Tail Convexity
How much the far-OTM put wing is curving up beyond the 25-delta point.
Definition
A measure of left-wing curvature in implied vol, comparing the gradient between 10-delta and 25-delta puts to the gradient between 25-delta puts and ATM.
Formula
tail_convexity = (put_10d_iv − put_25d_iv) − (put_25d_iv − atm_iv)
Positive = accelerating upward curvature in the far-OTM wing. Zero = linear skew. Negative = wing is flattening.
Inputs
put_10d_ivput_25d_ivatm_iv
Output
tail_convexity (vol points)
Interpretation
- Positive: far-OTM wing richly curved — strong tail-fear pricing.
- Near zero: skew is roughly linear — normal regime.
- Negative: far-OTM wing flattening — complacency or data issue.
API Reference
Endpoint
GET /v1/volatility/{symbol}
Tier
Growth
Response field
tail_convexity
Why Tail Convexity Matters for Trading
TL;DR
Tail convexity measures whether the far-OTM put wing is curving up (fat-tail fear) or flattening out (complacency). A complement to skew, but focused on the very tails.
- What it measures
- The second-difference of IV across the put wing, comparing the 10d-to-25d slope against the 25d-to-ATM slope.
- What it signals
- Whether the market is paying up for deep-tail protection relative to normal put-spread levels.
- Why we measure it
- Raw skew tells you the 25-delta wing is rich or cheap. Tail convexity tells you whether that persists deeper into the wing or flattens out.
- Who uses it
- Tail-risk traders, put-ratio spread sellers, structured-product desks.
How to read Tail Convexity
High positive
- Deep-tail puts extremely rich
- Put-ratio sells (sell 25d, buy 10d) work
- Contrarian long-equity setup
- Typical at capitulation
Good for: put ratio spreads, contrarian longs
Negative / flattening
- Deep-tail puts cheaper than expected
- Long-tail-hedge opportunity
- Often signals tail-risk complacency
- Pre-selloff warning
Bad for: naked short wings — good for: tail hedges
Near zero
- Linear skew across the wing
- Trade skew on 25d alone
- Normal equity regime
- No convexity-specific edge
Linear
Rules of thumb
- Pair with skew. Skew is level; tail convexity is shape. Both needed for wing-trading setups.
- Extremes revert fast. Tail convexity spikes at capitulation and collapses in days. Don't chase — entry window is narrow.
- Single-stock noisier than index. SPX is the cleanest signal; single stocks often show spurious tail convexity from thin wing quotes.
- Watch for flat-to-negative. In complacent regimes, tail convexity can go negative as the 10-delta vol fails to keep up. Rare and usually a warning.
- Compare against 252-day distribution. Absolute levels aren't comparable across names; percentile rank is.
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