DeFi Liquidation Risk Modeling Using Geometric Brownian Motion

Paper: arXiv 2505.08100

Authors: Timofei Belenko, Georgii Vosorov

Abstract

In this paper, we propose an analytical method to compute the collateral liquidation probability in decentralized finance (DeFi) stablecoin single-collateral lending. Our approach models the collateral exchange rate as a zero-drift geometric Brownian motion, and derives the probability of it crossing the liquidation threshold. Unlike most existing methods that rely on computationally intensive simulations such as Monte Carlo, our formula provides a lightweight, exact solution. This advancement offers a more efficient alternative for risk assessment in DeFi platforms.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents significant mathematical derivation, including stochastic differential equations, Itô’s lemma, the reflection principle, and the inverse Gaussian distribution, which aligns with a high math complexity score. However, empirical validation is limited to a single histogram and Monte Carlo simulations using synthetic parameters without real-world backtesting or trading implementation, resulting in a lower empirical rigor score.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>Compute Collateral Liquidation<br>Probability in DeFi"] --> B["Key Methodology:<br>Zero-Drift Geometric Brownian Motion"]
  B --> C["Computational Process:<br>Analytical Derivation<br>vs.<br>Monte Carlo Simulation"]
  C --> D["Key Outcome:<br>Lightweight Exact Formula<br>for Liquidation Probability"]