On Hilberg's Law and Its Links with Guiraud's Law

Hilberg (1990) supposed that finite-order excess entropy of a random human text is proportional to the square root of the text length. Assuming that Hilberg's hypothesis is true, we derive Guiraud's law, which states that the number of word types in a text is greater than proportional to the square root of the text length. Our derivation is based on some mathematical conjecture in coding theory and on several experiments suggesting that words can be defined approximately as the nonterminals of the shortest context-free grammar for the text. Such operational definition of words can be applied even to texts deprived of spaces, which do not allow for Mandelbrot's ``intermittent silence'' explanation of Zipf's and Guiraud's laws. In contrast to Mandelbrot's, our model assumes some probabilistic long-memory effects in human narration and might be capable of explaining Menzerath's law.Comment: To appear in Journal of Quantitative Linguistic

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

Reduction of systemic risk by means of Pigouvian taxation

We analyze the possibility of reduction of systemic risk in financial markets through Pigouvian taxation of financial institutions, which is used to support the rescue fund. We introduce the concept of the cascade risk with a clear operational definition as a subclass and a network related measure of the systemic risk. Using financial networks constructed from real Italian money market data and using realistic parameters, we show that the cascade risk can be substantially reduced by a small rate of taxation and by means of a simple strategy of the money transfer from the rescue fund to interbanking market subjects. Furthermore, we show that while negative effects on the return on investment (ROI) are direct and certain, an overall positive effect on risk adjusted return on investments (ROIRA) is visible. Please note that the taxation is introduced as a monetary/regulatory, not as a _scal measure, as the term could suggest. The rescue fund is implemented in a form of a common reserve fund

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

An Empirical Study of the Mexican Banking System's Network and Its Implications for Systemic Risk

With the purpose of measuring and monitoring systemic risk, some topological properties of the interbank exposures and the payments system networks are studied. We propose non-topological measures which are useful to describe the individual behavior of banks in both networks. The evolution of such networks is also studied and some important conclusions from the systemic risks perspective are drawn. A unified measure of interconnectedness is also created. The main findings of this study are: the payments system network is strongly connected in contrast to the interbank exposures network; the type of exposures and payment size reveal different roles played by banks; behavior of banks in the exposures network changed considerably after Lehmans failure; interconnectedness of a bank, estimated by the unified measure, is not necessarily related with its assets size

Credit Contagion in Financial Markets: A Network-Based Approach

We propose a network-based model of credit contagion and examine the e�ects of idiosyncratic and systemic shocks to individual banks and the banking system. The banking system is built as a network in which banks are connected to each other through the interbank market. The microstructure captures the relation between debtors and creditors, and the macroeconomic events capture the sensitivity of the banks' �nancial strenght to macroeconomic events, such as housing. We have demonstrated that while idiosyncratic shocks do not have a potential to substantially disturb the banking system, macroeconomic events of higher magnitudes could be highly harmful, especially if they also spur contagion. In a concerted default of more banks, the stability of a banking system tends to decrease disproportionately. In addition, credit risk analysis is highly sensitive to the network topology and exhibits a nonlinear characteristic. Capital ratio and recovery rates are two additional factors that contribute to the stability of the �nancial system