Abstract

The rapid evolution of Decentralized Finance (DeFi) has established Automated Market Makers (AMMs) as the cornerstone of decentralized liquidity, yet these protocols remain highly susceptible to market instability. This project introduces a DeFi AMM Volatility Simulator, a robust computational framework designed to model and stress-test liquidity pool dynamics under diverse market regimes. By leveraging the Constant Product Market Maker (CPMM) invariant, $x \clot y = k$, the simulator quantifies the critical relationship between token price volatility and Impermanent Loss (IL) for liquidity providers. The system utilizes stochastic processes, such as Geometric Brownian Motion (GBM), to replicate realistic price paths, allowing users to analyse how rapid fluctuations influence slippage, pool rebalancing, and overall capital efficiency. Ultimately, this simulator serves as a vital risk assessment tool, bridging the gap between theoretical algorithmic trading and practical liquidity management by providing data-driven insights into the sustainability of decentralized exchanges during periods of extreme market turbulence.