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Estimation of zero-intelligence models by L1 data

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  • Martin Šmíd

Abstract

A unit volume zero-intelligence (ZI) model is defined and the distribution of its L1 process is recursively described. Further, a generalized ZI 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.

Suggested Citation

  • Martin Šmíd, 2016. "Estimation of zero-intelligence models by L1 data," Quantitative Finance, Taylor & Francis Journals, vol. 16(9), pages 1423-1444, September.
    • Handle: RePEc:taf:quantf:v:16:y:2016:i:9:p:1423-1444
    DOI: 10.1080/14697688.2016.1149612
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    References listed on IDEAS

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