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

56
The generating processes of market quotes are given by Eqs. (3.2) and (3.3),
at ¼ mt þ w a t ¼
¼ mt þ a m at ð 1 mt 1ÞþAx;tðLÞ
0 xt þ EC
a ðat1bt1Þþ" a t
bt ¼ mt w b t ¼
¼ mt þ b m mt ð 1 bt 1ÞþBx;tðLÞ
0 xt þ EC
ð Þþ" b t :
b at 1 bt 1
(3.2)
(3.3)
In Eqs. (3.2)–(3.3), at and b t are the result of adding a time-varying stationary
premium (w t a ) and subtracting a time-varying stationary discount (wt b ), respectively,
to the efficient price. These transitory components are time-varying
because we assume they are determined by the recent history of trades and quotes.
We allow the magnitudes of these two components to differ. Therefore, a t and b t
may not be symmetrically posted about m t. 7 Moreover, we impose 0< m a