The Meixner process for financial data

The most famous Black-Scholes model is based on the assumption that the log-returns of financial data follow a normal distribution. Several studies performed show empirical evidence against such normality since the log-returns of most financial data show a significant leptokurtosis. The Meixner distribution is an infinitely divisible distribution and therefore a Lévy process can be associated with it, which is called the Meixner process. The Meixner process because of its simple and extreme flexible structure was proposed as a model for representing efficiently the empirical distributions of the log-returns of financial data. In this paper we studied the dynamics of the USD/EuR exchange rates. After testing that the normal distribution provides a poor fit to the log-returns of the exchange rates, we applied the Meixner model fitting its underlying distribution to the data. performing a number of statistical tests we showed that the Meixner distribution provides an almost perfect fit to the data.