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Atlas-X Equity Financing: Unlocking New Methods to Securely Obfuscate Axe Inventory Data Based on Differential Privacy

Antigoni Polychroniadou, Gabriele Cipriani, Richard Hua, Tucker Balch

TL;DR

Atlas-X tackles the privacy risk of daily axe inventories by proposing a differential private continual aggregator to obfuscate published data while preserving the bank's P&L, formalizing a continual data-release problem in finance. The method develops a continual aggregator over a stream with mechanisms such as windowed and binary constructions that achieve $2ε$-DP and poly-logarithmic error bounds, including $O\left(\frac{T^{1/4}\sqrt{Δ}}{ε}\right)$ and $O\left( (\log T)\sqrt{Δ\log T}/ε \right)$ variants. It demonstrates production deployment across three regions with real and synthetic benchmarks, reporting modest P&L impact and controlled leakage, thereby validating a practical, privacy-preserving approach to market-data dissemination. The work represents a pioneering DP deployment in finance, offering a framework for secure continual publication of asset-axe data with tangible implications for privacy, market integrity, and operational efficiency.

Abstract

Banks publish daily a list of available securities/assets (axe list) to selected clients to help them effectively locate Long (buy) or Short (sell) trades at reduced financing rates. This reduces costs for the bank, as the list aggregates the bank's internal firm inventory per asset for all clients of long as well as short trades. However, this is somewhat problematic: (1) the bank's inventory is revealed; (2) trades of clients who contribute to the aggregated list, particularly those deemed large, are revealed to other clients. Clients conducting sizable trades with the bank and possessing a portion of the aggregated asset exceeding $50\%$ are considered to be concentrated clients. This could potentially reveal a trading concentrated client's activity to their competitors, thus providing an unfair advantage over the market. Atlas-X Axe Obfuscation, powered by new differential private methods, enables a bank to obfuscate its published axe list on a daily basis while under continual observation, thus maintaining an acceptable inventory Profit and Loss (P&L) cost pertaining to the noisy obfuscated axe list while reducing the clients' trading activity leakage. Our main differential private innovation is a differential private aggregator for streams (time series data) of both positive and negative integers under continual observation. For the last two years, Atlas-X system has been live in production across three major regions-USA, Europe, and Asia-at J.P. Morgan, a major financial institution, facilitating significant profitability. To our knowledge, it is the first differential privacy solution to be deployed in the financial sector. We also report benchmarks of our algorithm based on (anonymous) real and synthetic data to showcase the quality of our obfuscation and its success in production.

Atlas-X Equity Financing: Unlocking New Methods to Securely Obfuscate Axe Inventory Data Based on Differential Privacy

TL;DR

Atlas-X tackles the privacy risk of daily axe inventories by proposing a differential private continual aggregator to obfuscate published data while preserving the bank's P&L, formalizing a continual data-release problem in finance. The method develops a continual aggregator over a stream with mechanisms such as windowed and binary constructions that achieve -DP and poly-logarithmic error bounds, including and variants. It demonstrates production deployment across three regions with real and synthetic benchmarks, reporting modest P&L impact and controlled leakage, thereby validating a practical, privacy-preserving approach to market-data dissemination. The work represents a pioneering DP deployment in finance, offering a framework for secure continual publication of asset-axe data with tangible implications for privacy, market integrity, and operational efficiency.

Abstract

Banks publish daily a list of available securities/assets (axe list) to selected clients to help them effectively locate Long (buy) or Short (sell) trades at reduced financing rates. This reduces costs for the bank, as the list aggregates the bank's internal firm inventory per asset for all clients of long as well as short trades. However, this is somewhat problematic: (1) the bank's inventory is revealed; (2) trades of clients who contribute to the aggregated list, particularly those deemed large, are revealed to other clients. Clients conducting sizable trades with the bank and possessing a portion of the aggregated asset exceeding are considered to be concentrated clients. This could potentially reveal a trading concentrated client's activity to their competitors, thus providing an unfair advantage over the market. Atlas-X Axe Obfuscation, powered by new differential private methods, enables a bank to obfuscate its published axe list on a daily basis while under continual observation, thus maintaining an acceptable inventory Profit and Loss (P&L) cost pertaining to the noisy obfuscated axe list while reducing the clients' trading activity leakage. Our main differential private innovation is a differential private aggregator for streams (time series data) of both positive and negative integers under continual observation. For the last two years, Atlas-X system has been live in production across three major regions-USA, Europe, and Asia-at J.P. Morgan, a major financial institution, facilitating significant profitability. To our knowledge, it is the first differential privacy solution to be deployed in the financial sector. We also report benchmarks of our algorithm based on (anonymous) real and synthetic data to showcase the quality of our obfuscation and its success in production.
Paper Structure (19 sections, 3 theorems, 37 equations, 18 figures)

This paper contains 19 sections, 3 theorems, 37 equations, 18 figures.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. Our Contributions
  4. Related work
  5. Technical Overview
  6. Preliminaries
  7. Differential Privacy
  8. Financial Concepts
  9. Obfuscation Metrics
  10. P&L
  11. Leakage Probability
  12. Axe Obfuscation via Continual Aggregator DP Mechanism
  13. Binary Mechanism with Less Error
  14. Atlas-X Performance
  15. Conclusion
  16. ...and 4 more sections

Key Result

Corollary 3.3

Suppose $\theta_i$’s are independent random variables, where each $\theta_i$ has Laplace distribution $Lap(b_i)$ and suppose $Y=\sum_i \theta_i$ for $i\in [t]$. The quantity $|Y|$ is at most $O(\sqrt{\sum_i b_i^2}\log\frac{1}{\delta})$. We use the following property of the sum of independent Laplace

Figures (18)

  • Figure 1: The daily direction (Buy or Sell) of two axe lists that differ only in the positions of a single concentrated client should be statistically indistinguishable.
  • Figure 2: Example of an obfuscated published axe (in orange color) for a given asset, together with the historical data for the bank's true axe (in blue color) and the positions of a highly concentrated client (in green color). The Y-axis refers to the axe quantity while the X-axis the observation date.
  • Figure 3: Marginal P&L profile (Y-axis) of a long axe trade as a function of the axe quantity traded by a client (X-axis).
  • Figure 4: Expected inventory P&L difference (Y-axis) between the case in which the bank publishes the DP obfuscated axe including the most concentrated client versus those calculated with the true (un-obfuscated) axe, measured in dollar per day per asset and calculated for different privacy budgets $\epsilon$ (X-axis) as well as obfuscation parameters.
  • Figure 5: Expected inventory P&L difference (Y-axis) between publishing the obfuscated axe with and without the concentrated client, respectively, measured in dollar per day per asset and calculated for different privacy budgets $\epsilon$ (X-axis) as well as obfuscation parameters.
  • ...and 13 more figures

Theorems & Definitions (8)

  • Definition 3.1
  • Definition 3.2
  • Corollary 3.3
  • Definition 6.1
  • Definition 6.2
  • Definition 6.3
  • Theorem 6.4
  • Theorem 6.5: Utility