Essays on Networks: Theory and Applications

Networks have proven to be a useful representation of various systems. Social and economic interactions, biological and ecological systems, the internet can be understood better if modelled as networks. Intuitively, a network describes a collection of nodes and the links between them. The notion of nodes is fairly general, they may be individuals or firms or countries. A link between two nodes represents a direct relation between them; for instance, a link could be a friendship tie between people, a research and development agreement between firms, or, in the context of countries, a link may be a mutual defense pact. The study of networks spans across disciplines. A central field in sociology and studied in depth by mathematicians over the past fifty years, networks have recently received extensive attention in statistical physics, computer science, business strategy and organization theory. While economists have occasionally showed interest in networks, a literature has emerged only in the last decade. This thesis brings two contributions. On the one hand, it aims to enhance the role of network theories in solving economic issues, by proposing a network representation of financial systems. On the other hand, it aims to enrich the set of methods used to analyze networks, by introducing economic microfoundations to a preferential attachment model of network formation

On the Computational Complexity of Measuring Global Stability of Banking Networks

Threats on the stability of a financial system may severely affect the functioning of the entire economy, and thus considerable emphasis is placed on the analyzing the cause and effect of such threats. The financial crisis in the current and past decade has shown that one important cause of instability in global markets is the so-called financial contagion, namely the spreading of instabilities or failures of individual components of the network to other, perhaps healthier, components. This leads to a natural question of whether the regulatory authorities could have predicted and perhaps mitigated the current economic crisis by effective computations of some stability measure of the banking networks. Motivated by such observations, we consider the problem of defining and evaluating stabilities of both homogeneous and heterogeneous banking networks against propagation of synchronous idiosyncratic shocks given to a subset of banks. We formalize the homogeneous banking network model of Nier et al. and its corresponding heterogeneous version, formalize the synchronous shock propagation procedures, define two appropriate stability measures and investigate the computational complexities of evaluating these measures for various network topologies and parameters of interest. Our results and proofs also shed some light on the properties of topologies and parameters of the network that may lead to higher or lower stabilities.Comment: to appear in Algorithmic

Sparse Pseudospectral Approximation Method

Multivariate global polynomial approximations - such as polynomial chaos or stochastic collocation methods - are now in widespread use for sensitivity analysis and uncertainty quantification. The pseudospectral variety of these methods uses a numerical integration rule to approximate the Fourier-type coefficients of a truncated expansion in orthogonal polynomials. For problems in more than two or three dimensions, a sparse grid numerical integration rule offers accuracy with a smaller node set compared to tensor product approximation. However, when using a sparse rule to approximately integrate these coefficients, one often finds unacceptable errors in the coefficients associated with higher degree polynomials. By reexamining Smolyak's algorithm and exploiting the connections between interpolation and projection in tensor product spaces, we construct a sparse pseudospectral approximation method that accurately reproduces the coefficients of basis functions that naturally correspond to the sparse grid integration rule. The compelling numerical results show that this is the proper way to use sparse grid integration rules for pseudospectral approximation

Systemic risk and macroeconomic fat tails

We propose a mechanism for shock amplification that potentially can account for fat tails in the distribution of the growth rate of national output. We argue that extreme macroeconomic events, such as the Great Depression and the Great Recession, were preceded by significant turmoil in the banking system. We have developed a model of bank network formation and presented numerical simulations that show that, for the benchmark case, aggregate credit follows a random walk. When we introduce fire sales the model does not only produce larger variations in the growth of aggregate credit but also shows that there is an asymmetry between booms and busts that is also consistent with empirical evidence

Exclusive Intermediation

In this paper, we argue that an important function fulfilled by intermediaries is to facilitate trust by enabling social pressure towards the enforcement of informal agreements. To that end, we develop a new model that uses network theory to show that intermediaries who have exclusivity over a large enough number of interaction opportunities are able to exploit their position in the chains of interactions in the market to overcome incentive problems that would otherwise shut down the market. We derive conditions on the network structure under which intermediaries fulfill this function. Finally, we analyze two applications: (1) the market for short termapartment rentals; and (2) a financial market with investors and entrepreneurs. We provide additional examples suggesting that this paper uncovers an important channel through which intermediaries operate

Systemic importance of financial institutions: regulations, research, open issues, proposals

In the field of risk management, scholars began to bring together the quantitative methodologies with the banking management issues about 30 years ago, with a special focus on market, credit and operational risks. After the systemic effects of banks defaults during the recent financial crisis, and despite a huge amount of literature in the last years concerning the systemic risk, no standard methodologies have been set up to now. Even the new Basel 3 regulation has adopted a heuristic indicator-based approach, quite far from an effective quantitative tool. In this paper, we refer to the different pieces of the puzzle: definition of systemic risk, a set of coherent and useful measures, the computability of these measures, the data set structure. In this challenging field, we aim to build a comprehensive picture of the state of the art, to illustrate the open issues, and to outline some paths for a more successful future research. This work appropriately integrates other useful surveys and it is directed to both academic researchers and practitioners

Systemic Risk, Contagion, and Financial Networks: A Survey

The recent crisis has highlighted the crucial role that existing linkages among banks and financial institutions plays in channeling and amplifying shocks hitting the system. The structure and evolution of such web of linkages can be fruitfully characterized using concepts borrowed from the theory of (complex) networks. This paper critically surveys recent theoretical work that exploits this concept to explain the sources of contagion and systemic risk in financial markets. We taxonomize existing contributions according to the impact of network connectivity, bank heterogeneity, existing uncertainty in financial markets, portfolio composition of the banks. We end with a discussion of the most important challenges faced by theoretical network-based models of systemic risk. These include a better understanding of the causal links between network structure and the likelihood of systemic risk and increasingly using the empirical knowledge about real-world financial-network structures to calibrate theoretical models