文章背景与核心概要
在金融衍生品定价和风险管理中，生成式模型被广泛用于模拟隐含波动率曲面（Implied Volatility Surfaces）。然而，传统的生成式方法往往会产生违反静态无套利条件（如日历套利和蝶式套利）的曲面，从而导致严重的金融逻辑错误。本文研究了生成式模型生成隐含波动率曲面所需的静态无套利约束，旨在从几何学角度解决这一难题。
作者在隐空间（latent space）中提出了一种与架构无关的通用框架，为每个隐编码（latent code）根据其生成的曲面的无套利条件分配一个标量裕度。该研究的主要贡献包括定义了非负裕度的可容许隐集、建立边界稳定性的水平集公式，并证明了该方法适用于变分自编码器（VAE）、生成对抗网络（GAN）等具有确定性实现映射的各种生成架构。实证结果表明，该方法不仅能恢复已知边界，还能修正产生套利违背的隐编码，对金融工程中的机器学习应用具有重要意义。
Latent-Space No-Arbitrage Geometry of Generative Models for Implied Volatility Surfaces
Summary
This paper investigates the static no-arbitrage constraints required for generative models producing implied volatility surfaces. The authors propose an architecture-agnostic framework in the latent space, where each latent code is assigned a scalar margin based on the no-arbitrage conditions of its generated surface.
Key contributions and findings include: * Admissible Latent Set: Defining the region of codes with nonnegative margins. * Level-Set Formulation: Establishing conditions for boundary stability and formulating a level-set equation targeting the zero-margin boundary for regular boundary components. * General Applicability: The approach applies to Variational Autoencoders (VAEs), Generative Adversarial Networks (GANs), and other generative architectures with a deterministic realization map. * Empirical Insights: Tests on analytic examples successfully recover known boundaries, while experiments using a VAE trained on Heston surfaces reveal that similar reconstruction errors can map to vastly different admissible regions, and that latent priors often concentrate within these admissible spaces. Furthermore, the calculated boundaries can be leveraged to correct latent codes producing arbitrage violations.
Metadata
- arXiv ID: arXiv:2609.00332 [q-fin.CP]
- Authors: Jing Wang, Shuaiqiang Liu, Cornelis Vuik
- Primary Subject: Computational Finance (
q-fin.CP)- Secondary Subjects: Artificial Intelligence (
cs.AI), Machine Learning (cs.LG), Numerical Analysis (math.NA)- Submitted Date: August 31, 2026
- DOI: 10.48550/arXiv.2609.00332