  Order submission and cancellation are two constituent actions of stock
trading behaviors in order-driven markets. Order submission dynamics has been
extensively studied for different markets, while order cancellation dynamics is
less understood. There are two positions associated with a cancellation, that
is, the price level in the limit-order book (LOB) and the position in the queue
at each price level. We study the profiles of these two order cancellation
positions through rebuilding the limit-order book using the order flow data of
23 liquid stocks traded on the Shenzhen Stock Exchange in the year 2003. We
find that the profiles of relative price levels where cancellations occur obey
a log-normal distribution. After normalizing the relative price level by
removing the factor of order numbers stored at the price level, we find that
the profiles exhibit a power-law scaling behavior on the right tails for both
buy and sell orders. When focusing on the order cancellation positions in the
queue at each price level, we find that the profiles increase rapidly in the
front of the queue, and then fluctuate around a constant value till the end of
the queue. These profiles are similar for different stocks. In addition, the
profiles of cancellation positions can be fitted by an exponent function for
both buy and sell orders. These two kinds of cancellation profiles seem
universal for different stocks investigated and exhibit minor asymmetry between
buy and sell orders. Our empirical findings shed new light on the order
cancellation dynamics and pose constraints on the construction of order-driven
stock market models.
