This paper presents a novel application of generative adversarial networks (GANs) to simulate multivariate equity option market data, specifically implied volatilities of EURO STOXX 50 options. The authors transform option prices into discrete local volatilities (DLVs) to enforce no-arbitrage constraints and reduce dimensionality via PCA. They formulate the simulation as a conditional generative model mapping noise and state to next-step log-DLVs, using recurrent and temporal convolutional architectures. Training methods include GANs, Wasserstein GANs with gradient penalty (WGAN-GP), and quasi-maximum likelihood estimation (qMLE), with a vector autoregressive (VAR) model and unconditional TCN as baselines.

Extensive evaluation using distributional (density, skewness, kurtosis), dependence (ACF), and cross-correlation metrics shows that adversarial training significantly outperforms classical methods. The explicit GAN model achieves the best overall scores, generating realistic paths that capture volatility clustering, bimodal distributions, and cross-correlation structures. PCA compression reduces dimensionality but slightly degrades performance. This work demonstrates for the first time that GANs can successfully generate multivariate financial time series, providing a valuable tool for training and evaluating option trading strategies with augmented data.