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

In this paper, we present an efficient methodology for generating synthetic financial market data, based on the diffusion model approach. Diffusion models [19], [20], [6], [21], [22], a class of deep generative models, are mathematical models designed to generate synthetic data by Monte Carlo simulating a reverse-time stochastic process, which is specified as an Ito stochastic differential equation (diffusion process). The diffusion model strategy to synthetic data generation and is a two stage process: encoding and decoding. This process employs the use of linear stochastic differential equations. These models have demonstrated impressive results across various applications, including computer vision, natural language processing, time series modeling, multimodal learning, waveform signal processing, robust learning, molecular graph modeling, materials design, and inverse problem solving [26]. Despite their successes, certain aspects of diffusion models, particularly those related to the learning mechanism, require further refinement and development. Ongoing research efforts focus on addressing these performance-related challenges and enhancing the overall capabilities of diffusion modeling methodologies.