Estimation of Zero Intelligence Models by L1 Data

TL;DR

This paper develops and estimates zero intelligence market models, including a generalized version, using L1 data, and finds that simple models perform nearly as well as more complex variants in predicting stock prices.

Contribution

It introduces a generalized ZI model with formulas for quote distribution and price impact, and demonstrates the estimators' consistency and normality on real stock data.

Findings

Simple ZI models perform nearly as well as complex variants.

MLE estimators are consistent and asymptotically normal.

Complex models do not significantly improve prediction accuracy.

Abstract

A unit volume zero intelligence (ZI) model is defined and the distribution of its L1 process is recursively described. Further, a generalized ZI (GZI) model allowing non-unit market orders, shifts of quotes and general in-spread events is proposed and a formula for the conditional distribution of its quotes is given, together with a formula for price impact. For both the models, MLE estimators are formulated and shown to be consistent and asymptotically normal. Consequently, the estimators are applied to data of six US stocks from nine electronic markets. It is found that more complex variants of the models, despite being significant, do not give considerably better predictions than their simple versions with constant intensities.