The Dynamics of Discrete Bid and Ask Quotes

Abstract

This paper describes a general approach to the estimation of security price dynamics when the phenomena of interest are of the same scale or smaller than the tick size. The model views discrete bid and ask quotes as arising from three continuous random variables: the efficient price of the security, a cost of quote exposure (information and processing costs) on the bid side and a similar cost of quote exposure on the ask side. The bid quote is the efficient price less the bid cost rounded down to the next tick; the ask quote is the efficient price plus the ask cost rounded up to the next tick. To deal with situations in which the cost of quote exposure both stochastic and deterministic components and the increments of the efficient price are nonstationary, the paper employs 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 persistent intraday volatility. More importantly they establish the existence of a persistent stochastic component of quote exposure costs that is large relative to the deterministic intraday “U” component.