Arbitrage Flags

Q: What are arbitrage flags?

Violations of no-arb conditions in the vol surface. Butterfly = non-convex smile. Calendar = variance decreasing with time.

Q: Should I trade them?

In liquid names, flags usually reflect stale quotes. In illiquid names, real arb can persist. Always check spread width.

Q: Why does Arbitrage Flags matter for trading?

Arbitrage flags are the surface-health diagnostic that separates tradeable fits from broken ones. On a clean surface, flags are zero and every derived output (fitted Greeks, fair vol, wing prices) is reliable. On a broken surface, flags fire and those same outputs become dangerous. Serious quant vol traders never skip this check.

Q: When is Arbitrage Flags good versus bad for a trader?

Zero flags is a green light for any vol strategy. Many flags is a red light — stand down on model-based trades until the surface cleans up. A few wing flags is usually workable if you stick to liquid strikes. Alpha tier required.

Canonical definition, formula, interpretation, and API reference.

Definition

Butterfly and calendar spread violations in the vol surface. Free money if real, usually noise in liquid names.

Formula

Butterfly: d2w/dk2 < 0. Calendar: w(k,T2) < w(k,T1) for T2>T1

Where w is total implied variance.

Inputs

SVI-fitted variance surface

Output

arbitrage_flags[] with type, strikes, tenors

Interpretation

Butterfly: smile has a dip — riskless butterfly possible
Calendar: near-term has more variance than far — riskless calendar
Real arb rare in liquid names, common in illiquid

API Reference

Endpoint

GET /v1/adv_volatility/{symbol}

Tier

Alpha+

Response field

arbitrage_flags[]

Why Arbitrage Flags Matters for Trading

TL;DR

Arbitrage flags are the diagnostic alarms on the vol surface. Zero flags = fit is clean. Many flags = fit is broken, surface is unusable.

What it measures: Binary markers raised when a vol surface fit violates butterfly (static arb) or calendar (time arb) constraints.
What it signals: Surface health. Used as a go/no-go for model-dependent trading.
Why we measure it: A vol surface that permits arbitrage produces wrong Greeks, wrong prices, wrong hedge ratios. Flags are the validity check.
Who uses it: Quant vol traders, market makers, exotic-pricing desks. ALPHA TIER.

How to read Arbitrage Flags

Zero flags

Surface is arb-free
Safe for exotic pricing
Fitted Greeks reliable
Core tradable state

Good for: any vol strategy

Many flags

Fit is broken
Raw quotes inconsistent
Don't trust derived outputs
Stale or crossed quotes likely

Bad for: any model-based trade

Few wing flags

Most flags at deep wings
Core surface fine
Cap strategy to liquid strikes
Typical mid-cap state

Tradeable with caution

Rules of thumb

Zero flags = go; many flags = stop. Binary filter before any model-based trade.
Wing flags are most common. Deep OTM quotes are crossed more often — flags cluster there.
Pair with IV dispersion. Dispersion is continuous; flags are discrete. Use together.
Event days raise flag counts. Earnings mornings often flag temporarily — fades by midday.
Flags are tier-gated. Alpha-tier only. Without them, you're flying blind on surface quality.