Maximum entropy and network approaches to systemic risk and foreign exchange
Becker, Alexander Paul
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The global financial system is an intricate network of networks, and recent financial crises have laid bare our insufficient understanding of its complexity. In response, within the five chapters of this thesis we study how interconnectedness, interdependency and mutual influence impact financial markets and systemic risk. In the first part, we investigate the community formation of global equity and currency markets. We find remarkable changes to correlation structure and lead-lag relationships in times of economic turmoil, implying significant risks to diversification based on historical data. The second part focuses on banks as creators of credit. Bank portfolios generally share some overlap, and this may introduce systemic risk. We model this using European stress test data, finding that the system is stable across a broad range of asset liquidity and risk tolerance. However, there exists a phase transition: If banks become sufficiently risk averse, even small shocks may inflict great losses. Failure to address portfolio overlap thus may leave the banking system ill-prepared. Complete knowledge of the financial network is prerequisite to such systemic risk analyses. When lacking this knowledge, maximum entropy methods allow a probabilistic reconstruction. In the third part of this thesis, we consider Japanese firm-bank data and find that reconstruction methods fail to generate a connected network. Deriving an analytical expression for connection probabilities, we show that this is a general problem of sparse graphs with inhomogeneous layers. Our results yield confidence intervals for the connectivity of a reconstruction. The maximum entropy approach also proves useful for studying dependencies in financial markets: On its basis, we develop a new measure for the information content in foreign exchange rates in part four of this thesis and use it to study the impact of macroeconomic variables on the strength of currency co-movements. While macroeconomic data and the law of supply and demand drive financial markets, foreign exchange rates are also subject to policy interventions. In part five, we classify the roles of currencies within the market with a clustering algorithm and study changes after political and monetary shocks. This methodology may further provide a quantitative underpinning to existing qualitative classifications.
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