  In order to investigate the origin of large price fluctuations, we analyze
stock price changes of ten frequently traded NASDAQ stocks in the year 2002.
Though the influence of the trading frequency on the aggregate return in a
certain time interval is important, it cannot alone explain the heavy tailed
distribution of stock price changes. For this reason, we analyze intervals with
a fixed number of trades in order to eliminate the influence of the trading
frequency and investigate the relevance of other factors for the aggregate
return. We show that in tick time the price follows a discrete diffusion
process with a variable step width while the difference between the number of
steps in positive and negative direction in an interval is Gaussian
distributed. The step width is given by the return due to a single trade and is
long-term correlated in tick time. Hence, its mean value can well characterize
an interval of many trades and turns out to be an important determinant for
large aggregate returns. We also present a statistical model reproducing the
cumulative distribution of aggregate returns. For an accurate agreement with
the empirical distribution, we also take into account asymmetries of the step
widths in different directions together with crosscorrelations between these
asymmetries and the mean step width as well as the signs of the steps.
