Learning jump diffusion patterns from high frequency data with conditional diffusion models
Learning Transition Kernels of Jump-Diffusion Processes with Conditional Diffusion Models
Machine Learning
Summary
The paper focuses on how to learn and predict the behavior of complex systems that can jump or change suddenly, using detailed observations taken at many moments in time. The authors use a type of AI called conditional diffusion models to generate new simulated paths of these systems based on observed data. They provide mathematical guarantees on how well their method works and test it with both simulated and real-world data. This helps create better probabilistic forecasts of systems with sudden changes.
What this means in practice
- •For financial modelers: Generate realistic future scenarios of asset prices modeled with jumps and diffusion from high-frequency historical data for better risk assessment.
- •For weather forecasters: Produce probabilistic forecasts of weather variables that exhibit sudden shifts by learning transition dynamics from dense time-series observations.
Authors
Yuzhen Zhao, Yating Liu, Quentin Guibert
Abstract
We study the problem of learning transition kernels for time-homogeneous jump-diffusion processes using conditional diffusion models, with the goal of generating new sample paths from training data consisting of N independent trajectories observed on a high-frequency discrete time grid. On the theoretical side, we establish non-asymptotic bounds for the conditional score estimation error and for the KL divergence between the laws of the true and generated discretely observed paths. On the numerical side, we first evaluate our method on synthetic data to assess the theoretical findings and benchmark its performance against the approach of Gao et al. (2025). We then apply our method to real-world data and investigate its performance on a probabilistic forecasting task.