On Triangular Arbitrage in the Currency Market, Yeomin Yoon, Youngna Choi, ?, 2004
Abstract
Typical international finance textbooks explain the triangular arbitrage process via
numerical examples, using a single quote per bank, i.e., assuming no bid and asked
spread or no transaction cost. In the real world, however, banks always use bid and
asked prices when they announce their currency quotations and this makes the
explanation or derivation of the arbitrage conditions rather complicated. This paper
provides a rigorous but simple derivation of triangular arbitrage conditions based on bid
and asked prices.
Introduction
Most Triangular arbitrage examples in finance textbooks
- quoted by one bank
- no bid ask spread
- no transaction cost
In real world
- interbank market
- bid ask spread exist
ARBITRAGE CONDITION WITH NO TRANSACTION COST
Case #1
Step 1: At Bank C, sell $1 and buy €1.0810.
Step 2: At Bank B, sell €1.0810 and buy £0.6006 x 1.0810.
Step 3: At Bank A, sell £0.6006 x 1.0810 and buy $1.5422 x 0.6006 x 1.0810 = $1.001271.
Case #2
Step 1: At Bank A, sell $1 and buy £ 1/1.5402
Step 2: At Bank B, sell £ 1/1.5402 and buy €1/1.5402 * 1/0.5885
Step 3: At Bank C, sell € 1/1.5402* 1/0.5885 and buy $1/1.5402 * 1/ 0.5885 * 1/1.0806 = $1/0.97946416
= $1.020966
3 Steps for Triangular Arbitrage with no bid ask spread
Step 1: At Bank C, sell $1 and buy €C
Step 2: At Bank B, sell €C and buy £BC
Step 3: At Bank A, sell £BC and buy $ABC
Alternatively
Step 1: At Bank A, sell $1 and buy £1/A
Step 2: At Bank B, sell £ 1/A and buy €1/(AB)
Step 3: At Bank C, sell € 1/(AB) and buy $ 1/(ABC)
profitable as long as $1/(ABC) > $1, or ABC < 1
ARBITRAGE CONDITIONS BASED ON BID AND ASKED PRICES: A REAL WORLD CASE
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