Variance Surface
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.
Related Concepts
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