Arbitrage
A python tool to find arbitrage opportunities given current exchange rates. Based on the pricenomics.com coding puzzle. http://priceonomics.com/jobs/puzzle/.
Introduction
Daily trading volume in currency exchange markets often exceeds $1 trillion. Sometimes, these currency pairs drift in a way that creates arbitrage loops where you can convert through a certain sequence of currencies to return a profit in your base currency. This is referred to as an arbitrage loop. For example, you could do the following trades with $100 US and the exchange data below:
| TO | |||||
| USD | EUR | JPY | BTC | ||
| USD | - | 0.7779 | 102.4590 | 0.0083 | |
| FROM | EUR | 1.2851 | - | 131.7110 | 0.01125 |
| JPY | 0.0098 | 0.0075 | - | 0.0000811 | |
| BTC | 115.65 | 88.8499 | 12325.44 | - |
- Trade $100 to €77.79
- Trade €77.79 to .8751375 BTC
- Trade .8751375 BTC for $101.20965.
Assumptions
- Market where prices are independent of supply and demand
- Trading/Transaction costs are waived
Approach
In the graph of currency transactions we need to find a negative cycle.
=> w1w2w3.....*wn > 1 => log (w1 * w2 * w3 ... ) > log(1) => log(w1) + log(w2) + .... log(wn) > 0
=> log(w1) + log(w2) + log(w3) ... < 0(taking negative logarithms)
We can identify a negative cycle in a graph using the Bellman-Ford algorithm and the predecessor array to obtain the chain of transactions involved in the arbitrage loop
Data Source
The currency exchange rates are pulled from http://fx.priceonomics.com/v1/rates/