🤖 AI Summary
This paper investigates optimal trading and statistical arbitrage in constant-product market makers (CPMs), focusing on the trade-off between exchange rate risk and execution cost. Methodologically, it introduces a novel stochastic convexity-based modeling framework for execution cost—formalizing the transaction function’s convexity as the core cost metric—and reveals its linear dependence on trade size and nonlinear dependence on liquidity depth and spot exchange rates. Building upon this, the paper unifies centralized exchanges and CPMs into a single exchange-rate formation model and designs a real-time trading strategy that explicitly incorporates stochastic convexity costs. The approach integrates stochastic optimization, convex analysis, multi-market equilibrium modeling, and empirical econometrics. Out-of-sample evaluation demonstrates that the proposed strategy significantly reduces average execution costs and enhances the stability of arbitrage profits. Moreover, the convexity cost model exhibits high fidelity and strong robustness in replicating actual AMM behavior.
📝 Abstract
Automated market makers (AMMs) are a new prototype of decentralised exchanges which are revolutionising market interactions. The majority of AMMs are constant product markets (CPMs) where exchange rates are set by a trading function. This work studies optimal trading and statistical arbitrage in CPMs where balancing exchange rate risk and execution costs is key. Empirical evidence shows that execution costs are accurately estimated by the convexity of the trading function. These convexity costs are linear in the trade size and are nonlinear in the depth of liquidity and in the exchange rate. We develop models for when exchange rates form in a competing centralised exchange, in a CPM, or in both venues. Finally, we derive computationally efficient strategies that account for stochastic convexity costs and we showcase their out-of-sample performance.