The Statistical Properties of the Maximum Drawdown in Financial Time Series

The purpose of this work is to study the statistical properties of the MDD for stochastic processes characterized by the stylized facts of real financial time series. The numerical results obtained using a Monte Carlo code are firstly validated against the analytical predictions available within the academic framework of the Brownian motion. The statistics of the maximum drawdown is then analyzed in term of both its expectation value and distribution function for processes whose increments are not independent and present non vanishing excess kurtosis and skewness. The expectations for the maximum drawdown are finally compared, along with their confidence intervals, to the events observed in the historical financial time series of different asset classes