Evaluating Arbitrage After Variable and Fixed Trading Fees
Summary
The document explains how to assess an arbitrage across venues with different percentage-based and fixed transaction fees. Its suggested method is to adjust each venue’s bid and offer prices for the variable fee, evaluate the resulting arbitrage as usual, then subtract the fixed fees for the venues used. This accounts for the fact that fixed charges affect profitability per transaction rather than per unit traded.
The answer gives a numerical illustration of how a percentage fee changes effective bid and offer prices. It also distinguishes fixed fees charged per transaction from fees charged per unit volume: the latter can be incorporated into adjusted prices in the same way as variable fees. The discussion is brief and does not provide a general optimization algorithm, a proof of optimality, or a treatment of order size, market impact, and execution constraints. Its guidance is therefore a way to evaluate candidate arbitrages, not a complete method for choosing the best sequence of orders.
Key ideas
- Adjust each venue’s bid and offer for its percentage fee before comparing prices.
- Subtract fixed per-transaction fees from the profit of an arbitrage using those venues.
- A fee charged per unit volume can be incorporated into adjusted prices.
- The method describes profitability accounting, not a complete order-sequencing algorithm.
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Full text
# Calculating most profitable arbitrage orders on multiple market with fixed and variable fees # Calculating most profitable arbitrage orders on multiple market with fixed and variable fees If I have multiple markets (let's say 5, but the solution should be generic) trading the same stock/commodity/whatever, and the markets differ in both variable fees (which are in % of the trade order) and fix fees (which are in absolute number of $ per trade order), and suppose there exists an arbitrage opportunity on more than 2 markets at the same time, how do you calculate the absolutely most profitable sequence of market orders? (order of orders matters) The variable fees are not a problem, but the fix fees complicate the whole algorithm tremendously. Is this a traveling salesman type of problem? Or, is there any paper which deals with this problem. The fees might be something like this (shown as an example): - 1st market: $5 + 1 % - 2nd market: $4 + 2 % - 3rd market: $0 + 5 % - 4th market: $10 + 0 % - 5th market: $3 + 3 % ## Answer by Jason Nordwick (score 1) https://quant.stackexchange.com/a/16184 Why can't you just adjust your book prices by the variable price and then subtract the fixed price off the PNL when calculating that up? For exchange, with a 2% variable fee, a book 98 bid 100, resting offer at $100 would go up too $102 and bid go down to $96.04. Note evaluate your arbs like you normally would and subtract off the fixed fees from the corresponding venues. This assumes the fixed fee is per transaction. If the fixed fee is per unit volume, then you can augment the book like the variable fees instead.
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.