LP
Modeling
Consider the world’s currency market. Given two currencies, say the Yen and the US Dollar, there is an exchange rate between them (currently about 119 Yen to the Dollar). It is axiomatic of a arbitrage-free market that there is no method of converting, say, a Dollar to Yens then to Euros, then Pounds, and to Dollars so that you end up with more than a dollar. How would you recognize when there is an arbitrage possibility?
These are actual trade on February 14, 2002.
|
|
Dollar |
Euro |
Pound |
Yen |
|
Dollar Euro Pound Yen |
1.1486 .7003 133.38 |
.8706 .6097 116.12 |
1.4279 1.6401 190.45 |
.00750 .00861 .00525 |
It is not obvious, but the Dollar-Pound-Yen-Dollar conversion actually makes $0.0003 per dollar converted. How would you formulate a linear program to recognize this?