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cloud.google.com·7h ago
AI Research
arXiv CS.AI·Sep 2·6 min read
Latent-Space No-Arbitrage Geometry of Generative Models for Implied Volatility Surfaces
TL;DR
Generative models for implied volatility surfaces can be constrained by no-arbitrage conditions in latent space. This study establishes a framework for identifying admissible latent codes that satisfy these constraints, enhancing the reliability of generative outputs.
✦ Why It Matters
Implement this framework to ensure your generative models produce valid implied volatility surfaces today.
Key Takeaways
- Explore latent space to identify admissible codes for generative models.
- Use level-set equations to navigate zero-margin boundaries effectively.
- Adjust latent codes to correct outputs that violate no-arbitrage conditions.
- Validate your model's outputs against known analytic boundaries.
How It Works
The study assigns a scalar margin to each latent code based on no-arbitrage conditions, forming an admissible latent set. A level-set equation is developed to direct the dynamics of these codes toward the zero-margin boundary, ensuring that generated surfaces remain valid.