1. Marginal Price Optimization
- Author
-
Loesch, Stefan and Richardson, Mark Bentley
- Subjects
Quantitative Finance - Mathematical Finance - Abstract
We introduce a new framework for optimal routing and arbitrage in AMM driven markets. This framework improves on the original best-practice convex optimization by restricting the search to the boundary of the optimal space. We can parameterize this boundary using a set of prices, and a potentially very high dimensional optimization problem (2 optimization variables per curve) gets reduced to a much lower dimensional root finding problem (1 optimization variable per token, regardless of the number of the curves). Our reformulation is similar to the dual problem of a reformulation of the original convex problem. We show our reformulation of the problem is equivalent to the original formulation except in the case of infinitely concentrated liquidity, where we provide a suitable approximation. Our formulation performs far better than the original one in terms of speed - we obtain an improvement of up to 200x against Clarabel, the new CVXPY default solver - and robustness, especially on levered curves., Comment: 103 pages, 25 figures, 15 tables, 34 references
- Published
- 2025