On detecting spoofing strategies in high-frequency trading

Abstract

The optimal strategy of a potential spoofer is described and applied to Level 2 data on TMX

Acknowledgments

We thank the Fields Institute for the organization of the many ‘Fields-China Joint Industrial Problem Solving Workshop’ from which this problem stems. We also thank TMX and in particular the TMX Analytics Team for supporting this project with profound datasets, high-performing computing facilities as well as precious market insights in high-frequency trading.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 In 2010, trader Navinder Singh Sarao was accused of exacerbating a flash crash by placing thousands of E-mini S&P 500 stock index futures contract orders in one day and changed or moved those orders more than 20 million times before they were canceled.

2 In 2019, the high-frequency company Tower Research Capital agreed to pay a fine of about $60 million over spoofing allegations. In 2020, JP Morgan settles spoofing lawsuit alleging fraud for about $920 million.

3 Aside from obvious cases or exogenous approaches as for insider prosecution.

4 Since we consider the limit order book beyond its top, a dynamic version of the present approach would result in a fairly complex and high dimensional dynamic programing problem.

5 It does not address OTC or darkpool situations.

6 That is ${\overline{v}}_0^{-}$ is the volume posted at bid price $p^{-}<p$, ${\overline{v}}_1^{-}$ the volume posted at $p^{-}-\delta$, etc.

7 The subsequent theoretical study adapts to eventual joint distribution of price movement due to limit and market orders also jointly dependent on the imbalance. The exposition of which is no longer explicit but can be solved numerically.

8 Taking different target variance implies a linear scaling of the frequency and depth.

9 In this paper, we do not consider spoofing strategies involving only limit orders.

10 This stylized situation makes strong assumptions and simplifications. First H is decided at time 0 even if it is executed after the price movement. This is to prevent conditional optimization. Second, the liquidation of the inventory H and v occurs separately. Once again, to provide simplified optimization problem, while we could numerically consider a liquidation of the net inventory H−v. Finally, a second spoofing could happen at the second stage as in the previous section to liquidate the inventory.

11 Combining both in terms of $H-v{1}_{\{y>k\}}$ is cost effective but complicates the exposition of the result.

12 Significance level 0.05 corresponds to a ${\mathcal{X}}_6^2\left(0.95\right)=12.592$.

13 The former fits well with a joint normal distribution, while the second one with a skewed normal distribution, see figure A3. Other parametrization could eventually be used too.

Additional information

Funding

The financial supports from the National Science Foundation of China [grant number 11971310], [grant number 11671257]; as well as from Shanghai Jiao Tong University [grant number AF0710020]; are gratefully acknowledged. Andrew Day gratefully acknowledges the funding provided by Mitacs, the Ontario Graduate Scholarship (OGS) [grant number: it11389], Natural Sciences and Engineering Research Council of Canada post-graduate scholarship (NSERC PGS) [grant number: 444814-2013].