Variational Autoencoders for Completing the Volatility Surfaces

Variational Autoencoders (VAEs) have emerged as a promising tool for modeling volatility surfaces, with particular significance for generating synthetic implied volatility scenarios that enhance risk management capabilities. This study evaluates VAE performance using synthetic volatility surfaces, chosen specifically for their arbitrage-free properties and clean data characteristics. We demonstrate how these synthetic surfaces can serve as powerful tools for stress testing and scenario analysis, enabling risk managers to explore extreme market conditions that may not be present in historical data. Through a comparative analysis between traditional encoder-decoder reconstruction and latent space optimization methods, we explicitly test the resulting surfaces for arbitrage violations. Our results demonstrate that accurate, arbitrage-free surface reconstruction is achievable using only 5\% of the original data points, facilitating rapid generation of diverse implied volatility scenarios. This finding has important implications for market risk analysis, derivatives pricing, and the development of more robust risk management frameworks. The ability to generate synthetic yet realistic volatility surfaces enables more comprehensive stress testing, helps identify potential model vulnerabilities, and supports the validation of pricing and risk models across a wider range of market conditions than historical data alone would permit.