New geometry framework analyzes no-arbitrage in generative models

Researchers have developed a geometric framework to analyze no-arbitrage constraints within the latent space of generative models used for implied volatility surfaces. This approach assigns a margin to each latent code, defining an admissible latent set where generated surfaces satisfy financial no-arbitrage conditions. The study establishes conditions for code stability and characterizes the boundary of the admissible set, which can be directed towards zero-margin surfaces via a level-set equation. This methodology is applicable to various generative model architectures, including Variational Autoencoders and Generative Adversarial Networks, and has been numerically tested on analytic examples and Heston surfaces. AI

IMPACT This research could lead to more financially sound generative models for complex financial data.

RANK_REASON Academic paper detailing a new theoretical framework for generative models. [lever_c_demoted from research: ic=1 ai=0.7]

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• generative adversarial network
• Generative Models
• Heston surfaces
• Implied volatility surfaces during the period of global financial crisis
• Latent.Space
• Variational Autoencoders

• paper
• other

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