FX Triangular Visualization

Triangular analysis of exchange rate dynamics across three currencies

Visualization About

Configuration

Currency Triple

A

B

C

Date Range

From

To

Granularity

Granularity

Daily — one data point per ECB trading day.

Weekly — arithmetic mean of all trading days within each calendar week.

Monthly — arithmetic mean of all trading days within each calendar month (typically 19–23 days).

Quarterly — arithmetic mean of all trading days within each quarter (Q1 Jan–Mar, Q2 Apr–Jun, Q3 Jul–Sep, Q4 Oct–Dec).

Yearly — arithmetic mean of all trading days within each calendar year (typically 250–262 days).

Aggregated periods use period-end dates as labels. Partial periods at the start or end of the selected range are noted below the chart.

Normalization

Normalization

Corrects small deviations from the triangular no-arbitrage condition u×v×w = 1, which arise from rounding and quote timing in the ECB feed.

Each rate is divided by the geometric mean g = (u·v·w)^(1/3), distributing the correction equally across all three currencies.

Disabling shows raw log-transformed rates; deviations from zero are typically below 0.01%.

Triangular Consistency

Triangular Consistency (u × v × w)

For a currency triple (A, B, C), the three loop rates u, v, w must satisfy u×v×w = 1 by the triangular no-arbitrage condition.

Any deviation from 1.0 arises from rounding, quote timing differences or bid-ask spreads in the source data. With ECB reference rates the deviation is typically below 0.01%.

When normalization is enabled, this value is corrected to exactly 1.000000 by dividing each rate by the geometric mean g = (u·v·w)¹⁄₃.

u × v × w (should be ≈ 1.000000)

Requesting market data from ECB — this may take a moment for longer time ranges.