Generative Diffusion Model for Risk-Neutral Derivative Pricing

Paper: arXiv 2603.20582

Authors: Nilay Tiwari

Abstract

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.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 5.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents an innovative, mathematically rigorous bridge between generative diffusion models (DDPMs) and no-arbitrage risk-neutral derivative pricing via a score-function shift. While the theoretical formulation is strong and backed by martingale proofs, the empirical validation relies primarily on a simple GBM benchmark, leaving full-scale real-market backtesting for future work.

Research Flowchart

  flowchart TD
    A[Research Goal: Arbitrage-Free Derivative Pricing via DDPMs] --> B[Input: Physical Measure Log-Return Dynamics]
    B --> C[Derive Reverse-Time SDE & Analyze Forward Diffusion]
    C --> D[Apply Measure Change: Additive Shift to Score Function]
    D --> E[Incorporate Closed-Form Risk-Neutral Epsilon Shift]
    E --> F[Generate Paths Satisfying Risk-Neutral Martingale Condition]
    F --> G[Outcomes: Accurate Pricing of European & Path-Dependent Options]

Cited References (13)

1. Denoising Diffusion Probabilistic Models (2020)
2. Generative Modeling by Estimating Gradients of the Data Distribution (2019)
3. Score-Based Generative Modeling through Stochastic Differential Equations (2021)
4. Reverse-Time Diffusion Equation Models (1982)
5. Reaction-rate theory: forty years after Kramers (1990)
6. A Note on the Derivation of the Fisher Identity (2000)
7. Stochastic Differential Equations: An Introduction with Applications (2003)
8. Stochastic Calculus for Finance II: Continuous-Time Models (2004)

0 of 13 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.