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. Through a comprehensive comparison with traditional methods including thin-plate spline interpolation, parametric models (SABR and SVI), and deterministic autoencoders, we demonstrate that our VAE approach with latent space optimization consistently outperforms existing methods, particularly in scenarios with extreme data sparsity. Our findings show that accurate, arbitrage-free surface reconstruction is achievable using only 5% of the original data points, with errors 7–12 times lower than competing approaches in high-sparsity scenarios. We rigorously validate the preservation of critical no-arbitrage conditions through probability distribution analysis and total variance strip non-intersection tests. The framework we develop overcomes traditional barriers of limited market data by generating over 13,500 synthetic surfaces for training, compared to typical market availability of fewer than 100. These capabilities have important implications for market risk analysis, derivatives pricing, and the development of more robust risk management frameworks, particularly in emerging markets or for newly introduced derivatives where historical data are scarce. Our integration of machine learning with financial theory constraints represents a significant advancement in volatility surface modeling that balances statistical accuracy with financial relevance.