LOB-ID: Evaluating Synthetic Market Data by Inception Distances

2026-08-13

AI Summary

Existing evaluation methods for generative limit order book (LOB) models predominantly rely on stylized facts or marginal statistics, which fail to comprehensively capture the joint temporal and cross-level structure of LOBs. This work proposes the LOB-ID framework, which introduces Fréchet and Monge Inception Distances (FID/MIND) to the evaluation of LOB generative models for the first time. By training DeepLOB on real Level-2 data to obtain domain-specific embeddings, the framework constructs embedding-based distance metrics that effectively reveal structural distortions undetectable by conventional statistical measures. The proposed approach demonstrates robustness across time, assets, and model checkpoints, accurately discriminates among five classes of generative models, and yields scores highly consistent with each model’s ability to capture the joint dynamic structure of the order book.

Abstract

Generative models of limit orderbook (LOB) data have advanced rapidly, but their evaluation often focuses on stylised facts and selected market statistics. These measures provide useful diagnostics but may not capture the joint temporal and cross-level structure of order-book trajectories. We introduce LOB-ID, an embedding-based framework that adapts the Fréchet Inception Distance (FID) and Monge Inception Distance (MIND) to LOB data. To obtain domain-specific embeddings, we train the DeepLOB architecture on four months of Level-2 order-book data for five equities. We show that LOB-ID is stable across time, instruments, and embedding checkpoints, and rises monotonically under controlled distortions. We then construct a moment-matching attack against FID and a deep-book perturbation that evades statistic-based evaluation. MIND remains substantially more sensitive to both distortions. Finally, we score five generative LOB models, spanning stochastic baselines and deep learning approaches, and find that LOB-ID ranks them in line with the joint temporal and cross-level structure each captures by construction.

Problem

• limit order book
• generative models
• evaluation metrics
• temporal structure
• cross-level structure

Innovation

• LOB-ID
• Fréchet Inception Distance
• Monge Inception Distance
• DeepLOB
• generative evaluation