Los procesos α-estables y su relación con el exponente de autosimilitud: paridades de los tipos de cambio dólar estadounidense, dólar canadiense, euro y yen

In this research we analyze the performance of the exchange rates of USA Dollar, Canadian Dollar, Euro and Yen; we estimate the basic statistics, α-stable parameters, we performed tests of goodness fit Kolmogorov-Smirnov, Anderson-Darling and Lilliefors; we estimate self-similarity exponents and we performed t y F tests, ruling that the series of the exchange rates are multi-fractal; we estimate confidence intervals of the exchange rates and we conclude that the estimated α-stable distributions are more efficient than the gaussian distribution to quantify market risks and the series are self-similar; by the ℵ index we infer the risk of events and we indicate that exchange rates are anti-persistent, have mean reversión, short-term memory, negative correlation and high risk in the short and medium term; the estimation and validation of α-stable distributions and the exponent of self-similarity are important for pricing and the creation of innovative investment instruments by financial engineering, risk management and derivatives pricing.