Creating Synthetic Volatility Surfaces using Generative Adversarial Networks with Static Arbitrage Loss Conditions

Financial options are traded by various market participants, including market makers, hedgers, and speculators. An implied volatility surface is used to price options contracts across different views at maturity and strike price, capturing a comprehensive investor view of future financial market trends. A problem often encountered with sparsely traded instruments such as options on the Johannesburg Stock Exchange All-share index (ALSI) is the lack of volatility surface data available to market participants. We propose an entirely data-driven framework to generate synthetic volatility surfaces using generative adversarial networks (GANs). We use the Wasserstein distance between the data distribution generated by the GAN, using a Variational Auto Encoder (VAE) as a benchmark, and the true distribution from the historical dataset as our performance metric. We note that the vanilla GAN outperforms the VAE. We further observe an improvement from incorporating static arbitrage conditions while training GANs since the framework cannot directly learn the static arbitrage condition. The generated distribution of synthetic ALSI volatility surfaces is true to the historical data. Arbitrage-free artificial surfaces produced can be used in stress testing to complement regulatory requirements in financial institutions and in realistic market simulations in alpha models to develop quantitative investment strategies. They can also be used by insurance for the valuation or pricing of exotic or embedded options. We illustrate our framework and show results using ALSI index option market data.