Dynamic Estimation of Implied Volatility Surface

Abstract

In this study, we investigate the application of Autoencoder networks and Principal Component Analysis (PCA) for learning and predicting high-dimensional implied volatility surfaces in the financial domain. Both Autoencoder and PCA are widely recognized as prominent dimensionality reduction techniques in machine learning and deep learning. In the financial industry, these models are employed to replicate market prices and value financial instruments, focusing on low training loss and robust extrapolation capabilities. The implied volatility surface is empirically calculated using machine learning and deep learning methods, demonstrating that these innovative approaches offer enhanced flexibility and accuracy in generating realistic, arbitrage-free option prices. Four diff erent models are applied to the IvyDB dataset, a comprehensive source of historical price, implied volatility, and sensitivity data for the entire US listed index and equity options markets. Subsequently, the latent factors are t into the autoregressive moving average–generalized autoregressive conditional heteroscedasticity (ARMA-GARCH) model for future data prediction. To evaluate the models’ performance, a backtesting procedure is conducted by iteratively training and testing on two-thirds of the data up to the end. The comparative analysis reveals that incremental principal component analysis outperforms the other models while exhibiting shorter execution times. Furthermore, the optimal number of latent factors required to minimize both prediction and reconstruction errors in the models is examined.