A Cubic Momentum Model of Periodic Bubbles and Crashes

Summary

The document proposes a parsimonious discrete-time simulation for endogenous bubbles and periodic crashes. It aims to represent how herd behavior and panic selling can interact, using market momentum to shape the balance between buying and selling.

A cubic momentum function encourages trend-following during bubble formation and triggers abrupt crashes when momentum passes a critical threshold. Trading frequency also rises with accumulated momentum, in a mechanism inspired by self-exciting Hawkes processes. Simulations are said to reproduce nonlinear bubble patterns, including concurrent increases in price and liquidity followed by sharp collapses. These are simulation results from a proposed model, not evidence that the mechanism predicts real market crashes; the excerpt gives no calibration, empirical validation, or parameter details.

Key ideas

• A discrete-time simulation models endogenous bubble formation and collapse.
• A cubic function of momentum governs the balance of trading directions.
• Trend-following arises during the bubble phase, while a threshold can trigger a crash.
• Trading frequency increases with accumulated momentum in a Hawkes-inspired mechanism.
• The reported support comes from simulation rather than empirical validation.

Tags

# Dynamics of Periodic Bubbles and Crashes: Modeling Market Overheating and Panic Selling via Cubic Momentum


# Dynamics of Periodic Bubbles and Crashes: Modeling Market Overheating and Panic Selling via Cubic Momentum









This paper proposes a simple and parsimonious discrete-time simulation model to describe the endogenous formation and periodic collapse of financial bubbles. While existing literature has extensively explored the statistical properties of locally explosive bubble dynamics, capturing the micro-level interplay of investor herd behavior and panic selling within a unified framework remains a challenge. Our model addresses this by introducing a cubic function of market momentum to determine the balance of trading directions. This mechanism drives both trend-following behavior during the bubble phase and sudden market crashes when the momentum exceeds a critical threshold. Furthermore, inspired by the self-exciting nature of the Hawkes process, the model endogenizes``market frenzy" by linking trading frequency directly to the accumulated momentum. Simulation results demonstrate that this minimal setup successfully replicates the complex, nonlinear dynamics of bubbles, including simultaneous surges in liquidity and price, followed by dramatic crashes.

Shown in full with attribution under the source's licence. Licence: abstract CC0

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