Detection of Arbitrage Opportunities and Forecasting in the Foreign Exchange Markets
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.
Habibi, R. (2020). Detection of Arbitrage Opportunities and Forecasting in the Foreign Exchange Markets. Journal of Applied Economic Sciences, Volume XV, Winter, 4(70), 855-859. https://doi.org/10.57017/jaes.v15.4(70).12
[1] Bjork, T. 2009. Arbitrage Theory in Continuous Time. 3rd Edition. Oxford University Press.
[2] Calin, O. 2012. An Introduction to Stochastic Calculus with Applications to Finance. Ebook.
[3] Chauvin, B. 1991. Product martingales and stopping lines for branching Brownian motion. The Annals of Probability 19, 1195-1205.
[4] Cherny, A.S. 2011. Some Particular Problems Od Martingale Theory. Technical Reports. On the occasion of 70th birthday of A.N. Shiryaev. Moscow State University. Russia.
[5] Hao, H. 2014. The Exchange Rate Effect of Multi-Currency Risk Arbitrage. Technical Reports. Swiss Finance Institute. Swiss.
[6] Ma, M. 2008. Identifying Foreign Exchange Arbitrage Opportunities Through Matrix Approach. Technical Reports. School of Management and Economics. Beijing Institute of Technology. China.
[7] Saaty, T.L. 1980. The Analytic Hierarchy Process. McGraw Hill, New York.
[8] Tian, L. 2011. Combining Martingales, Stochastic Integrals, and Applications Tolog-Rank Test and Cox's Model. Lecture Notes of Course STAT331. Stanford University. USA.