Liquidity Jump, Liquidity Diffusion, and Crypto Wash Trading

We develop a new framework to detect wash trading in crypto assets through real-time liquidity fluctuation. We propose that short-term price jumps in crypto assets results from wash trading-induced liquidity fluctuation, and construct two complementary liquidity measures, liquidity jump (size of fluctuation) and liquidity diffusion (volatility of fluctuation), to capture the behavioral signature of wash trading. Using US stocks as a benchmark, we demonstrate that joint elevation in both liquidity metrics indicates wash trading in crypto assets. A simulated regulatory treatment that removes likely wash trades confirms this dynamic: it reduces liquidity diffusion significantly while leaving liquidity jump largely unaffected. These findings align with a theoretical model in which manipulative traders amplify both the level and variance of price pressure, whereas passive investors affect only the level. Our model offers practical tools for investors to assess market quality and for regulators to monitor manipulation risk on crypto exchanges without oversight.