A New Wavelet-based Ultra-High-Frequency Analysis of Triangular Currency Arbitrage

We develop a new framework to characterize the dynamics of triangular (three-point) arbitrage in electronic foreign exchange markets. To examine the properties of arbitrage, we propose a wavelet-based regression approach that is robust to estimation errors, measurement bias and persistence. Relying on this wavelet-based (denoising) inference, we consider various liquidity and market risk indicators to predict arbitrage in a unique ultra-high-frequency exchange rate data set. We find strong empirical evidence that limit order book, realized volatility and cross-correlations help forecast triangular arbitrage profits. The estimates are statistically significant and relevant for investors such that on average 80−100 arbitrage opportunities exist with a short duration (100−500 milliseconds) on a daily basis. Our analysis also reveals that triangular arbitrage opportunities are counter-cyclical at ultra-high-frequency levels: arbitrage returns tend to increase (decrease) in periods when volatility risk and correlations are relatively low (high). We show that liquidity-driven microstructure measures, however, appear to be more powerful in exploiting arbitrage profits when compared to market-driven factors