N ≥ 4

Introduction

How Many Are There?

The high-precision timestamp (HPT) files from Eurex make it possible to infer the reaction time behind every order insert (including those leading to aggressive trades). One question I get asked fairly regularly: How many firms are there in the most competitive latency bucket? Is this just a single participant who is faster than everybody else? Or are there 20 firms with basically the same tech stack?

EOBI + HHI

EOBI 11 (go-live in Nov 2022) brought with it a new era of market transparency on Eurex: the Herfindahl–Hirschman index (HHI) for each level in the book in real-time with every book update. In short, the HHI is a measure of market concentration. In the context of EOBI, the HHI of a level in the book measures the market concentration of the resting volume on the level. For example, if there is just a single order on the level or if all orders on the level belong to the same participant then the HHI for the level is 1. In the limit where there are an infinite number of equally-sized orders, the HHI approaches 0. The HHI itself is not published as this would make it possible to unambiguously identify which orders on a level belong to the same participant. Instead, only an integer representing a range of HHI values is disseminated (1à(0.0, 0.2], 2à(0.2, 0.4], …).

In mid-December 2022 the feature was enabled for the Schatz future (FGBS), a number of the most liquid futures followed in mid-January 2023, most notable the Euro STOXX 50 future (FESX).

FESX

The FESX is the most liquid future on Eurex (and probably Europe) and hence extremely competitive. Additionally, due to its tick size, its book is “thick”, i.e., we typically have dozens of orders on each price level. And even for passive inserts, the latency race is on for FESX as market makers compete for favorable queue position.

Methodology

The newly-added HHI info allows us to compute bounds for the number of participants in a particular latency range. First, we need to compute the reaction time for each resting order in the book. Since we are only interested in the most competitive latencies, we only have to consider trade triggers. We take the t3a for each AddOrder ot ModifyOrder update from the HPT All file. For each of these then, we determine the t9d timestamp for most recent trade which could have triggered this order (i.e., with a t9d at least 2,725 ns prior to the t3a of the insert).

We then parse the EOBI data. After every book update we look at the affected level. If it only comprises orders within the wire-to-wire latency range of interest (< 50 ns), then compute the minimum number of distinct order owners compatible with the published HHI range. Perform this for all book updates, for all instruments with published HHI data, and for all dates since mid-January. Pick the highest such minimum.

Results

There are plenty of “hits” for levels with a minimum number of at least 4 distinct owners. The chart below is just one example (instrument, date, timestamp provided for verification). It shows a level with 5 orders on it and a HHI range or 0.2-0.4 (HHI Indicator 2). Given the quantities of the orders, there is no permutation to assign these orders to just three owners which is compatible with this HHI range. If, for example, the smallest three orders belonged to the same participant, then this would result in an HHI index value of 0.42 so that the HHI Indicator would be 3 (range: 0.4-0.6). The colors in the chart denote one possible assignment of orders to owners but this is not unique. Theoretically, each of the 5 orders could have a distinct owner; this would result in an HHI value still within the same range. Over the range of dates and instruments searched, there was no instance where the number of distinct owners had to be 5 or greater.

NB: The numbers above the level denote the inferred wire-to-wire reaction times of the order insert. We see that this are not monotonic. This is because there is the possibility of overtaking within the order access network between the switch and the partition-specific gateway.

Limitations

With this approach we can only estimate the number of participants who *quote for this instrument*. Theoretically, it is possible that a lot of participants do have comparable reaction times but only use them to trade aggressively or to trade other instruments. Or they only use the fastest setup to trade aggressively and use slower configurations for market making activities.?

#lowlatency #eurex #hft #asics #fpga #algotrading #marketmaking #derivativestrading