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Generative Diffusion Model for Risk-Neutral Derivative Pricing

Denoising diffusion probabilistic models (DDPMs) have emerged as powerful generative models for complex distributions, yet their use in arbitrage-free derivative pricing remains largely unexplored. Financial asset prices are naturally modeled by stochastic differential equations (SDEs), whose forward and reverse density evolution closely parallels the forward noising and reverse denoising structure of diffusion models. In this paper, we develop a framework for using DDPMs to generate risk-neutral asset price dynamics for derivative valuation. Starting from log-return dynamics under the physical measure, we analyze the associated forward diffusion and derive the reverse-time SDE. We show that the change of measure from the physical to the risk-neutral measure induces an additive shift in the score function, which translates into a closed-form risk-neutral epsilon shift in the DDPM reverse dynamics. This correction enforces the risk-neutral drift while preserving the learned variance and higher-order structure, yielding an explicit bridge between diffusion-based generative modeling and classical risk-neutral SDE-based pricing. We show that the resulting discounted price paths satisfy the martingale condition under the risk-neutral measure. Empirically, the method reproduces the risk-neutral terminal distribution and accurately prices both European and path-dependent derivatives, including arithmetic Asian options, under a GBM benchmark. These results demonstrate that diffusion-based generative models provide a flexible and principled approach to simulation-based derivative pricing.

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