Abstract

CLIMENT HERNANDEZ, José Antonio; HOYOS REYES, Luis Fernando  and  RODRIGUEZ BENAVIDES, Domingo. The α-stable processes and their relationship with the exponent of self-similarity: Exchange rates of USA Dollar, Canadian Dollar, Euro and Yen. Contad. Adm [online]. 2017, vol.62, n.spe5, pp.1479-1500. ISSN 0186-1042.  https://doi.org/10.1016/j.cya.2017.09.003.

This research work analyzes the yields of the exchange rate parities of the American dollar, Canadian dollar, Euro, and Yen; estimates the basic statistics and the α-stables; carries out the Kolmogorov-Smirnov, Anderson-Darling, and Lilliefors goodness of fit tests; estimates the self-similar exponents and carries out the t and F tests, ruling out that the series of parities are multifractal. It also estimates the confidence intervals of the exchange rate parities and concludes that the estimated α-stable distributions are more efficient than the Gaussian distribution to quantify the risks of the market, and that the series are self-similar. Through the ℵ index, we can infer the risk of the events, indicating that the parities are anti-persistent and thus have short-term memory, mean reversion, and a negative correlation with the high risk in the short and medium term. The estimation and validation of the α-stable distributions and the self-similar exponent are important in the evaluation and creation of innovative investment instruments through financial engineering, risk administration, and the evaluation of derived products.

Keywords : α-Stable processes; Self-similar exponent; Financial engineering; C16; C46; C14; D81; G12; G13.

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