Tim Olson
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53 lines
2.9 KiB
Markdown
53 lines
2.9 KiB
Markdown
---
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description: "FX triangular arbitrage that exploits momentary mispricing across three currency pairs by executing a circular chain of exchanges to lock in a riskless profit."
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tags: [fx, arbitrage, triangular, market-microstructure]
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---
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# FX Triangular Arbitrage
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**Section**: 8.5 | **Asset Class**: FX | **Type**: Arbitrage
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## Overview
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Triangular arbitrage involves three currencies (A, B, C) and three currency pairs. If the cross-rate implied by trading A→B→C→A differs from the direct rate, a riskless profit exists. Such mispricings are extremely short-lived and require fast market data feeds and execution systems.
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## Construction / Mechanics
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Given three currencies A, B, C and their bid/ask prices, there are two chains:
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1. A → B → C → A
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2. A → C → B → A (equivalent to swapping B and C in chain 1)
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Focus on chain 1. The relevant rates are:
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- Bid(A→B): rate at which A is exchanged into B
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- Bid(B→C): rate at which B is exchanged into C
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- Ask(C→A): rate at which C is exchanged back into A (cost = 1/Ask(C→A))
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Note: Bid(B→A) = 1/Ask(B→A) and Ask(A→B) = 1/Bid(A→B).
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The overall round-trip exchange rate for chain 1 is:
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```
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R(A→B→C→A) = Bid(A→B) × Bid(B→C) × (1 / Ask(C→A)) (453)
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```
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**Profit condition:** If R(A→B→C→A) > 1, the trader profits by executing all three legs simultaneously. Starting with 1 unit of A, the trader ends with R > 1 units of A.
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## Return Profile
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The P&L per unit of A is R - 1 when R > 1. Profits are typically very small per trade (fractions of a pip) but can be accumulated at high frequency. The strategy is notionally riskless if all three legs are executed simultaneously; execution lag introduces market risk.
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## Key Parameters / Signals
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| Parameter | Description |
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|-----------|-------------|
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| R(A→B→C→A) | Round-trip rate; > 1 signals a profitable arbitrage |
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| Bid(A→B), Bid(B→C) | Bid rates for the two intermediate legs |
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| Ask(C→A) | Ask rate for the closing leg |
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| Execution speed | Critical: mispricings disappear in milliseconds |
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## Variations
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- **Multi-currency arbitrage**: extend to more than 3 currency pairs (N-currency chains); computational complexity increases but can uncover deeper mispricings.
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- **Chain 2** (A→C→B→A): identical logic with B and C swapped; both chains should be monitored simultaneously.
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## Notes
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- Opportunities are ephemeral; the strategy is effectively a latency arbitrage and is dominated by high-frequency traders with co-located infrastructure.
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- Bid-ask spreads are the primary cost; even small spreads can eliminate the theoretical profit, so only very tight markets are viable.
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- Unlike statistical arbitrage, this is a near-deterministic arbitrage: no model risk, but significant execution/technology risk.
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- Applicable to crypto exchanges where cross-exchange and cross-pair mispricings can be larger and more persistent than in professional FX markets.
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