  Although behavioral economics has demonstrated that there are many situations
where rational choice is a poor empirical model, it has so far failed to
provide quantitative models of economic problems such as price formation. We
make a step in this direction by developing empirical models that capture
behavioral regularities in trading order placement and cancellation using data
from the London Stock Exchange. For order placement we show that the
probability of placing an order at a given price is well approximated by a
Student distribution with less than two degrees of freedom, centered on the
best quoted price. This result is surprising because it implies that trading
order placement is symmetric, independent of the bid-ask spread, and the same
for buying and selling. We also develop a crude but simple cancellation model
that depends on the position of an order relative to the best price and the
imbalance between buying and selling orders in the limit order book. These
results are combined to construct a stochastic representative agent model, in
which the orders and cancellations are described in terms of conditional
probability distributions. This model is used to simulate price formation and
the results are compared to real data from the London Stock Exchange. Without
adjusting any parameters based on price data, the model produces good
predictions for the magnitude and functional form of the distribution of
returns and the bid-ask spread.
