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

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An important determinant of liquidity is the inside spread between the best ask and
bid price. The bid-ask spread determines the cost of crossing the market and thus
the cost of utilizing market orders. Cohen et al. (1981) show that the existence of a
bid-ask spread is a result of the “gravitational pull” of a limit order and is an
equilibrium property of the market. Handa et al. (2003) demonstrate that the size of
the spread increases with the degree of adverse selection and the difference in
valuation between low and high valuation investors. However, while these studies
focus on the existence and properties of the spread, Foucault’s model provides
testable implications regarding the impact of the spread on the aggressiveness in
market trading and limit order trading, and this is formulated as Hypothesis (4):
(4)The higher the bid-ask spread, the lower the aggressiveness in market trading
and the higher the aggressiveness in limit order trading.
These formulated hypotheses underpin the rationale for the construction of
appropriate explanatory variables in Sect. 5.
3 The econometric approach
A. D. Hall, N. Hautsch
The arrival of aggressive market orders, limit orders and cancellations is modelled
as a multivariate (financial) point process. The econometric literature on the
modelling of financial point processes was originated by the seminal paper by
Engle and Russell (1998) who introduced the class of autoregressive conditional
duration (ACD) models. While this model was successfully applied to univariate
duration processes, 5 it is not easily extended to a multivariate framework. The
reason is that in a multivariate context the individual processes occur
asynchronously, which is difficult to address in a discrete time duration model.
A natural way to model multivariate point processes is to specify the
(multivariate) intensity function leading to a continuous-time framework. In this
paper, we apply a six-dimensional version of the autoregressive conditional
intensity (ACI) model proposed by Russell (1999). 6 Following the notation of Hall
k
and Hautsch (2004), let t denote the calendar time and define ti , k =1, ..., K, as the
arrival times of a K-dimensional point process. Let N kðÞ¼ t
P
i 1 1 tk f i tg
and
M kðÞ¼ t
P
i 1 1 tk i