Currency Arbitrage

Currency arbitrage involves exploiting differences in exchange rates to make a profit with a series of currency trades. Given exchange rates, we can find sequences that start and end with the same currency while gaining value.

Java example:

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boolean findArbitrage(double[][] rates) {
  
  int n = rates.length;

  // Convert rates to graph
  double[][] graph = new double[n][n];
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      graph[i][j] = Math.log(rates[i][j]);
    }
  }

  // Check for negative weight cycle
  for (int k = 0; k < n; k++) {
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < n; j++) {
        graph[i][j] = Math.max(graph[i][j], graph[i][k] + graph[k][j]);  
      }
    }
  }

  // Arbitrage exists if graph has negative cycle
  for (int i = 0; i < n; i++) {
    if (graph[i][i] < 0) return true;
  }

  return false;
}

C++ example:

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bool findArbitrage(vector<vector<double>>& rates) {

  int n = rates.size();
  
  // rates to graph
  vector<vector<double>> graph(n, vector<double>(n));
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      graph[i][j] = log(rates[i][j]);
    }
  }

  // Bellman-Ford
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      for (int k = 0; k < n; k++) {
        graph[j][k] = max(graph[j][k], graph[j][i] + graph[i][k]);  
      }
    }
  }

  // Check for negative cycle
  for (int i = 0; i < n; i++) {
    if (graph[i][i] < 0) return true;
  }

  return false;
}

Python example:

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import math

def find_arbitrage(rates):
  
  n = len(rates)
  
  graph = [[0] * n for _ in range(n)]
  for i in range(n):
    for j in range(n):
      graph[i][j] = -math.log(rates[i][j])
      
  # Bellman-Ford   
  for k in range(n):
    for i in range(n):
      for j in range(n):
        graph[i][j] = max(graph[i][j], graph[i][k] + graph[k][j]) 
        
  for i in range(n):
    if graph[i][i] < 0:
      return True
  
  return False

Currency arbitrage takes advantage of exchange rate mismatches for profit. Useful knowledge for finance and Forex markets.

Currency arbitrage is a financial strategy where you exploit differences in currency exchange rates to make a profit. Imagine you can trade between dollars, euros, and yen. If you can buy euros with dollars, then yen with euros, and finally convert yen back to more dollars than you started with, you’ve successfully performed currency arbitrage.

Code Examples

Java

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public class CurrencyArbitrage {
  public static void main(String[] args) {
    double[][] rates = {{1, 0.5, 0.8}, {2, 1, 1.6}, {1.25, 0.625, 1}};
    if (arbitrageExists(rates)) {
      System.out.println("Arbitrage exists.");
    } else {
      System.out.println("No arbitrage opportunity.");
    }
  }

  public static boolean arbitrageExists(double[][] rates) {
    int n = rates.length;
    for (int i = 0; i < n; i++) {
      if (rates[i][i] > 1) {
        return true;
      }
    }
    return false;
  }
}

C++

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#include <iostream>
using namespace std;

bool arbitrageExists(double rates[][3], int n) {
  for (int i = 0; i < n; i++) {
    if (rates[i][i] > 1) {
      return true;
    }
  }
  return false;
}

int main() {
  double rates[3][3] = {{1, 0.5, 0.8}, {2, 1, 1.6}, {1.25, 0.625, 1}};
  if (arbitrageExists(rates, 3)) {
    cout << "Arbitrage exists.\n";
  } else {
    cout << "No arbitrage opportunity.\n";
  }
}

Python

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def arbitrage_exists(rates):
    n = len(rates)
    for i in range(n):
        if rates[i][i] > 1:
            return True
    return False

rates = [[1, 0.5, 0.8], [2, 1, 1.6], [1.25, 0.625, 1]]
if arbitrage_exists(rates):
    print("Arbitrage exists.")
else:
    print("No arbitrage opportunity.")

In all these code snippets, we simply scan the diagonal elements of the rate matrix. If any of them are greater than 1, arbitrage exists. Note that this is a simplified example and real-world scenarios may require more complex logic.