Risk evaluation with enhanced covariance matrix and extreme fluctuations of stock price dynamics

Janusz Holyst

Warsaw University of Technology, Center of Excellence for Complex Systems Research, Warsaw, Poland

We propose a route for the evaluation of risk based on a transformation of the covariance matrix. The approach uses a 'potential' or 'objective' function that take into account extreme events from fat tails of prices probability distribution. This allows us to rescale data from different assets (or sources) such that each data set then has similar statistical properties in terms of their probability distributions. The method is tested using historical data from both the New York and Warsaw stock exchanges.