用几何布朗运动建模金融时间序列生成，更真实还原市场波动特征。
A diffusion-based generative model for financial time series via geometric Brownian motion
- 将几何布朗运动融入扩散过程，按价格比例加噪以捕捉异方差性。
- 生成的收益率分布具厚尾、波动集聚和杠杆效应，符合金融实证规律。
- 适合研究金融模拟、风险建模或需要高仿真数据的量化分析者。
我们提出一种基于扩散模型的新型金融时间序列生成框架，将几何布朗运动（GBM）——Black-Scholes理论的基础——引入前向加噪过程。与传统基于得分的模型将价格轨迹视为通用数值序列不同，本方法在每一步按资产价格比例加噪，反映金融时间序列中观察到的异方差性。通过精确平衡漂移项与扩散项，推导出的对数价格过程退化为方差爆炸的随机微分方程，与基于得分的生成模型形式一致。反向生成过程采用基于Transformer的架构，基于条件得分匹配训练，源自条件得分扩散插补（CSDI）框架。在历史股票数据上的实证评估表明，该模型比传统扩散模型更真实地重现了重尾收益分布、波动集聚和杠杆效应等关键金融特征。
原文摘要 · Abstract (English)
We propose a novel diffusion-based generative framework for financial time series that incorporates geometric Brownian motion (GBM), the foundation of the Black--Scholes theory, into the forward noising process. Unlike standard score-based models that treat price trajectories as generic numerical sequences, our method injects noise proportionally to asset prices at each time step, reflecting the heteroskedasticity observed in financial time series. By accurately balancing the drift and diffusion terms, we show that the resulting log-price process reduces to a variance-exploding stochastic differential equation, aligning with the formulation in score-based generative models. The reverse-time generative process is trained via denoising score matching using a Transformer-based architecture adapted from the Conditional Score-based Diffusion Imputation (CSDI) framework. Empirical evaluations on historical stock data demonstrate that our model reproduces key stylized facts heavy-tailed return distributions, volatility clustering, and the leverage effect more realistically than conventional diffusion models.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。