Filling in Missing FX Implied Volatilities with Uncertainties: Improving VAE-Based Volatility Imputation

ArXiv ID: 2411.05998 “View on arXiv”

Authors: Unknown

Abstract

Missing data is a common problem in finance and often requires methods to fill in the gaps, or in other words, imputation. In this work, we focused on the imputation of missing implied volatilities for FX options. Prior work has used variational autoencoders (VAEs), a neural network-based approach, to solve this problem; however, using stronger classical baselines such as Heston with jumps can significantly outperform their results. We show that simple modifications to the architecture of the VAE lead to significant imputation performance improvements (e.g., in low missingness regimes, nearly cutting the error by half), removing the necessity of using $β$-VAEs. Further, we modify the VAE imputation algorithm in order to better handle the uncertainty in data, as well as to obtain accurate uncertainty estimates around imputed values.

Keywords: Imputation, Variational Autoencoders (VAEs), Heston Model with Jumps, Implied Volatility, Uncertainty Estimation, FX Options

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 6.5/10
• Quadrant: Holy Grail
• Why: The paper is heavily mathematical, involving detailed derivations of variational autoencoders (ELBO, reparameterization, deep latent variable models) and advanced statistical concepts, justifying a high math score; it also demonstrates concrete empirical improvements on FX implied volatility data with specific architectures and comparisons to baselines like Heston, indicating strong data and implementation focus.

  flowchart TD
    A["Research Goal: Impute Missing FX Implied Volatilities<br>using VAEs & Handle Uncertainty"] --> B["Data: Historical FX Option Implied Volatilities"]
    B --> C["Methodology 1: Strong Classical Baseline<br>Heston Model with Jumps"]
    B --> D["Methodology 2: VAE-Based Imputation<br>with Architecture Modifications"]
    C --> E["Computational Process<br>Model Fitting & Prediction"]
    D --> E
    E --> F{"Key Findings / Outcomes"}
    F --> G["1. VAE Modifications<br>Outperform Prior VAEs & Reduce Error<br>(e.g., ~50% in low missingness)"]
    F --> H["2. Classical Heston Baseline<br>Can Outperform Baseline VAEs"]
    F --> I["3. Uncertainty Quantification<br>Accurate estimates around imputed values"]