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From debt crises to financial crashes (and back): a stock-flow consistent model for stock price bubbles
Document de travail   Open Access

From debt crises to financial crashes (and back): a stock-flow consistent model for stock price bubbles

Matheus R. Grasselli et Adrien Nguyen-Huu
07/03/2026

Résumé

Stock-flow consistency Financial instability Credit dynamics Endogenous crash risk Jump--diffusion Asset price bubbles 91B55, 60H10, 60G44, 34D20, 37N40 C - Mathematical and Quantitative Methods/C.C6 - Mathematical Methods • Programming Models • Mathematical and Simulation Modeling/C.C6.C63 - Computational Techniques • Simulation Modeling G - Financial Economics/G.G1 - General Financial Markets/G.G1.G17 - Financial Forecasting and Simulation
We develop a stochastic macro-financial model in continuous time by integrating two specifications of the Keen economic framework with a financial market driven by a jump-diffusion process. The economic block of the model combines monetary debt-deflation mechanisms with Ponzi-type financial destabilization and is influenced by the financial market through a stochastic interest rate that depends on asset price returns. The financial market block of the model consists of an asset with jump--diffusion price process with endogenous, state-dependent jump intensities driven by speculative credit flows. The model formalizes a feedback loop linking credit expansion, crash risk, perceived return dynamics, and bank lending spreads. Under suitable parameter restrictions, we establish global existence and non-explosion of the coupled system. Numerical experiments illustrate how variations in credit sensitivity and jump parameters generate regimes ranging from stable growth to recurrent boom--bust cycles. The framework provides a tractable setting for analyzing endogenous financial fragility within a mathematically well-posed macro--financial system.

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