Stock market fluctuations simulation within lowly volatile and highly volatile periods

The simulation of stock price fluctuations is analyzed. The statistical criteria application allows drawing the conclusion on the investigated models’ validity. Alongside with well-known Kolmogorov-Smirnov and Anderson-Darling criteria, comparatively new Christoffersen and Berkowitz criteria are used to assess interval predictions. Berkowitz criterion is particularly effective when used to assess extreme price leaps within highly volatile periods, since it gives good results also for a small number of observations. It is shown that the customarily used time-series models with normal distribution and with Student distribution are applicable exclusively during relatively stable periods. Under the unstable conditions at the financial markets, models by means of which it is possible to describe a high probability of great price leaps are required. The time-series model with the heavy tailed distribution is studied. The recommendations on the portfolio management under the crisis time are provided on the basis of the performed calculations.