A very simple representation is a 2nd order polynomial which captures the slope of the price impact of a marker order, and the curve (concave,linear,convex).
p(t,q(i)) = r(t) + a*(q(i)^b)
where q(i) is the size of the market order in shares, for q(i) i 1 to 200,000 in increments of 100 shares for example.
p(t,q(i)) = marginal price in terms of percentage diff from midpoint based on market order of size q(i). p(t-1)
a and b are the parameters to be estimated from the order book and specialist quotes and forecasted into the future.
m(t) is the is the midpoint price at time t
Higher order polynomials will more accurately capture the detailed shape of the book, but could be more difficult to interpret.
Quote from TSGannGalt:
Define liquidity in terms of a formula.
