Implied volatility surfaces describe option-implied volatilities across strikes, and maturities and play a central role in derivative pricing and risk management. However, in practice, they are often incomplete due to illiquidity or sparse trading, requiring reliable reconstruction of missing regions. Existing approaches typically rely on parametric assumptions or latent space optimisation methods, which may be restrictive or computationally intensive. This study proposes a data-driven framework based on conditional generative adversarial networks (GANs) to map partially observed surfaces to completed ones in a single forward pass. The approach is evaluated in a controlled setting using synthetic data generated from the Heston stochastic volatility model, with varying levels of missingness (10–96%). The generator objective incorporates penalty terms enforcing the absence of call-spread, butterfly-spread, and calendar-spread arbitrage, together with a smoothness regulariser on the implied risk-neutral density. Compared with a conditional variational autoencoder (VAE), the Bates model, and the stochastic volatility-inspired (SVI) parameterisation, the proposed approach achieves lower reconstruction errors across all levels of missingness, including unseen cases, while preserving the no-arbitrage properties. An ablation study shows that the conditional GAN implicitly learns no-arbitrage behaviour, with density smoothness regularisation being the only constraint that meaningfully improves reconstruction quality.
Maoneni et al. (Thu,) studied this question.