Abstract
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.