  In this paper, we propose a generative adversarial network (GAN) approach for
efficiently computing volatility surfaces. The idea is to make use of the
special GAN neural architecture so that on one hand, we can learn volatility
surfaces from training data and on the other hand, enforce no-arbitrage
conditions. In particular, the generator network is assisted in training by a
discriminator that evaluates whether the generated volatility matches the
target distribution. Meanwhile, our framework trains the GAN network to satisfy
the no-arbitrage constraints by introducing penalties as regularization terms.
The proposed GAN model allows the use of shallow networks which results in much
less computational costs. In our experiments, we demonstrate the performance of
the proposed method by comparing with the state-of-the-art methods for
computing implied and local volatility surfaces. We show that our GAN model can
outperform artificial neural network (ANN) approaches in terms of accuracy and
computational time.
