Using Variance Swaps as an Input Feature in Equity Models

Variance swaps—derivatives that pay the realized variance minus a fixed strike—provide a pure measure of volatility expectations. Unlike options, which embed both volatility and jump risk, variance swaps isolate the variance component. Using variance-swap prices as features in machine learning models for equity trading can improve predictive accuracy by capturing volatility dynamics absent from raw price data.

Variance Swaps Fundamentals

A variance swap payoff at maturity is:

Payoff = Notional × (Realized Variance - Strike)

Realized variance is computed from log returns over the swap period (typically scaled by 252 for annual basis). The strike is set so the swap has zero initial value, implying the strike equals the market's expectation of future variance.

Unlike options, variance swaps have linear payoff with respect to variance. The variance-swap strike provides a "pure" volatility forecast from the market.

Why Variance Swaps Matter for Equity Prediction

Traditional equity models rely on price and volume data. However, these miss important information: expected future volatility shapes expected returns. An equity about to experience heightened volatility will see temporary liquidity premium and wider spreads.

Variance-swap implied volatility (the swap strike divided by annualized basis) provides forward-looking volatility information. Including this in predictive models improves performance.

Feature Engineering from Variance Swaps

Useful features extracted from variance-swap data:

• Implied volatility levels: direct use of variance-swap strike as volatility proxy
• Term structure: ratio of 3M to 1M implied volatility, indicates upward/downward volatility trend
• Volatility of volatility: how dispersed are vol levels across strikes/tenors
• Vol-spot correlation: relationship between equity price and volatility (typically negative)
• Forward volatility rates: extract expected volatility between consecutive swap tenors

Multi-Asset Feature Relationships

Variance swaps on related underlyings (equity index and individual stocks) are correlated. Models that jointly leverage variance-swap data across an index and components often outperform single-asset models.

For example, predicting stock returns using:

• Stock's own variance swap implied vol
• Index variance swap implied vol
• Correlation between them
• Recent realized vs implied vol differences

creates a richer feature set than price/volume alone.

Predicting Volatility Regimes

Classification models can predict volatility regime (low, medium, high) for the next period using variance-swap features. This enables regime-switching trading strategies.

Practical Data Challenges

Variance swaps are traded over-the-counter in lower volume than options. Data availability is less comprehensive: not all underlyings have liquid variance swaps. Bid-ask spreads are wider.

Also, variance swaps trade relatively infrequently. Prices may not update every second like equity prices. Features must account for potential stale data.

Conclusion

Variance swaps provide rich information about volatility expectations that improves equity prediction models. By treating variance-swap data as an input feature, machine learning captures forward-looking volatility dynamics that traditional price-based features miss.