Strategy #0000000042 · FX and market microstructure
FX triangular arbitrage
Align quote conventions, compare currency-conversion paths and include all three legs.
Triangular arbitrage compares a direct FX rate with the cross rate implied by two other quotes. EUR/USD and USD/JPY imply EUR/JPY through multiplication. An executable cycle needs the correct bid/ask for each leg, synchronised timestamps and consistent notionals; a mid-price residual is not risk-free profit.
A cross-rate discrepancy may be fleeting; synchronisation, bid/ask and latency determine execution.
Three ways in
Understand the story. Then inspect the risk.
Start with a familiar situation, check the payoff, then test how the numbers change.
The idea · in two minutes
Does a cross-rate discrepancy survive three-leg bid/ask and execution costs?
Jack multiplies EUR/USD 1.08 by USD/JPY 150 to get 162.00; a direct quote of 162.20 appears about 12 bp away.
Rose notes that three mid quotes do not establish arbitrage. Each leg crosses a different bid/ask and quotes may not be simultaneous.
The simulator calculates only the directional residual and subtracts assumed costs. A real check needs cash amounts, depth, latency and fees for the full currency cycle.
- Implied EUR/JPYCalculate implied EUR/JPY, compare the direct quote and subtract assumed costs in bp.
- Assumed direct quoteMid-price arithmetic only; excludes bid/ask, fill sequence, quote latency and partial fills.
- Residual less assumed three-leg costIllustrative expiry outcome.
Illustrative research examples only. They are not live signals or a recommendation.
The mechanics · payoff and exposure
S_{EUR/JPY}^{implied}=S_{EUR/USD}S_{USD/JPY},\quad epsilon_{bp}=10000(S_{direct}/S_{implied}-1)
Quotes mean units of quote currency per base currency; EUR/USD × USD/JPY = EUR/JPY. Residual is in bp and is not converted to currency P&L.
Greeks: the directional intuition
- 報價方向
- Measures sensitivity to implied volatility.
- 同步與延遲
- Measures sensitivity to implied volatility.
- Bid/ask
- Measures sensitivity to implied volatility.
S_{EUR/JPY}^{implied}=S_{EUR/USD}S_{USD/JPY},\quad epsilon_{bp}=10000(S_{direct}/S_{implied}-1)
Practical context · published observations
FX triangular arbitrage: read the record with its caveats.
The chart uses the published figures or explicitly labelled study inputs below. A historical index or model replay is not the same as an investor’s realised account return.
只用 mid-price 算術，不模擬 bid/ask、成交順序、報價延遲或部分成交。 Source ↗ · Methodology ↗
Change assumptions and inspect the scenario
Inputs illustrate the strategy mechanics; they are not live quotes, forecasts or investment advice.
Variants · same family, different risk levers
Related methods change their signal or exposure.
Each entry states the mechanism and trade-off.
| Related strategy | Relationship | What changes | New cost or risk |
|---|---|---|---|
| Spot FX triangle | Three spot legs | Convert three currencies and return to the start. | Bid/ask, latency and credit-line risk. |
| Cross-venue triangle | Different venues | Compare direct and implied cross rates across venues. | Venue latency, fees and settlement. |
| Statistical triangular relative value | Residual model | Models persistence and reversion of cross-rate deviations. | A signal is not risk-free arbitrage. |
Mid-price arithmetic only; excludes bid/ask, fill sequence, quote latency and partial fills.
Read beyond the summary
References
Primary sources and research used to describe the strategy and its limits.