Determine trader participation distribution and optimal number of synthetic traders for metaorder reconstruction

Determine the precise distribution of trader participation frequencies and the optimal number N of synthetic traders to specify in Algorithm 1 (Mapping Function) when generating synthetic metaorders from public transaction and quote data using Algorithms 1 and 2.

Background

The paper generates synthetic metaorders from public high-frequency data using a mapping-based procedure that requires two key inputs: the number of synthetic traders N and a distribution F governing their participation frequencies. The authors test both homogeneous and power-law trader participation distributions and vary N to assess robustness.

While power-law behavior is a reasonable assumption for trader activity, the exact form of the participation distribution and the appropriate choice of N are not known beforehand. The authors note that mis-specification of these inputs can affect empirical properties such as the concavity of execution profiles, underscoring the need to identify these parameters more precisely.