Mixtures of Laws: a New Method to Estimate the Parameters

The main aim of this paper is to examine the qualities of the mixed diffusion-jump process whose parameters are random variables. The hypothesis of a Wiener geometric process applied to exchange rate has become doubtful at the beginning of the nineties, fact determined by a high leptokurtosis of the empirical distributions. The alternative of another distribution was studied in several articles. The mathematical model proposed in this paper has as fundamental hypothesis the fact that the distribution of the continuous part of the variations in the logarithms of exchange rate is a mixture of two normal laws, whose parameters are random variables. In the final section we present the main results obtained by using the model developed in the second section and the method presented in the third section. The parameters of the model were estimated from the daily quotations of the exchange rates of the EURO over the period from 01.01.2001 till 19.09.2002.