A diffusion-based generative model for financial time series via geometric Brownian motion
Gihun Kim, Sun-Yong Choi, Yeoneung Kim
我们提出了一种新颖的基于扩散的金融时间序列生成框架，该框架将Black-Scholes理论的基石——几何布朗运动(GBM)纳入正向噪声过程。与将价格轨迹视为通用数值序列的标准分数模型不同，我们的方法在每个时间步按资产价格比例注入噪声，反映了金融时间序列中观察到的异方差性。通过精确平衡漂移项和扩散项，我们证明所得对数价格过程可简化为方差爆炸型随机微分方程，这与基于分数的生成模型公式一致。逆向生成过程通过去噪分数匹配进行训练，使用基于Transformer的架构（改编自条件分数扩散插补CSDI框架）。对历史股票数据的实证评估表明，与传统扩散模型相比，我们的模型更真实地复现了关键典型事实：厚尾收益分布、波动率聚集和杠杆效应。
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 ...