The Dynamics of Discrete Bid and Ask Quotes

Abstract

This analysis models discrete quotes as arising from two continuous random variables, the efficient price and a cost of quote exposure (information and processing costs). The former less the latter rounded down to the next tick yields the bid; the former plus the latter rounded up yields the ask. To deal with situations in which the cost of quote exposure possesses both stochastic and deterministic components, the paper proposes a nonlinear state-space estimation method. The method is applied to intraday quotes at fifteen-minute intervals for Alcoa (a randomly chosen Dow stock). The results confirm the existence of deterministic and stochastic components of the cost that are of roughly comparable magnitudes.