Abstract
In this paper, the existence of no arbitrage assumption over time and triangular arbitrage in a foreign exchange market is tested. Also, forecasting the exchange rates are studied. An optimal property of exchange rates returns to guarantee the no arbitrage assumption as well as for forecasting exchange rates is the martingale property. Some theoretical results under the risk neutral measure and their equivalents form in physical probability measure are given. Also, based on a real data set, it is seen that this assumption works well for forecasting purposes. Using the Doob maximal inequality, the accuracy of forecasts is surveyed. Then, a theoretical relation between beta market risks of exchange rates is surveyed. Finally, a conclusion section is also proposed.
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