Beyond Monte Carlo: Harnessing Diffusion Models to Simulate Financial Market Dynamics

ArXiv ID: 2412.00036 “View on arXiv”

Authors: Unknown

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.

Keywords: Synthetic data generation, Diffusion models, Covariance matrix regularization, Statistical tests, Monte Carlo simulation, Equities

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematics including diffusion models, stochastic differential equations (SDEs), and score matching with detailed derivations, indicating high math complexity. It demonstrates strong empirical rigor through validation on equity data, statistical tests (Cramer-von Mises), and practical regularization benefits (lower condition numbers), making it backtest-ready.

  flowchart TD
    A["Research Goal: Efficient Generation of<br>Financial Market Synthetic Data"] --> B["Data Input: Large Equity Dataset"]
    B --> C["Core Methodology: Diffusion Model<br>with Numerical Integration Algorithm"]
    C --> D["Computational Process: Generate<br>Large Set of Synthetic Market Data"]
    D --> E["Key Finding 1: Statistical Validation<br>Passes C-vM & Q-Q Tests"]
    D --> F["Key Finding 2: Covariance Matrices<br>Lower Condition Number vs. Observed"]
    D --> G["Key Finding 3: Methodology<br>Highly Efficient & Accurate"]