Convexity Premium
The wing-richness component of the volatility risk premium.
Definition
The vol premium priced into the out-of-the-money wings above ATM IV. It isolates how much extra IV the market charges for tail options versus at-the-money options.
Formula
convexity_premium = fair_vol − atm_iv
fair_vol is derived from the variance swap integral of the full vol smile; atm_iv is the raw ATM implied vol.
Inputs
fair_vol (from variance surface)atm_ivSVI fit
Output
convexity_premium (vol points)
Interpretation
- Positive premium: wings are rich vs ATM. Tail insurance is expensive.
- Negative premium: wings are cheap vs ATM. Rare and usually signals surface stress.
- Near zero: wings are priced fairly vs ATM. Typical regime.
API Reference
Endpoint
GET /v1/volatility/{symbol}
Tier
Alpha
Response field
convexity_premium
Why Convexity Premium Matters for Trading
TL;DR
Convexity premium is the slice of VRP that comes from wings being priced richer than ATM. Positive = selling wings is rich; negative = buying wings is cheap.
- What it measures
- The vol premium on out-of-the-money options above at-the-money implied vol, derived from the variance-swap integral of the full smile.
- What it signals
- Whether wing-based strategies (OTM short strangles, put-ratio spreads, long-wing tail hedges) are trading rich or cheap.
- Why we measure it
- Raw VRP blends ATM and wing premium together. Separating them tells you where the edge actually lives.
- Who uses it
- Systematic vol sellers, dispersion desks, tail-risk hedgers. Alpha tier.
How to read Convexity Premium
High positive premium
- Wings overpriced vs ATM
- OTM short strangles harvest premium
- Put-ratio spread sellers win
- Typical pre-event or elevated-skew regime
Good for: wing sellers, ratio spread income
Negative premium
- Wings cheaper than ATM
- Rare — signals surface stress or data issue
- Tail hedges (long wings) are cheap
- Check arb flags before trading
Good for: long wings, tail hedges
Near zero
- Wings fairly priced
- No wing-specific edge
- Trade ATM strategies
- Typical calm regime
Fair
Rules of thumb
- Decompose VRP before sizing. A rich raw VRP with a negative convexity premium means ATM is expensive but wings are cheap — entirely different trades.
- Pair with skew. Steep skew often comes with a higher convexity premium. Both inform wing pricing.
- Watch for arbitrage flags. Negative convexity premium is rare in healthy markets. Check the surface before acting.
- Event days inflate wings. Earnings and CPI temporarily balloon convexity premium — back it out of cross-sectional comparisons.
- Alpha tier. Requires SVI fit + variance-surface integration. Free/basic tiers don't expose fair_vol.
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