Reconstructing The Volatility Surface : A Comparison of a GARCH Option Pricing Model and a Variational Autoencoder

Sammanfattning

Implied volatility surfaces are a central input to option pricing, hedging, and risk manage-ment, but in low-liquidity markets they are often constructed from a small set of marketobservations. Reconstruction approaches, such as parametric volatility models and non-parametric interpolation techniques, can degrade as the proportion of unobserved quotes increases. Parametric models require a sufficient number of observations to estimate their parameters reliably, while interpolation techniques rely on having points nearby to fit local curvature. This motivates the search for reconstruction techniques that remain accurateunder high sparsity. This thesis investigates two reconstruction methods and compares their ability to reconstruct implied volatility surfaces from limited market observations:the Garch Option Pricing Model (GOPM) and a Variational Autoencoder (VAE). Both models are calibrated and evaluated on AAPL options from 2025 with varying numbers of known points. The GOPM produces option prices close to those observed in the market but fails to reproduce the shape and level of the implied volatility surface. The VAE consistently achieves a lower mean squared error than the GOPM on both observed and hidden points across all sparsity levels, and visually reconstructs surfaces that are closer to the market shape. This indicates that the VAE is the more promising approach for reconstructing volatility surfaces under sparsity.