
harvesting sustainable
Pathways towards instability in financial networks
Following the financial crisis of 2007–2008, a deep analogy between the origins of instability in financial systems and complex ecosystems has been pointed out: in both cases, topological features of network structures influence how easily distress can spread within the system. However, in financial network models, the details of how financial institutions interact typically play a decisive role, and a general understanding of precisely how network topology creates instability remains lacking. Here we show how processes that are widely believed to stabilize the financial system, that is, market integration and diversification, can actually drive it towards instability, as they contribute to create cyclical structures which tend to amplify financial distress, thereby undermining systemic stability and making large crises more likely. This result holds irrespective of the details of how institutions interact, showing that policy-relevant analysis of the factors affecting financial stability can be carried out while abstracting away from such details
Financial instability from local market measures
We study the emergence of instabilities in a stylized model of a financial
market, when different market actors calculate prices according to different
(local) market measures. We derive typical properties for ensembles of large
random markets using techniques borrowed from statistical mechanics of
disordered systems. We show that, depending on the number of financial
instruments available and on the heterogeneity of local measures, the market
moves from an arbitrage-free phase to an unstable one, where the complexity of
the market - as measured by the diversity of financial instruments - increases,
and arbitrage opportunities arise. A sharp transition separates the two phases.
Focusing on two different classes of local measures inspired by real markets
strategies, we are able to analytically compute the critical lines,
corroborating our findings with numerical simulations.Comment: 17 pages, 4 figure