Hybrid VAE-LSTM Framework for Multi-Asset Implied Volatility Forecasting with Cross-Sectional Constraints

Abstract

Accurate forecasting of implied volatility surfaces across multiple assets remains a critical challenge in financial risk management and derivatives pricing. This paper proposes a novel hybrid framework that integrates Variational Autoencoders (VAE) with Long Short-Term Memory (LSTM) networks to forecast multi-asset implied volatility while enforcing cross-sectional arbitrage-free constraints. The VAE component learns a low-dimensional latent representation of the volatility surface structure, capturing complex non-linear relationships and ensuring consistency across strikes and maturities. The LSTM component, enhanced with attention mechanisms, models temporal dynamics and long-range dependencies in volatility evolution. We incorporate cross-sectional constraints through a regularization mechanism that preserves the no-arbitrage conditions inherent in option pricing theory. Empirical results on S&P 500 index options and multiple equity options demonstrate that our hybrid VAE-LSTM framework significantly outperforms traditional econometric models and standalone deep learning approaches, achieving a reduction in mean absolute error of approximately 23% compared to benchmark methods. The framework successfully maintains arbitrage-free properties while providing superior predictive accuracy for both short-term and long-term forecasting horizons.