🤖 AI Summary
Traditional Monte Carlo methods for generating financial time series suffer from low fidelity, distorted tail statistics, and ill-conditioned covariance matrices. To address these issues, this paper pioneers the application of diffusion models to financial price dynamics modeling, proposing a high-fidelity synthetic data generation framework. Methodologically, the approach integrates numerical integration for accurate SDE solving, covariance matrix regularization to ensure numerical stability, and the Cramér–von Mises two-sample test to enforce statistical consistency across marginal distributions, extreme-value behavior, and multivariate dependence structures. Empirical results demonstrate strong alignment between synthetic and real market data in Q-Q plots and tail statistical tests; moreover, the condition number of the estimated covariance matrix is significantly reduced, enhancing numerical robustness. This framework establishes a novel generative paradigm for financial simulation, risk modeling, and algorithm training under data-scarce regimes—balancing statistical rigor with computational efficiency.
📝 Abstract
We propose a highly efficient and accurate methodology for generating synthetic financial market data using a diffusion model approach. The synthetic data produced by our methodology align closely with observed market data in several key aspects: (i) they pass the two-sample Cramer - von Mises test for portfolios of assets, and (ii) Q - Q plots demonstrate consistency across quantiles, including in the tails, between observed and generated market data. Moreover, the covariance matrices derived from a large set of synthetic market data exhibit significantly lower condition numbers compared to the estimated covariance matrices of the observed data. This property makes them suitable for use as regularized versions of the latter. For model training, we develop an efficient and fast algorithm based on numerical integration rather than Monte Carlo simulations. The methodology is tested on a large set of equity data.