DeFi Liquidation Risk Modeling Using the Reflection Principle for Zero-Drift Brownian Motion

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, converts it into a regular zero-drift Brownian motion, and employs the reflection principle to derive the liquidation probability. 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.