  We study the statistics of record-breaking events in daily stock prices of
366 stocks from the Standard and Poors 500 stock index. Both the record events
in the daily stock prices themselves and the records in the daily returns are
discussed. In both cases we try to describe the record statistics of the stock
data with simple theoretical models. The daily returns are compared to i.i.d.
RV's and the stock prices are modeled using a biased random walk, for which the
record statistics are known. These models agree partly with the behavior of the
stock data, but we also identify several interesting deviations. Most
importantly, the number of records in the stocks appears to be systematically
decreased in comparison with the random walk model. Considering the
autoregressive AR(1) process, we can predict the record statistics of the daily
stock prices more accurately. We also compare the stock data with simulations
of the record statistics of the more complicated GARCH(1,1) model, which, in
combination with the AR(1) model, gives the best agreement with the
observational data. To better understand our findings, we discuss the survival
and first-passage times of stock prices on certain intervals and analyze the
correlations between the individual record events. After recapitulating some
recent results for the record statistics of ensembles of N stocks, we also
present some new observations for the weekly distributions of record events.
