Arbitrage-Free Implied Volatility Surface Generation with Variational Autoencoders
This addresses the need for realistic and arbitrage-free volatility modeling in quantitative finance, representing an incremental improvement through hybrid techniques.
The paper tackles the problem of generating arbitrage-free implied volatility surfaces consistent with historical data by proposing a hybrid method combining Variational Autoencoders with stochastic differential equation models, achieving superior out-of-sample generative performance.
We propose a hybrid method for generating arbitrage-free implied volatility (IV) surfaces consistent with historical data by combining model-free Variational Autoencoders (VAEs) with continuous time stochastic differential equation (SDE) driven models. We focus on two classes of SDE models: regime switching models and Lévy additive processes. By projecting historical surfaces onto the space of SDE model parameters, we obtain a distribution on the parameter subspace faithful to the data on which we then train a VAE. Arbitrage-free IV surfaces are then generated by sampling from the posterior distribution on the latent space, decoding to obtain SDE model parameters, and finally mapping those parameters to IV surfaces. We further refine the VAE model by including conditional features and demonstrate its superior generative out-of-sample performance.