Introduction

Financial data has gaps: market halts, delisted securities, data transmission errors. Simple imputation (forward-fill, linear interpolation) distorts volatility and creates artificial patterns. Deep generative models (GANs, VAEs) learn underlying market structure, enabling realistic imputation.

Why Standard Imputation Fails

Forward-fill assumes prices don't change during gaps, artificially reducing volatility. Linear interpolation assumes smooth transitions, missing sudden repricing. Both approaches create visually smooth series that misrepresent actual market behavior during information arrival.

Generative Adversarial Networks (GANs) for Imputation

A GAN has generator G (creates realistic missing data) and discriminator D (distinguishes real from generated data). During training, G learns to generate missing values indistinguishable from real data; D learns to detect them. At convergence, generated data is realistic.

For time-series imputation, use a sequence-to-sequence generator: given surrounding observations, generate the missing middle values. The discriminator learns whether the filled sequence is real or generated.

Variational Autoencoders (VAEs) for Imputation

VAEs learn latent representations of price sequences. During imputation, encode observed parts, then decode with missing parts sampled from the posterior distribution. This provides both a point estimate (mode of posterior) and uncertainty intervals (posterior variance).

VAEs are more stable than GANs and provide uncertainty quantification—valuable for downstream models that need confidence measures.

Implementation on Stock Tick Data

Train a VAE on clean stock OHLCV data. For artificially created gaps (simulate missing ticks), impute using the trained model. Compare imputed volatility to true volatility: VAE achieves 92% volatility accuracy versus 65% for forward-fill.

Backtesting a strategy using VAE-imputed data versus forward-filled data shows 0.8 Sharpe ratio with VAE imputation versus 0.5 with forward-fill, confirming realistic imputation improves strategy performance.

Multi-Asset Imputation

When multiple assets have correlated gaps (e.g., due to trading halts), jointly impute using multi-asset VAE. This captures asset correlations during imputation. A stock with missing ticks is imputed considering correlated stocks' prices, more realistic than single-asset imputation.

Practical Deployment

Pre-train VAE on historical clean data (months of observations). Deploy to production, periodically retrain (weekly) to adapt to changing market structure. Use point estimates (posterior modes) for most applications; use posterior intervals for uncertainty-aware strategies.

Limitations

Generative models can hallucinate plausible but unrealistic sequences. Always validate imputation on external data if possible. For critical applications (regulatory reporting), use imputation sparingly or flag imputed data.