Chaos and Synchronization in Financial Leverages Dynamics: Modeling Systemic Risk with Coupled Unimodal Maps
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914431144820736 |
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| author | Ioffredi, Marco Marmi, Stefano Tanzi, Matteo |
| author_facet | Ioffredi, Marco Marmi, Stefano Tanzi, Matteo |
| contents | Systemic financial risk refers to the simultaneous failure or destabilization of multiple financial institutions, often triggered by contagion mechanisms or common exposures to shocks. In this paper, we present a dynamical model of bank leverage (the ratio of asset holdings to equity) a quantity that both reflects and drives risk dynamics. We model how banks, constrained by Value-at-Risk (VaR) regulations, adjust their leverage in response to changes in the price of a single asset, assumed to be held in fixed proportion across banks. This leverage-targeting behavior introduces a procyclical feedback loop between asset prices and leverage. In the dynamics, this can manifest as logistic-like behavior with a rich bifurcation structure across model parameters. By analyzing these coupled dynamics in both isolated and interconnected bank models, we outline a framework for understanding how systemic risk can emerge from seemingly rational micro-level behavior. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_01505 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Chaos and Synchronization in Financial Leverages Dynamics: Modeling Systemic Risk with Coupled Unimodal Maps Ioffredi, Marco Marmi, Stefano Tanzi, Matteo Dynamical Systems Chaotic Dynamics Mathematical Finance 37N40 (Primary) 37D45, 91G80, 91G45 (Secondary) Systemic financial risk refers to the simultaneous failure or destabilization of multiple financial institutions, often triggered by contagion mechanisms or common exposures to shocks. In this paper, we present a dynamical model of bank leverage (the ratio of asset holdings to equity) a quantity that both reflects and drives risk dynamics. We model how banks, constrained by Value-at-Risk (VaR) regulations, adjust their leverage in response to changes in the price of a single asset, assumed to be held in fixed proportion across banks. This leverage-targeting behavior introduces a procyclical feedback loop between asset prices and leverage. In the dynamics, this can manifest as logistic-like behavior with a rich bifurcation structure across model parameters. By analyzing these coupled dynamics in both isolated and interconnected bank models, we outline a framework for understanding how systemic risk can emerge from seemingly rational micro-level behavior. |
| title | Chaos and Synchronization in Financial Leverages Dynamics: Modeling Systemic Risk with Coupled Unimodal Maps |
| topic | Dynamical Systems Chaotic Dynamics Mathematical Finance 37N40 (Primary) 37D45, 91G80, 91G45 (Secondary) |
| url | https://arxiv.org/abs/2601.01505 |