Variance Surface

Q: What is a variance surface?

Grid of total variance (IV^2 x time) across all strike/expiry combinations. Correct representation for no-arb checks.

Q: Why variance instead of IV?

No-arb conditions are linear in variance but nonlinear in IV. Calendar arb detection is straightforward in variance space.

Q: Why does Variance Surface matter for trading?

The variance surface is the institutional representation of implied vol. Because variance is additive over time, it's the natural input for path-dependent and time-integrated vol trades — variance swaps, dispersion trades, exotic pricing. Every quant vol book builds off the variance surface, not the raw IV surface.

Q: When is Variance Surface good versus bad for a trader?

Clean, arbitrage-free surfaces are good for variance-swap pricing, dispersion trades, and exotic replication. Distorted or arb-flagged surfaces are bad for any of these — the fit can't be trusted. Available Alpha-tier only.

Canonical definition, formula, interpretation, and API reference.

Definition

Grid of total variance (IV^2 x T) across strikes and expiries. The correct surface for arbitrage detection.

Formula

Total Variance = IV^2 x T

Grid indexed by (moneyness, tenor). Must be non-decreasing in time.

Inputs

SVI parametersforward pricesexpirations

Output

total_variance_surface grid

Interpretation

Total variance (not IV) is correct for no-arb conditions
Calendar arb: must increase with maturity
Butterfly arb: must be convex in log-moneyness

API Reference

Endpoint

GET /v1/adv_volatility/{symbol}

Tier

Alpha+

Response field

total_variance_surface

Why Variance Surface Matters for Trading

TL;DR

The variance surface expresses IV as total variance w(k,T) — the grid used by exotic-pricing, variance-swap, and dispersion trades.

What it measures: The function w(k,T) = σ²·T across log-moneyness k and time-to-expiry T.
What it signals: The market's clean, arb-free vol surface in variance space.
Why we measure it: Variance is additive over time; volatility is not. For any path-dependent or time-integrated vol trade, variance is the natural unit.
Who uses it: Quants, variance-swap traders, dispersion traders. ALPHA TIER.

How to read Variance Surface

Smooth, arb-free

Variance-swap pricing clean
Dispersion trades work
Exotic replication reliable
Core institutional tool

Good for: variance swaps, dispersion

Distorted / flagged

Raw quotes disagree with fit
Arb flags fire
Variance trades unreliable
Don't use for pricing

Bad for: model-dependent trades

Mild distortion at wings

ATM stable, wings noisy
Cap exposure to liquid strikes
Workable with caveats
Common mid-cap surface

Usable

Rules of thumb

Variance is time-additive. Total variance w(k,T) = integral of instantaneous variance. Cleaner than IV for time-dependent trades.
Check arbitrage flags before trading. If butterfly or calendar arb flags fire, the surface is broken.
Pair with SVI. SVI produces the variance surface in a parametric form.
Foundation of variance swaps. Variance swap fair strikes are integrals over this surface.
Institutional-only. Variance-surface trades require the Alpha tier — not accessible on free/basic plans.