VolGAN: A Generative Model for Arbitrage-Free Implied Volatility Surfaces.

Area of Science:

• Quantitative Finance
• Machine Learning
• Computational Finance

Background:

• Implied volatility surfaces are crucial for option pricing and risk management.
• Existing models often struggle to capture the complex dynamics and correlations within these surfaces.
• Generating realistic scenarios for joint dynamics of volatility surfaces and underlying assets remains a challenge.

Purpose of the Study:

• To introduce VolGAN, a novel generative model for arbitrage-free implied volatility surfaces.
• To enable the simulation of realistic joint dynamics for implied volatility surfaces and underlying asset prices.
• To demonstrate the application of VolGAN in developing advanced hedging strategies.

Main Methods:

• VolGAN, a generative adversarial network (GAN), is trained on time series data of implied volatility surfaces and underlying prices.
• The model learns the covariance structure of co-movements in implied volatilities.
• It is capable of simulating scenarios with non-Gaussian distributions and time-varying correlations.

Main Results:

• VolGAN successfully learns the covariance structure of implied volatilities from SPX data.
• The model generates realistic dynamics for the VIX (Volatility Index).
• Simulated scenarios capture non-Gaussian properties and time-varying correlations.
• Data-driven hedging strategies derived from VolGAN outperform Black-Scholes delta and delta-vega hedging.

Conclusions:

• VolGAN provides a powerful tool for generating realistic implied volatility surfaces and asset dynamics.
• The model's ability to capture complex statistical properties enhances its applicability in financial modeling.
• VolGAN-based hedging strategies offer a promising alternative to conventional methods, potentially improving portfolio risk management.