[Paper Review] A Data-driven Market Simulator for Small Data Environments

H. Bühler, Blanka Horvath+3 more|arXiv (Cornell University)|Jun 21, 2020

Generative Adversarial Networks and Image Synthesis58 references4 citations

TL;DR

This paper proposes a data-driven market simulator using a parsimonious Variational Autoencoder (VAE) combined with rough path signatures to generate realistic financial time series in low-data regimes. By leveraging the lead-lag transformation and signature-based encoding, the model achieves high-fidelity simulation even with minimal training data, outperforming classical methods in capturing stylized facts and volatility dynamics.

ABSTRACT

Neural network based data-driven market simulation unveils a new and flexible way of modelling financial time series without imposing assumptions on the underlying stochastic dynamics. Though in this sense generative market simulation is model-free, the concrete modelling choices are nevertheless decisive for the features of the simulated paths. We give a brief overview of currently used generative modelling approaches and performance evaluation metrics for financial time series, and address some of the challenges to achieve good results in the latter. We also contrast some classical approaches of market simulation with simulation based on generative modelling and highlight some advantages and pitfalls of the new approach. While most generative models tend to rely on large amounts of training data, we present here a generative model that works reliably in environments where the amount of available training data is notoriously small. Furthermore, we show how a rough paths perspective combined with a parsimonious Variational Autoencoder framework provides a powerful way for encoding and evaluating financial time series in such environments where available training data is scarce. Finally, we also propose a suitable performance evaluation metric for financial time series and discuss some connections of our Market Generator to deep hedging.

Motivation & Objective

• To develop a flexible, model-free market simulator that operates effectively in environments with limited historical financial data.
• To address the challenge of generating realistic financial time series when training data is scarce, a common issue in finance.
• To integrate rough path theory and signature-based representations to encode complex path dependencies efficiently.
• To propose a computationally efficient Maximum Mean Discrepancy (MMD) metric for evaluating the similarity between real and generated stochastic processes.
• To demonstrate the model's utility in data anonymization, anomaly detection, and deep hedging applications.

Proposed method

• The method uses the lead-lag transformation of time series to extract volatility and path structure, enabling better encoding of financial paths.
• It applies signature-based encoding of the lead-lag transformed paths to capture non-Markovian and rough path features crucial for financial modeling.
• A Variational Autoencoder (VAE) with a low-dimensional latent space is trained on signature-encoded paths to learn a generative model of market dynamics.
• Conditional VAEs are employed to allow generation of paths conditioned on market indicators such as volatility or return regimes.
• A computationally efficient MMD metric is used to evaluate the statistical similarity between real and synthetic path distributions.
• Postprocessing of VAE outputs involves decoding signatures back into time series paths using inverse signature techniques.

Experimental results

Research questions

• RQ1 Can a generative model based on signatures and VAEs produce realistic financial time series when only a small amount of training data is available?
• RQ2 How does signature-based encoding improve the modeling of rough volatility and path dependencies compared to standard returns-based approaches?
• RQ3 What performance metrics are most effective for evaluating the statistical fidelity of synthetic financial paths?
• RQ4 How does the proposed model compare to classical stochastic models in simulating stylized facts such as volatility clustering and heavy tails?
• RQ5 To what extent can the model be used for deep hedging and data anonymization in low-data settings?

Key findings

• The model generates synthetic time series that closely match the statistical properties of real financial data, including volatility clustering and heavy-tailed returns, even with limited training data.
• Signature-based encoding significantly improves the model’s ability to capture rough path features and path dependencies compared to returns-based methods.
• The proposed MMD-based evaluation metric effectively quantifies the similarity between real and synthetic path distributions, enabling reliable performance assessment.
• Numerical experiments on S&P 500 data and rough volatility model paths show that the model preserves key stylized facts and outperforms baseline methods in fidelity metrics.
• The model demonstrates strong conditioning capability, allowing generation of paths responsive to market regimes such as high or low volatility.
• The framework is compatible with deep hedging, as it can generate realistic market scenarios for training hedging strategies under data-scarce conditions.