Abstract
Implied volatility surfaces form a three-dimensional grid of option volatilities across varying
strike prices and maturities. They play a central role in derivative pricing, hedging, and
risk management. However, in practice, these surfaces are often only partially observed,
with missing regions that must be reconstructed to enable reliable use in these tasks.
Traditional methods for filling these gaps typically rely on strong assumptions that may not
hold under real market conditions.
This dissertation investigates the use of generative adversarial networks (GANs) to
reconstruct missing regions in implied volatility surfaces. Within a controlled environment
based on the Heston stochastic volatility model, we simulate data loss by removing
sections of the surfaces. Three GAN variants are trained and evaluated across different
levels of sparsity. Their performance is assessed through visual inspection, financial
arbitrage checks, and various statistical error metrics. Our results show that GANs can
successfully reconstruct missing regions of implied volatility surfaces, producing outputs
that closely resemble the original data while maintaining financial consistency. This
demonstrates the practical value of GAN-based inpainting for derivative pricing, hedging,
and risk management in settings where market data is sparse or incomplete.