Application of drifted Brownian motion in dynamic pricing of constant function market makers - Peng, Jiajun (Nanyang Technological University, 2024)
This paper builds upon the price dynamics models proposed by Joseph Najnudel et al. Within this paper, we propose a reference price following geometric Brownian motion with drift μ. The Constant Function Market Makers (CFMM) price is bounded by γ·(reference price) and (1/γ)·(reference price) for some constant fee factor γ. Through the use of random walks and First-Step analyses, we derived the first hitting times of a reflecting Brownian motion with drift, as well as several numerical results including the expected value, variance, and limiting distribution of the discretized CFMM price process.