Introduction

Financial markets operate within a vastly interconnected world where information, capital, and goods transit rapidly across global networks. Traditional financial models, typically built on assumptions of equilibrium and rational actors, often fail to capture the unpredictable, non-linear behaviours observed in these markets. The emergence of big data and globalisation has prompted a “complexity turn”, leading to the adoption of multidisciplinary frameworks from econobiology and econophysics to better understand market dynamics. These approaches view macro-level outcomes as more than the sum of individual actions, shifting focus towards collective system behaviour arising from complex system dynamics.

Financial markets as complex systems

Neoclassical economics has long assumed that rational agents drive markets towards equilibrium. However, empirical evidence shows that investors exhibit biases and possess incomplete information, a concept known as bounded rationality. Markets frequently display “stylised facts”, which are stable statistical patterns such as heavy tails, volatility clustering, and aggregational Gaussianity. Recent studies have found that 8 out of 11 identified stylised facts persist in modern US stock markets despite significant regulatory shifts. Viewing markets as ecosystems allows for the analysis of how agents and strategies evolve and adapt continuously in response to collective outcomes rather than settling into static equilibrium.

Market insights for investors and investment professionals

A complex systems lens provides unique insights into investor behaviour, such as herding, where groups of agents act in unison without central control. This can create positive feedback loops, leading to self-reinforcing price movements and asset bubbles. Additionally, network effects influence asset pricing; for instance, the rise of index-based products has strengthened links between previously uncorrelated assets. Interconnectedness can also transmit financial distress if institutions share common asset holdings, where the liquidation of an asset by one entity impacts the price for others. Understanding these effects is crucial for anticipating regime shifts, which are qualitative changes in system behaviour induced by small parameter adjustments.

Complex systemic risk

Systemic risk refers to disruptions that impair parts of the financial system, potentially causing serious negative consequences for the real economy. Traditional market-based measures, such as conditional value at risk (CoVaR) and marginal expected shortfall (MES), often inadequately capture the full complexities of systemic risk, including asymptotic tail dependence. Contagion, which occurs when instability spreads across the system, is often more complex than a simple domino effect. Real financial networks exhibit self-organisation and adaptation, meaning the system can become fragile even if individual components appear stable. Macroprudential regulation seeks to address these vulnerabilities by assessing the structural integrity of the system as a whole.

Systemic risk vs. systematic risk

Systemic risk focuses on the structural integrity and potential collapse of the system, whereas systematic risk refers to broad market risk that cannot be diversified away, such as interest rate fluctuations. While distinct, they are related; a systemic event like a banking panic can trigger the realisation of systematic risk. Some asset owners, termed “beta activists”, now manage systemic risks as systematic risks. They believe that by using a systems-based lens to influence market conditions through stewardship, impact investing, or engagement on regulatory policies, they can enhance long-term value creation and build market-wide resilience into capital markets.

How to model complex financial systems

The transition to systems thinking requires new modelling techniques that go beyond linear calculus and normal distributions. Traditional models like the Capital Asset Pricing Model (CAPM) and Black-Scholes provide insights but rely on simplifying assumptions, such as representative agents, that make it difficult to simulate crises or adaptive behaviour. Modern approaches leverage big data and computing power to map system dynamics explicitly. Two primary methods have emerged: agent-based modelling, which simulates individual interactions among heterogeneous agents, and network theory, which maps structural interconnections and potential contagion channels to identify key leverage points.

Agent-based models to capture complex dynamics

Agent-based models (ABMs) are computational simulations of autonomous agents, such as investors or banks, following specific decision rules. They are particularly suited for capturing emergent phenomena like herding and volatility clustering. For example, the International Monetary Fund’s ABBA model simulates interactions between savers, loans, and banks to analyse systemic risks. While ABMs require significant computational power and are sensitive to initial assumptions, they allow regulators to conduct dynamic stress tests and “what-if” scenario simulations. These models reveal how policy changes, such as tightening capital requirements, might paradoxically increase short-term systemic risk while improving long-term resilience.

Network theory and graph models to capture system structure

Network theory uses mathematical graphs consisting of nodes and links to represent relationships such as interbank lending, payment flows, or asset correlations. Centrality metrics, including closeness and eigenvector centrality, identify critical hubs that may be “too central to fail”. These models help identify hidden vulnerabilities and map how shocks might propagate through a web of endogenous exposures. Although connections are dynamic and some parameters must be inferred, network analysis offers a systematic method for evaluating the architecture of financial systems. It provides valuable signals for risk management that complement traditional exogenous stress tests.

Case study: Network asset allocation

A case study involving European 10-year sovereign bond data from 2024 demonstrates how network theory can be applied to portfolio construction. Using a spanning tree methodology, researchers identified key correlations and used network topology to inform constraints in a minimum-variance optimisation. The analysis revealed that countries like Austria, Finland, and the Netherlands are interconnected due to low fiscal debts, while Spain and Italy are linked by high debt-to-GDP ratios. By applying upper-bound constraints to central assets identified via eigenvector centrality—specifically Finland, the Netherlands, and Portugal—the model aims to reduce total portfolio risk and address potential overfitting issues inherent in traditional historical data analysis.

Conclusion

Transitioning to a complex systems framework represents a foundational shift in how capital markets are understood. Integrating agent-based modelling and network analysis allows practitioners to navigate uncertainty, model contagion pathways, and identify structural vulnerabilities more effectively. This paradigmatic shift has significant implications for portfolio construction, risk management, and regulatory oversight. By acknowledging the dynamic and interconnected nature of contemporary financial systems, professionals and policymakers can contribute to the development of more resilient and adaptive global markets that are better equipped to handle structural transformations.