Volatility skew

Definition

Volatility skew is the pattern of implied volatility across strikes at a fixed expiration: in equity markets, downside (low-strike) puts typically trade at higher IV than at-the-money options, and upside calls at lower IV — the “smirk”. Skew is the market pricing asymmetric risk: crashes are violent and gap-driven; rallies are usually gradual. Under a literal Black-Scholes world skew would be flat; its persistent shape is measured market information.

How it works / structure

• Measurement: IV difference between fixed-delta points (e.g. 25-delta put IV minus 25-delta call IV, or put IV minus ATM IV), normalized variants (skew / ATM IV), or fitted-curve parameters. Definitions vary — any skew claim must state its measure.
• History: equity index skew steepened structurally after the October 1987 crash (Rubinstein 1994 documents the regime change; Bates 1991 shows crash risk was being priced in options around the event) — skew is a post-1987 permanent feature of index options.
• Shape by market: equity indexes smirk down; single names vary (M&A candidates can skew up); commodities and FX often show two-sided smiles reflecting different tail structures.
• Strategy relevance: skew is the pricing edge or cost in any structure with legs at different strikes — a collar buys the rich put wing and sells the cheaper call wing (strategy-collar pays the skew), while put ratio spreads sell the rich wing (strategy-ratio-spread collects it).
• Simulation parameters: per-strike IVs (never one flat IV) for any multi-strike structure; skew paths for stress runs.

When it applies

Pricing any multi-strike structure, reading tail-risk sentiment (steepening index skew = more crash protection demand — lens-sentiment), single-name event positioning (skew direction reveals which tail the market fears), and relative-value volatility theses (skew rich/cheap vs its own history).

Risk profile & failure modes

• Definition slippage: “skew is steep” means nothing without the measure, tenor, and reference history — cross-vendor skew numbers are not comparable.
• Skew persistence: index smirk is structural; theses that expect it to “normalize” flat mistake a permanent risk premium for a dislocation.
• Sticky-strike vs sticky-delta: how skew behaves as spot moves is a modeling convention; P&L attribution and hedges differ between assumptions.
• Crowded-wing traps: selling the expensive put wing collects the crash premium — the compensation exists because the crash does occasionally arrive (Bates 1991’s point in reverse).

Evidence & limits

Rubinstein (1994) and Bates (1991) document the crash-priced origin and structural steepening of index skew. Xing, Zhang and Zhao (2010) found steeper single-name smirks predicted underperformance over their sample — evidence that skew carries information about informed positioning, with the usual post-publication attenuation caveats. Claims that skew trades (e.g. systematic risk-reversal selling) earn reliable excess returns are unproven at the entry level and treated as strategy parameters to test.

Falsifiable-thesis examples

Illustrations only, not signals:

• “X’s 25-delta put-call IV spread, at S points today, will narrow by at least 2 points within 30 days” — falsified by the skew series.
• “Names in universe U with smirk steepness in the top decile will underperform the universe median over the next quarter” — falsified by the realized cross-sectional returns.

Cross-references

• The surface’s other axis: opt-term-structure; the level: opt-implied-volatility
• Exposure: greek-vega (bucketed by strike)
• Structures that trade skew: strategy-collar, strategy-ratio-spread, strategy-strangle
• Sentiment reading: lens-sentiment