Applications and Limitations of Stochastic Processes in Dealing with Fat-Tailed Return Distributions

This paper deals with the main theoretical problems regarding the application of stochastic processes to leptokurtic financial return distributions. A sort of statistical tests based on the stock index Banamex 30 is performed in order to choose the stochastic model that provide the best fit to the fat-tailed empirical distribution, allowing for a better return forecasting or value at risk estimate. In choosing that model the paper points out that any single set of stastistical criteria is not appropriate if it is not confronted with the risk manager's experience. Understanding the investor's aversion risk or the transaction costs involved in any trading strategy, among other elements, is very important to justify the use of any stochastic process in risk management techniques