Generative Modeling

Painting the market: generative diffusion models for financial limit order book simulation and forecasting ArXiv ID: 2509.05107 “View on arXiv” Authors: Alfred Backhouse, Kang Li, Jakob Foerster, Anisoara Calinescu, Stefan Zohren Abstract Simulating limit order books (LOBs) has important applications across forecasting and backtesting for financial market data. However, deep generative models struggle in this context due to the high noise and complexity of the data. Previous work uses autoregressive models, although these experience error accumulation over longer-time sequences. We introduce a novel approach, converting LOB data into a structured image format, and applying diffusion models with inpainting to generate future LOB states. This method leverages spatio-temporal inductive biases in the order book and enables parallel generation of long sequences overcoming issues with error accumulation. We also publicly contribute to LOB-Bench, the industry benchmark for LOB generative models, to allow fair comparison between models using Level-2 and Level-3 order book data (with or without message level data respectively). We show that our model achieves state-of-the-art performance on LOB-Bench, despite using lower fidelity data as input. We also show that our method prioritises coherent global structures over local, high-fidelity details, providing significant improvements over existing methods on certain metrics. Overall, our method lays a strong foundation for future research into generative diffusion approaches to LOB modelling. ...

Controllable Generation of Implied Volatility Surfaces with Variational Autoencoders ArXiv ID: 2509.01743 “View on arXiv” Authors: Jing Wang, Shuaiqiang Liu, Cornelis Vuik Abstract This paper presents a deep generative modeling framework for controllably synthesizing implied volatility surfaces (IVSs) using a variational autoencoder (VAE). Unlike conventional data-driven models, our approach provides explicit control over meaningful shape features (e.g., volatility level, slope, curvature, term-structure) to generate IVSs with desired characteristics. In our framework, financially interpretable shape features are disentangled from residual latent factors. The target features are embedded into the VAE architecture as controllable latent variables, while the residual latent variables capture additional structure to preserve IVS shape diversity. To enable this control, IVS feature values are quantified via regression at an anchor point and incorporated into the decoder to steer generation. Numerical experiments demonstrate that the generative model enables rapid generation of realistic IVSs with desired features rather than arbitrary patterns, and achieves high accuracy across both single- and multi-feature control settings. For market validity, an optional post-generation latent-space repair algorithm adjusts only the residual latent variables to remove occasional violations of static no-arbitrage conditions without altering the specified features. Compared with black-box generators, the framework combines interpretability, controllability, and flexibility for synthetic IVS generation and scenario design. ...

ByteGen: A Tokenizer-Free Generative Model for Orderbook Events in Byte Space ArXiv ID: 2508.02247 “View on arXiv” Authors: Yang Li, Zhi Chen Abstract Generative modeling of high-frequency limit order book (LOB) dynamics is a critical yet unsolved challenge in quantitative finance, essential for robust market simulation and strategy backtesting. Existing approaches are often constrained by simplifying stochastic assumptions or, in the case of modern deep learning models like Transformers, rely on tokenization schemes that affect the high-precision, numerical nature of financial data through discretization and binning. To address these limitations, we introduce ByteGen, a novel generative model that operates directly on the raw byte streams of LOB events. Our approach treats the problem as an autoregressive next-byte prediction task, for which we design a compact and efficient 32-byte packed binary format to represent market messages without information loss. The core novelty of our work is the complete elimination of feature engineering and tokenization, enabling the model to learn market dynamics from its most fundamental representation. We achieve this by adapting the H-Net architecture, a hybrid Mamba-Transformer model that uses a dynamic chunking mechanism to discover the inherent structure of market messages without predefined rules. Our primary contributions are: 1) the first end-to-end, byte-level framework for LOB modeling; 2) an efficient packed data representation; and 3) a comprehensive evaluation on high-frequency data. Trained on over 34 million events from CME Bitcoin futures, ByteGen successfully reproduces key stylized facts of financial markets, generating realistic price distributions, heavy-tailed returns, and bursty event timing. Our findings demonstrate that learning directly from byte space is a promising and highly flexible paradigm for modeling complex financial systems, achieving competitive performance on standard market quality metrics without the biases of tokenization. ...

Generating drawdown-realistic financial price paths using path signatures ArXiv ID: 2309.04507 “View on arXiv” Authors: Unknown Abstract A novel generative machine learning approach for the simulation of sequences of financial price data with drawdowns quantifiably close to empirical data is introduced. Applications such as pricing drawdown insurance options or developing portfolio drawdown control strategies call for a host of drawdown-realistic paths. Historical scenarios may be insufficient to effectively train and backtest the strategy, while standard parametric Monte Carlo does not adequately preserve drawdowns. We advocate a non-parametric Monte Carlo approach combining a variational autoencoder generative model with a drawdown reconstruction loss function. To overcome issues of numerical complexity and non-differentiability, we approximate drawdown as a linear function of the moments of the path, known in the literature as path signatures. We prove the required regularity of drawdown function and consistency of the approximation. Furthermore, we obtain close numerical approximations using linear regression for fractional Brownian and empirical data. We argue that linear combinations of the moments of a path yield a mathematically non-trivial smoothing of the drawdown function, which gives one leeway to simulate drawdown-realistic price paths by including drawdown evaluation metrics in the learning objective. We conclude with numerical experiments on mixed equity, bond, real estate and commodity portfolios and obtain a host of drawdown-realistic paths. ...