Variational-autoencoders-for-implied-volatility-surfaces-completion
Market data of non-liquid options is often incomplete. This project suggests a method based on variational autoencoders inspired by Bergeron et al’s research paper [1] to complete missing points on partially observed volatility surfaces without introducing static arbitrage. After drawing a parallel between autoencoders and principal component analysis, we compare our new variational autoencoder architecture to the architecture proposed in [1]. and we show its utility in completing and generating arbitrage-free equity volatilities.
This document covers my work during the first two months of my six-month internship at Marex Solutions in London. In this report, I studied in-depth the ability of variational autoencoders to reproduce implied volatility surfaces without creating any static arbitrage. In this work, I suggested a new variational autoencoder architecture dedicated to learning how to generate and complete arbitrage-free implied volatility surfaces.
Section 1: A brief introduction of the evolution of implied volatility models and the emergence of deep learning in finance.
Section 2: A definintion of deterministic and variational autoencoders with a proof that I elaborated to show the relationship between autoencoders and principal component analysis (PCA).
Section 3: A definition of delta implied volatility surfaces and a characterization of static arbitrage in terms of delta instead of usual characterizations in terms of log-forward moneyness.
Section 4: The data interpolation method that I opted for to have a fixed size implied surface from listed options. A presentation of the new architecture that I suggested to improve the results of the cited paper [1].
Section 5: All the numerical results of the new architecture and a comparison to the results yield by Bergeron et al’ variational autoencoder architecture on our internal data sets.
Section 6: Our method to complete missing points on partially observed implied volatility surfaces on illiquid options.
Section 7: A summary of our findings and ideas for further work that can be done beyond the scope of this project.
References
[1] Bergeron, M., Fung, N., Hull, J., Poulos, Z., and Veneris, A. Variational autoencoders: A hands-off approach to volatility, 2022.