Resumo

MOSINO, Alejandro; SALOMON-NUNEZ, Laura Andrea  e  MORENO-OKUNO, Alejandro Tatsuo. Empirical study on the MXN / USD exchange rate: geometric Brownian motion versus gamma-variance process. EconoQuantum [online]. 2019, vol.16, n.1, pp.33-56. ISSN 2007-9869.  https://doi.org/10.18381/eq.v16i1.7160.

In this paper, we analize the behavior of the foreign exchange market in Mexico, which is characterized by frequent extreme movements caused by the information generated within the financial market, and by international macroeconomic conditions. We model this extreme movements by means of a variance-gamma process (PVG), which allows us to capture the bias and the excess of kurtosis of exchange rate returns. We conclude that, in general, the PVG adjust better the data than the geometric brownian motion (MBG) -which is based on a normal density- and allows us to estimate more precisely the Value at Risk (VaR). We also show that the fit improves with the time window used to compute the returns in the exchange market. Finally, we backtest the VaR fit by means of the Kupiec’s test.

Palavras-chave : Exchange rate; geometric brownian motion; variance-gamma process; value-at-risk; Kupiec test; C12; C13; C15; F31.