What is Arbitrage? The Pursuit of Risk-Free Profit

Arbitrage is the simultaneous purchase and sale of an asset to profit from a difference in the price. Discover the math of triangular and spatial arbitrage.

Optimizing a triangular arbitrage bot in C++ for 16 hours made one thing clear: being 2 milliseconds too slow means you can't compete with institutional FPGAs. Arbitrage in its purest form is the simultaneous purchase and sale of the same asset in different markets to profit from tiny discrepancies in price.

The classic example is buying gold on the London exchange at $1,800/oz while simultaneously selling it on the New York exchange at $1,805/oz, locking in a risk-free profit of $5/oz (minus transaction costs). In reality, true arbitrage opportunities are fleeting and often require sophisticated technology to exploit.

As markets become more efficient, 'pure' arbitrage is increasingly rare. Quants now look for complex relationships between different instruments.

1. Triangular Arbitrage: Exploiting discrepancies between three different currencies (e.g., USD/EUR, EUR/GBP, and GBP/USD). If the cross-rate is misaligned, a circular trade yields profit. 2. Spatial Arbitrage: Buying an asset in one geographic location and selling it in another. This is common in commodities and energy markets. 3. Convertible Arbitrage: Buying a convertible bond and shorting the underlying stock to capture the mispricing of the embedded option. This involves understanding option greeks like gamma and theta.

To detect an arbitrage opportunity in FX, the product of the three exchange rates must deviate from 1 (ignoring spreads).