用扩散模型生成更真实金融数据，降低协方差矩阵条件数。
Beyond Monte Carlo: Harnessing Diffusion Models to Simulate Financial Market Dynamics
- 用数值积分替代蒙特卡洛模拟训练扩散模型，提升效率。
- 生成数据在资产组合上通过双重检验，尾部也匹配真实市场。
- 生成数据协方差矩阵条件数更低，可作真实数据正则化版本。
我们提出一种高效且准确的合成金融市场数据生成方法，基于扩散模型。生成数据在多个关键方面与真实市场数据高度一致：(i) 资产组合通过双样本Cramér-von Mises检验；(ii) Q-Q图显示各分位数（包括尾部）均与真实数据一致。此外，大规模合成数据生成的协方差矩阵条件数显著低于真实数据估计值，可作为后者的正则化版本。模型训练采用基于数值积分的高效算法，避免蒙特卡洛模拟。该方法在大规模股票数据集上进行了测试。
原文摘要 · Abstract (English)
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.
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