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Metaorder modelling and identification from public data

Ezra Goliath, Tim Gebbie

TL;DR

It is shown that the LMF theory can be validated using publicly available Johannesburg Stock Exchange (JSE) data by leveraging recently developed methods for reconstructing synthetic metaorders.

Abstract

Market-order flow in financial markets exhibits long-range correlations. This is a widely known stylised fact of financial markets. A popular hypothesis for this stylised fact comes from the Lillo-Mike-Farmer (LMF) order-splitting theory. However, quantitative tests of this theory have historically relied on proprietary datasets with trader identifiers, limiting reproducibility and cross-market validation. We show that the LMF theory can be validated using publicly available Johannesburg Stock Exchange (JSE) data by leveraging recently developed methods for reconstructing synthetic metaorders. We demonstrate the validation using 3 years of Transaction and Quote Data (TAQ) for the largest 100 stocks on the JSE when assuming that there are either N=50 or N=150 effective traders managing metaorders in the market.

Metaorder modelling and identification from public data

TL;DR

It is shown that the LMF theory can be validated using publicly available Johannesburg Stock Exchange (JSE) data by leveraging recently developed methods for reconstructing synthetic metaorders.

Abstract

Market-order flow in financial markets exhibits long-range correlations. This is a widely known stylised fact of financial markets. A popular hypothesis for this stylised fact comes from the Lillo-Mike-Farmer (LMF) order-splitting theory. However, quantitative tests of this theory have historically relied on proprietary datasets with trader identifiers, limiting reproducibility and cross-market validation. We show that the LMF theory can be validated using publicly available Johannesburg Stock Exchange (JSE) data by leveraging recently developed methods for reconstructing synthetic metaorders. We demonstrate the validation using 3 years of Transaction and Quote Data (TAQ) for the largest 100 stocks on the JSE when assuming that there are either N=50 or N=150 effective traders managing metaorders in the market.
Paper Structure (19 sections, 13 equations, 8 figures, 4 tables, 2 algorithms)

This paper contains 19 sections, 13 equations, 8 figures, 4 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Data Description
  3. Generating synthetic metaorders
  4. The metaorder generating algorithms
  5. The Square Root Law
  6. Time independence of metaorder impact
  7. The concave profile of metaorder impact
  8. Post metaorder execution impact decay
  9. Validation of the synthetic metaorders
  10. Example metaorder execution profile
  11. Testing the LMF theory
  12. Relationship between $\gamma$ and $\alpha$
  13. Empirical Estimation of $\alpha$ and $\gamma$
  14. Conclusion
  15. Acknowledgements
  16. ...and 4 more sections

Figures (8)

  • Figure 1: SQL for (a) GRT and GFI displayed individually and (b) all the stocks in the top 100 stocks compiled into a single line with the theoretical SQL given in red. In both cases a homogeneous distribution was used for the trader participation with the number of traders set to 4.
  • Figure 2: Approximate independence of metaorder impact with respect to the duration of the metaorder for (a) GFI (more liquid) and (b) GRT (less liquid). Majority of metaorders have a duration between 1 and 30 minutes.
  • Figure 3: Concave profile of metaorder impact. The dynamic impact is plotted as a function of $\phi$, the proportion of the metaorder which has been executed, for (a) GFI (more liquid) and (b) GRT (less liquid). Metaorders were generated by specifying 20 traders and a power-law trader participation distribution with $\delta = 2$. Only metaorders with 10 or more child orders were used for this analysis. The fitted curves are shown in red. See Table \ref{['tab:execution profile values']} for the fitted profiles for GFI and GRT respectively using Equation \ref{['eq:IQ-fitting-params']}.
  • Figure 4: Convex post execution decay of impact for GRT. Dynamic impact is plotted as a function of $z$, the rescaled time. Metaorders were generated by specifying 20 traders and a power-law trader participation distribution with $\delta = 2$. The fitted line is shown in red.
  • Figure 5: The execution profiles of a single metaorder from GRT when using (a), the peak impact $I(Q)$ and (b), when using the peak dynamic impact. Metaorders were generated by specifying 20 traders and a power-law trader participation distribution. The theoretical profiles are shown in red.
  • ...and 3 more figures