recent developments in high frequency financial ... - Index of

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1 Introduction
A. Escribano and R. Pascual
In this paper, we propose a new econometric approach to jointly model the time
series dynamics of the trading process and the revisions of ask and bid prices. We
use this model to test the validity of certain symmetry assumptions very common
among microstructure models. Namely, we test whether ask and bid quotes respond
symmetrically to trade-related shocks, and whether buyer-initiated trades and
seller-initiated trades are equally informative. In essence, the procedure we propose
generalizes Hasbrouck’s (1991) vector autoregressive model for signed trades and
changes in the quote midpoint by relaxing the implicit symmetry assumptions in
his model.
The properties of the empirical model are derived from a structural dynamic
model for ask and bid prices. In this model, ask and bid prices share a common
lung-run component, the efficient price. The long-term value of the stock varies
due to buyer-initiated shocks, seller-initiated shocks, and trade-unrelated shocks.
The transitory components of ask and bid prices are characterized by two correlated
and trade-dependent stochastic processes, whose dynamics are allowed to differ.
The trading process is endogenous. Buyer and seller-initiated trades are generated
by two idiosyncratic but mutually dependent stochastic processes. The generating
processes of quotes and trades both depend on several exogenous variables that
feature the trades and the market conditions.
We demonstrate that the empirical counterpart of this theoretical model is an
extended vector error correction (VEC) model with four dependent variables:
changes in the ask price, changes in the bid price, buyer-initiated trades, and sellerinitiated
trades. The bid–ask spread is the error correction term. Our VEC model
reverts to the Hasbrouck’s (1991) bivariate VAR model when: (a) ask and bid
responses to trade-related shocks perfectly match; (b) the generating processes of
buyer and seller-initiated trades are equivalent, and (c) the trade sign only matters
as far as the direction of the quote adjustments is concerned.
For robustness purposes, we implement the model using three different subsamples:
the 11 most frequently traded NYSE-listed stocks in 1996 and 2000,
and the 11 most active stocks at the Spanish Stock Exchange (SSE) in 2000.
With the two NYSE subsamples, we show that our main findings are not periodspecific.
We also show that our findings are unaltered by the dramatic increase in
trading activity and the progressive decrease in the minimum price variation
experienced by the NYSE from 1996 to 2000. With the Spanish data, we show
that our findings are not limited to the particular microstructure of the NYSE. We
perform additional robustness test considering alternative specifications of the
empirical model.
We find two main patterns characterizing the dynamics of market quotes. On
the one hand, ask and bid quotes do not respond symmetrically after trade-related
shocks. They tend to be revised in the same direction, but not by the same amount.
We show, however, that the likelihood of observing a symmetric response increases
with volatility. On the other hand, ask and bid prices error-correct after a trade,
which causes the spread to revert towards the minimum. The speed of reversion is
significantly non-linear. The wider the bid–ask spread, the quicker the response of
ask and bid quotes. These patterns result in two simultaneous but opposite effects
on the price dynamics: information-induced positive cross-serial correlation and
liquidity-induced negative cross-serial correlation.