Wray, CM; (2015) Complex systems models of financial and systemic risk. Doctoral thesis , UCL (University College London).

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Abstract

The primary purpose of this thesis is to develop mathematical models and tools that aid the understanding of financial systemic risk, by analysing and applying techniques from complexity science. Large systemic risks that arise in financial asset markets have proved that they can emerge virtually without warning, and create large financial and social costs. I argue that herd behaviour in asset markets is a source of such systemic risk. In this thesis, I present a new mathematical model of cascades on a stochastic pulse-coupled network, in the presence of binary opposing influences, and analyse it as both a mean field dynamical system, and probabilistically. I demonstrate that a critical coupling parameter exists separating a quiescent regime, from a volatile synchronous regime consisting of large cascades. Second, as an application to systemic risk, I develop a new model of a stylised financial market, using only minimal assumptions, and demonstrate how this replicates important empirical features of financial asset returns, such as long-memory volatility patterns, without recourse to strategy switching or stochastic volatility. Numerical evidence is presented that suggests this minimal market model self-organises to a critical regime, assuming only mild plausible optimising behaviour on the part of the agent. Lastly, I consider some implications for policy scenarios in light of my findings.

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