A simple script to use market data of variance indices to calculate Volatility Basis.

Mathematical Definitions Used in the Classes

Total Variance

Total Variance ($T \cdot \sigma_{spot}^2$): The cumulative "uncertainty energy" at time $T$.

Variance Gap

Variance Gap ($\Delta \text{Var}$): The amount of new variance energy added between two time points.

• For Index: $T_2 \sigma_2^2 - T_1 \sigma_1^2$
• For Futures: $\sigma_{fwd}^2 \cdot (T_2 - T_1)$

Forward Variance

Forward Variance ($\sigma_{fwd}^2$): The "intensity" or rate of variance added per day during a specific window.

$$\sigma_{fwd}^2 = \frac{\Delta \text{Var}}{\Delta T}$$

Volatility Basis

Volatility Basis: The difference between the Forward Volatility derived from SPX Options (Index) and that priced in VIX Futures.

$$\text{Basis} = \sigma_{fwd, \text{Index}} - \sigma_{fwd, \text{Futures}}$$

Visuals:

Total Variance:

Shows how much "Heat" is in the system. The Index-based approach consistently estimates a higher total energy for long horizons (365 days).

Variance Rate & Forward Vol:

You can see where the Index-based approach adds energy in "chunks" (VIX3M to VIX6M).

Volatility Basis:

The green area represents where the Options market is more expensive than the Futures market (Positive Basis). For March 2026 (~90 days), the markets are perfectly converged, but they diverge sharply thereafter.