How to use the cross-exchange arbitrage calculator
- Choose how the trade settles. Buy, transfer, then sell means you buy on exchange A, move the asset to exchange B and sell it there. Pre-funded on both exchanges means you already hold cash on A and the asset on B, so both legs execute at once.
- Enter the buy price on A and the sell price on B. Use the ask on A and the bid on B, not the last trade price: those are the prices you can actually deal at.
- Enter the quantity, the taker fee on each exchange and the slippage per side. Arbitrage orders usually take liquidity, so use taker fees. Slippage grows with size relative to the order book.
- Enter the transfer costs. In transfer mode, the withdrawal fee and any network or wire charge, the transfer time and the asset’s annual volatility. In pre-funded mode, the cost of a rebalancing transfer and how many trades it covers.
The formulas
Net = Gross − Q × PA × fA − Q × PB × fB − Q × (PA + PB) × s − TQ is the quantity, PA the buy price, PB the sell price, fA and fB the taker fees, s the slippage per side and T the transfer cost (the full fee, or the rebalancing fee divided by the trades it covers).
Break-even spread = Break-even PB ÷ PA − 1
Chance of a loss = Φ(−Net ÷ 1σ move)σ is the annual volatility, t the transfer time in minutes and 525,600 the minutes in a year of round-the-clock trading. Φ is the standard normal distribution function; the price change in transit is assumed normal with no drift.
A worked example
An asset is offered at $2,500 on exchange A and bid at $2,515 on exchange B, a gap of 0.60%. Buying 10 units costs $25,000 and the gap is worth a gross $150.00.
Taker fees take $50.15, slippage $25.08 and the transfer $5.00. The net profit is $69.77, 0.28% of the purchase. The trade breaks even at a spread of 0.32%, a sell price of $2,508.01.
The asset then spends 30 minutes in transit. With 60% annual volatility, a one-standard-deviation move over that time is 0.45% of the price, or $113.83 on the position: larger than the profit. The model puts the chance of ending with a loss at 27.0%.
Transfer or pre-fund: where the risk goes
The two settlement styles trade the same gap but carry different risks:
| Buy, transfer, sell | Pre-funded | |
|---|---|---|
| Net profit | $69.77 | $74.27 |
| Break-even spread | 0.32% | 0.30% |
| Capital tied up | $25,000 | $50,150 |
| Price risk in transit | $113.83 (1σ) | None at trade time |
In transfer mode the “arbitrage” is really a short-term directional position: you own the asset until you can sell it, and the gap that prompted the trade can close, or reverse, before you get there. The profit is fixed by fees; the risk is set by volatility and time. Cutting the transfer time to 5 minutes shrinks the 1σ move to $46.47 and the chance of a loss to 6.7%; stretching it to 120 minutes raises them to $227.67 and 38.0%. In a calmer asset with 20% volatility, the same 30-minute transfer carries a 1σ move of $37.94.
Pre-funding removes that exposure because both legs execute within seconds. It costs roughly twice the capital, and the return on that capital is only 0.15% per trade here. The inventory also drifts toward one side as you keep buying on A and selling on B, so it has to be moved back periodically, which the rebalancing fee covers.
How the spread changes the answer
Costs are almost fixed while the gross profit grows with the gap, so small spreads lose money and the payoff rises quickly once you pass break-even. At a 0.20% gap the example nets -$30.08, a loss; at 1.60% it nets $319.40. The table under the calculator runs the same comparison from zero to 2%.
Before acting on a gap, check that both quotes are live and deep enough for your size, that withdrawals and deposits are open on both venues, and that any transfer limits allow the amount. A gap that persists while everything else looks normal often means one of those conditions is not met.
What this calculator does not include
- Order book depth. Slippage is a flat percentage; large orders move prices more than proportionally.
- Counterparty and operational risk. An exchange can delay or suspend withdrawals, and funds held on a venue are exposed to its solvency.
- Currency conversion. Both prices are assumed to be in the same currency.
- Taxes. Each leg can be a taxable disposal, depending on the asset and where you live.
- Drift and fat tails. Price risk in transit uses a normal distribution with no drift, and volatility in a 24/7 market. For assets that trade only part of the day, scale volatility to trading time instead.