Paper: arXiv 2503.04164

Abstract

The generation of synthetic financial data is a critical technology in the financial domain, addressing challenges posed by limited data availability. Traditionally, statistical models have been employed to generate synthetic data. However, these models fail to capture the stylized facts commonly observed in financial data, limiting their practical applicability. Recently, machine learning models have been introduced to address the limitations of statistical models; however, controlling synthetic data generation remains challenging. We propose CoFinDiff (Controllable Financial Diffusion model), a synthetic financial data generation model based on conditional diffusion models that accept conditions about the synthetic time series. By incorporating conditions derived from price data into the conditional diffusion model via cross-attention, CoFinDiff learns the relationships between the conditions and the data, generating synthetic data that align with arbitrary conditions. Experimental results demonstrate that: (i) synthetic data generated by CoFinDiff capture stylized facts; (ii) the generated data accurately meet specified conditions for trends and volatility; (iii) the diversity of the generated data surpasses that of the baseline models; and (iv) models trained on CoFinDiff-generated data achieve improved performance in deep hedging task.

Complexity vs Empirical Score

  • Math Complexity: 7.0/10
  • Empirical Rigor: 8.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced mathematics, including diffusion models, cross-attention mechanisms, and Haar wavelet transformations, to tackle a complex generative modeling problem. Empirical rigor is high, featuring extensive statistical tests (kurtosis, Hill index, autocorrelation) on stylized facts, controllability experiments, diversity metrics, and a downstream deep hedging task with improved performance.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Controllable Financial Data Generation"] --> B["Methodology: CoFinDiff<br>Conditional Diffusion Model"]
  B --> C["Key Technique: Cross-Attention<br>Integrates Price Conditions"]
  C --> D{"Computational Process<br>Learn Relations: Conditions ↔ Data"}
  D --> E["Generate Synthetic Time Series<br>Aligning with Arbitrary Conditions"]
  E --> F["Key Findings & Outcomes"]
  
  F --> F1["Captures Stylized Facts"]
  F --> F2["Accurate Trend & Volatility Control"]
  F --> F3["Superior Data Diversity"]
  F --> F4["Improves Deep Hedging Performance"]

Cited References (44)

  1. A theory of power-law distributions in financial market fluctuations (2003) — link
  2. The limiting extremal behaviour of speculative returns: An analysis of intra-daily data from the Frankfurt stock exchange (1998) — link
  3. Scaling of the distribution of fluctuations of financial market indices (1999) — link
  4. AN ANALYSIS OF U.S. STOCK PRICE BEHAVIOR USING WAVELETS (1995) — link
  5. High-resolution image synthesis with latent diffusion models (2022)
  6. Get real: realism metrics for robust limit order book market simulations (2021) — link
  7. Denoising diffusion probabilistic models (2020)
  8. Generating synthetic data in finance: opportunities, challenges and pitfalls (2021) — link
and 36 more
  1. Deep hedging (2019) — link
  2. Deeper Hedging: A New Agent-based Model for Effective Deep Hedging (2023) — link
  3. A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options (1993) — link
  4. Auto-Encoding Variational Bayes (2022) — link
  5. Generative Adversarial Networks (2014) — link
  6. Generation of Realistic Synthetic Financial Time-series (2022) — link
  7. Adversarial Deep Hedging: Learning to Hedge without Price Process Modeling (2023) — link
  8. Sig-wasserstein GANs for time series generation (2022) — link
  9. Synthetic Data Augmentation for Deep Reinforcement Learning in Financial Trading (2022) — link
  10. FinDiff: Diffusion Models for Financial Tabular Data Generation (2023) — link
  11. Volatility Persistence and Stock Valuations: Some Empirical Evidence Using Garch (1988)
  12. Wasserstein generative adversarial networks (2017)
  13. Empirical properties of asset returns: stylized facts and statistical issues (2001) — link
  14. Least squares generative adversarial networks (2017)
  15. Quant GANs: deep generation of financial time series (2020)
  16. Generative Learning for Financial Time Series with Irregular and Scale-Invariant Patterns (2024) — link
  17. The Behaviour of Stock Market Prices (1965) — link
  18. A Simple General Approach to Inference About the Tail of a Distribution (1975) — link
  19. On Correlated Stock Market Time Series Generation (2023) — link
  20. Deep unsupervised learning using nonequilibrium thermodynamics (2015)
  21. Diffusion models beat gans on image synthesis (2021)
  22. Classifier-free diffusion guidance (2022) — link
  23. Empirical deep hedging (2023)
  24. Adversarial Deep Hedging: Learning to Hedge without Price Process Modeling (2023)
  25. Institutional Investors and Stock Market Volatility (2006) — link
  26. The flash crash: High-frequency trading in an electronic market (2017)
  27. Stylized facts of financial time series and three popular models of volatility (2010)
  28. Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation (1982)
  29. Generalized autoregressive conditional heteroskedasticity (1986)
  30. Rectified linear units improve restricted boltzmann machines (2010)
  31. Layer normalization (2016) — link
  32. Efficient capital markets: A review of theory and empirical work (1970)
  33. Generating realistic stock market order streams (2020)
  34. Sig-Wasserstein GANs for conditional time series generation (2024)
  35. Conditional Generative Adversarial Nets (2014) — link
  36. The pricing of options and corporate liabilities (1973)

0 of 44 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.