Detecting structural evolution of implied volatility surface using gradient-based features

Abstract

In this study, I aim to study how the implied volatility surface evolves over time by analyzing its structural changes using local gradients. I have developed a methodology to represent and quantify daily structural changes in the IV surface. I used a dateset of implied volatilities of S&P 500 index options across several moneyness and maturity levels and calculated changes in gradients at a set of points on the surface. I then used unsupervised clustering algorithm to identify distinct types of surface transformations based on these changes and movements in the index price.

My analysis revealed that there is a number of distinct types of surface transformations that can be identified and interpreted. Identified clusters represented specific skew or term structure dynamics for different levels of maturity and moneyness. My approach allows for flexible and model-free detection of IV surface transformations and allows to analyse the entire volatility surface.