Sizing Multi-Leg Arbitrage Trades for Slippage and Liquidity

Summary

The document poses an optimization problem for arbitrage across multiple products. Given current order book prices and liquidity, a trader wants to choose trade quantity that maximizes profit after accounting for slippage. A three-product cycle illustrates the problem: one book update may create an opportunity, and the optimal quantity depends on executable liquidity along the route.

The post does not present a solution or evidence from a model. It notes that sizing a single fixed path can be handled with algebra, then asks how to extend that calculation when many assets allow numerous possible paths. Its practical contribution is to frame the need for a method that combines path selection with quantity optimization using live book data. It leaves important details open, including fees, execution risk, changing liquidity, and how candidate paths should be searched or constrained.

Key ideas

• Optimal arbitrage quantity depends on prices and available liquidity across every leg of the route.
• Slippage makes the profit-maximizing size different from the maximum executable size.
• A fixed arbitrage path may admit a direct sizing calculation, while many possible paths create a broader optimization problem.
• The document asks for a general method but does not provide or evaluate one.

Tags

# Arbitrage optimal size model that accounts for slippage given a specific path?


# Arbitrage optimal size model that accounts for slippage given a specific path?












I'm interested in any model that helps calculating the optimal size to maximize PnL given the liquidity of an asset (or the slippage that I would incurr per unit of asset traded).

For instance, let's say that I'm arbing between 3 products A, B and C. At time T I know the liquidity and prices (order book) of the 3 of them, but there are no opportunities. At time T+1, an update on the order book of C comes in. Is there any model that serves as a plug-and-play formula where I'd just put the updated data from C and get the quantity that would maximize the PnL in this triangle?

Of course for 1 specific path sounds easy as it's just basic algebra to calculate this optimal size, but how to do it when you have 100 assets and the path on T+1 could be any combination?

If you know of any similar models but are not sure if it would help here, please share it anyway!

Thanks!

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