A new encoding of implied volatility surfaces for their synthetic generation

TL;DR

This paper introduces a PCA variational auto-encoder to encode implied volatility surfaces into a three-dimensional latent space, enhancing synthetic surface generation, extrapolation accuracy, and cross-asset inference for better risk management.

Contribution

A novel three-dimensional encoding of implied volatility surfaces using PCA variational auto-encoders, enabling more interpretable scenario generation and improved extrapolation.

Findings

Scenario generation is more interpretable.

Volatility extrapolation achieves better accuracy.

Enables inference of individual stock volatility from index data.

Abstract

In financial terms, an implied volatility surface can be described by its term structure, its skewness and its overall volatility level. We use a PCA variational auto-encoder model to perfectly represent these descriptors into a latent space of three dimensions. Our new encoding brings significant benefits for synthetic surface generation, in that (i) scenario generation is more interpretable; (ii) volatility extrapolation achieve better accuracy; and, (iii) we propose a solution to infer implied volatility surfaces of a stock from an index to which it belongs directly by modelling their relationship on the latent space of the encoding. All these applications, and the latter in particular, have the potential to improve risk management of financial derivatives whenever data is scarce.