On the origin of power-law tails in price fluctuations

We analyse large stock price changes of more than five standard deviations for (i) TAQ data for the year 1997 and (ii) order book data from the Island ECN for the year 2002. We argue that a large trading volume alone is not a sufficient explanation for large price changes. Instead, we find that a low density of limit orders in the order book, i.e. a small liquidity, is a necessary prerequisite for the occurrence of extreme price fluctuations. Taking into account both order flow and liquidity, large stock price fluctuations can be explained quantitatively.