Improved risk estimation in multifractal records: Application to the value at risk in finance.

We suggest a risk estimation method for financial records that is based on the statistics of return intervals between events above/below a certain threshold Q and is particularly suited for multifractal records. The method is based on the knowledge of the probability W(Q)(t;Deltat) that within the next Deltat units of time at least one event above Q occurs, if the last event occurred t time units ago. We propose an analytical estimate of W(Q) and show explicitly that the proposed method is superior to the conventional precursory pattern recognition technique widely used in signal analysis, which requires considerable fine tuning and is difficult to implement. We also show that the estimation of the Value at Risk, which is a standard tool in finances, can be improved considerably by the method.