Free lesson · Arbitrage

Triangular currency conversion

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A conversion triangle compares two paths back to the same currency. Currency units must cancel around the route.

Define each rate as destination currency per source currency and apply it to the balance from the preceding trade. Use executable sides, not three midpoints.

Covered FX parity extends this reasoning to domestic investment versus foreign investment with a forward hedge. Borrow/lend asymmetry, balance-sheet limits and collateral introduce a band.

Apply it in a strategy

• Audit fiat/stablecoin routes by units and account-level availability.
• Record the input timestamp, executable quantity, currency and horizon. Reconcile the result with a cash-flow or state table.
• Stress this failure condition: Transfer delays, redemption access and currency balances may prevent sequential completion.

Research deliverable

Build and explain a triangular currency conversion worksheet. Audit fiat/stablecoin routes by units and account-level availability.

Evidence boundary: Synthetic arithmetic and scenarios illustrate mechanics. They are not historical returns, a paper replication, or evidence of an executable edge. Research sources and their access limitations are recorded at the end of this module.

# Python 3.10+; standard library unless NumPy is imported below.
# Inputs and outputs use the units defined in this lesson. Synthetic teaching example.
def triangle(start,rates,fees):
    if len(rates)!=3 or len(fees)!=3 or start<0: raise ValueError("Three aligned legs required")
    value=start
    for rate,fee in zip(rates,fees):
        if rate<=0 or not 0<=fee<1: raise ValueError("Invalid conversion")
        value*=rate*(1-fee)
    return value,value-start

print(triangle(1000,[.9,160,.007],[0,0,0]))