Application of drifted Brownian motion in dynamic pricing of constant function market makers

• Main Author: Peng, Jiajun
• Other Authors: Nicolas Privault
• Format: Final Year Project
• Language: English
• Published: Nanyang Technological University 2024
• Subjects: Mathematical Sciences; Constant function market making; Drifted Brownian motion; First-step analysis; First hitting times
• Online Access: https://hdl.handle.net/10356/175535
• Institution: Nanyang Technological University

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.