Optimal Trading and Statistical Arbitrage in Constant Product AMMs

Summary

This work studies execution and statistical arbitrage in constant product markets, a common automated market maker design used by decentralised exchanges. In these markets, a trading function determines exchange rates. The analysis treats exchange-rate exposure and execution cost as linked considerations and examines how costs relate to the curvature, or convexity, of that function.

The empirical evidence indicates that convexity can estimate execution costs: the costs scale linearly with trade size and nonlinearly with liquidity depth and exchange rate. The work also models settings where exchange rates are determined by a competing centralized venue, by the constant product market, or by both. It derives computationally efficient strategies that account for stochastic convexity costs and reports out-of-sample performance. The description provides no specific assets, evaluation period, or performance measures, so the findings offer limited basis for judging transfer to other pools or market conditions.

Key ideas

• Constant product AMMs set exchange rates through a trading function whose convexity affects execution costs.
• The reported convexity costs scale linearly with trade size and nonlinearly with liquidity depth and exchange rate.
• The models consider price formation in an AMM, a competing centralized exchange, or both venues.
• The proposed trading strategies account for stochastic convexity costs and are computationally efficient.
• Out-of-sample performance is reported, but the supplied description omits specific markets and evaluation details.

Tags

# Decentralised Finance and Automated Market Making: Execution and Speculation


# Decentralised Finance and Automated Market Making: Execution and Speculation









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.

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