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Register a new userSystemic Cascades On Inhomogeneous Random Financial Networks
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T. R. Hurd
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This systemic risk paper introduces inhomogeneous random financial networks (IRFNs). Such models are intended to describe parts, or the entirety, of a highly heterogeneous network of banks and their interconnections, in the global financial system. Both the balance sheets and the stylized crisis behaviour of banks are ingredients of the network model. A systemic crisis is pictured as triggered by a shock to banks balance sheets, which then leads to the propagation of damaging shocks and the potential for amplification of the crisis, ending with the system in a cascade equilibrium. Under some conditions the model has ``locally tree-like independence (LTI), where a general percolation theoretic argument leads to an analytic fixed point equation describing the cascade equilibrium when the number of banks $N$ in the system is taken to infinity. This paper focusses on mathematical properties of the framework in the context of Eisenberg-Noe solvency cascades generalized to account for fractional bankruptcy charges. New results including a definition and proof of the ``LTI property of the Eisenberg-Noe solvency cascade mechanism lead to explicit $N=infty$ fixed point equations that arise under very general model specifications. The essential formulas are shown to be implementable via well-defined approximation schemes, but numerical exploration of some of the wide range of potential applications of the method is left for future work.
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We consider a random financial network with a large number of agents. The agents connect through credit instruments borrowed from each other or through direct lending, and these create the liabilities. The settlement of the debts of various agents at the end of the contract period can be expressed as solutions of random fixed point equations. Our first step is to derive these solutions (asymptotically), using a recent result on random fixed point equations. We consider a large population in which agents adapt one of the two available strategies, risky or risk-free investments, with an aim to maximize their expected returns (or surplus). We aim to study the emerging strategies when different types of replicator dynamics capture inter-agent interactions. We theoretically reduced the analysis of the complex system to that of an appropriate ordinary differential equation (ODE). We proved that the equilibrium strategies converge almost surely to that of an attractor of the ODE. We also derived the conditions under which a mixed evolutionary stable strategy (ESS) emerges; in these scenarios the replicator dynamics converges to an equilibrium at which the expected returns of both the populations are equal. Further the average dynamics (choices based on large observation sample) always averts systemic risk events (events with large fraction of defaults). We verified through Monte Carlo simulations that the equilibrium suggested by the ODE method indeed represents the limit of the dynamics.
The role of Network Theory in the study of the financial crisis has been widely spotted in the latest years. It has been shown how the network topology and the dynamics running on top of it can trigger the outbreak of large systemic crisis. Following this methodological perspective we introduce here the Accounting Network, i.e. the network we can extract through vector similarities techniques from companies financial statements. We build the Accounting Network on a large database of worldwide banks in the period 2001-2013, covering the onset of the global financial crisis of mid-2007. After a careful data cleaning, we apply a quality check in the construction of the network, introducing a parameter (the Quality Ratio) capable of trading off the size of the sample (coverage) and the representativeness of the financial statements (accuracy). We compute several basic network statistics and check, with the Louvain community detection algorithm, for emerging communities of banks. Remarkably enough sensible regional aggregations show up with the Japanese and the US clusters dominating the community structure, although the presence of a geographically mixed community points to a gradual convergence of banks into similar supranational practices. Finally, a Principal Component Analysis procedure reveals the main economic components that influence communities heterogeneity. Even using the most basic vector similarity hypotheses on the composition of the financial statements, the signature of the financial crisis clearly arises across the years around 2008. We finally discuss how the Accounting Networks can be improved to reflect the best practices in the financial statement analysis.
After the 2007/2008 financial crisis, the UK government decided that a change in regulation was required to amend the poor control of financial markets. The Financial Services Act 2012 was developed as a result in order to give more control and authority to the regulators of financial markets. Thus, the Financial Conduct Authority (FCA) succeeded the Financial Services Authority (FSA). An area requiring an improvement in regulation was insider trading. Our study examines the effectiveness of the FCA in its duty of regulating insider trading through utilising the event study methodology to assess abnormal returns in the run-up to the first announcement of mergers. Samples of abnormal returns are examined on periods, under regulation either by the FSA or by the FCA. Practically, stock price data on the London Stock Exchange from 2008-2012 and 2015-2019 is investigated. The results from this study determine that abnormal returns are reduced after the implementation of the Financial Services Act 2012; prices are also found to be noisier in the period before the 2012 Act. Insignificant abnormal returns are found in the run-up to the first announcement of mergers in the 2015-2019 period. This concludes that the FCA is efficient in regulating insider trading.
Management of systemic risk in financial markets is traditionally associated with setting (higher) capital requirements for market participants. There are indications that while equity ratios have been increased massively since the financial crisis, systemic risk levels might not have lowered, but even increased. It has been shown that systemic risk is to a large extent related to the underlying network topology of financial exposures. A natural question arising is how much systemic risk can be eliminated by optimally rearranging these networks and without increasing capital requirements. Overlapping portfolios with minimized systemic risk which provide the same market functionality as empirical ones have been studied by [pichler2018]. Here we propose a similar method for direct exposure networks, and apply it to cross-sectional interbank loan networks, consisting of 10 quarterly observations of the Austrian interbank market. We show that the suggested framework rearranges the network topology, such that systemic risk is reduced by a factor of approximately 3.5, and leaves the relevant economic features of the optimized network and its agents unchanged. The presented optimization procedure is not intended to actually re-configure interbank markets, but to demonstrate the huge potential for systemic risk management through rearranging exposure networks, in contrast to increasing capital requirements that were shown to have only marginal effects on systemic risk [poledna2017]. Ways to actually incentivize a self-organized formation toward optimal network configurations were introduced in [thurner2013] and [poledna2016]. For regulatory policies concerning financial market stability the knowledge of minimal systemic risk for a given economic environment can serve as a benchmark for monitoring actual systemic risk in markets.
This is an expanded version of the lecture given at the AMS Short Course on Mean Field Games, on January 13, 2020 in Denver CO. The assignment was to discuss applications of Mean Field Games in finance and economics. I need to admit upfront that several of the examples reviewed in this chapter were already discussed in book form. Still, they are here accompanied with discussions of, and references to, works which appeared over the last three years. Moreover, several completely new sections are added to show how recent developments in financial engineering and economics can benefit from being viewed through the lens of the Mean Field Game paradigm. The new financial engineering applications deal with bitcoin mining and the energy markets, while the new economic applications concern models offering a smooth transition between macro-economics and finance, and contract theory.
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