Skew

Skew describes how implied volatility changes across strikes at a single expiry. It tells you which direction the market is worried about.

Definition

Skew is the pattern of IV across strikes. If OTM puts have higher IV than OTM calls, that's put skew (the most common pattern).

Key Points

• Skew exists because demand differs across strikes - everyone wants crash protection
• Put skew = OTM puts more expensive than OTM calls = crash fear
• Call skew = OTM calls more expensive = upside FOMO (rare)
• Skew changes with market conditions - it steepens in selloffs, flattens in rallies

Types of Skew

Pattern

Shape

What It Means

When You See It

Put Skew (Smirk)

Crash fear, hedging demand

Most of the time in equities/crypto

Call Skew

Upside FOMO, speculative buying

Parabolic rallies, meme stocks

Smile

Big move expected, direction unknown

Pre-event, binary outcomes

Flat

No directional preference

Calm, range-bound markets

Build Your Own Skew

Play with the sliders to see how different market conditions create different skew shapes:

Build Your Own Skew

Calm market, mild put skew

ATM Vol: 50%

25Δ Risk Reversal: +4.0%

25Δ Butterfly: +5.3%

Strike	Delta	IV(click to edit)
$80k	10Δ Put	67%
$85k	15Δ Put	62%
$90k	25Δ Put	57%
$95k	40Δ Put	53%
$100k	ATM	50%
$105k	40Δ Call	51%
$110k	25Δ Call	53%
$115k	15Δ Call	56%
$120k	10Δ Call	59%

ATM Vol: 50%

Put Skew: +12 vol pts

Call Skew: +4 vol pts

Smile Width: 5

Click IV values in the table to edit directly. Invalid configurations will show arbitrage warnings.

Why Does Skew Exist?

If the Black-Scholes model were perfectly true, all strikes would have the same IV. Skew exists because reality is messier:

1. Crashes Happen Fast, Rallies Grind Slow

Markets don't move symmetrically. Drops are violent; rallies tend to be gradual. Historical data confirms negative skewness in returns.

2. Everyone Wants Crash Insurance

Portfolio managers buy OTM puts to hedge. This creates demand for puts. Meanwhile, there aren't many natural sellers of puts (it's risky), creating supply scarcity.

3. Volatility Rises When Prices Fall

When markets drop, volatility increases (the "leverage effect"). This makes puts more valuable than a constant-vol model would predict.

Black-Scholes assumes:

• Constant volatility across all strikes and time (false - skew proves this)
• Log-normal returns (false - fat tails exist)
• Continuous hedging is possible (false - gaps happen)
• No jumps in price (false - crashes jump)

These assumptions break down especially for OTM options, where tail risk matters most. The market prices these deviations into skew.

In practice, you never know future volatility in advance. The IV that makes Black-Scholes match the market price is just what the market is willing to pay for that particular option. Different strikes command different prices because they have different risk profiles.

Measuring Skew

Traders use standardized metrics to compare skew across time and assets.

25-Delta Risk Reversal

The most common measure. Compares 25-delta put IV to 25-delta call IV:

$$\text{25d RR} = \text{IV}_{25\Delta \text{ Put}} - \text{IV}_{25\Delta \text{ Call}}$$

How to interpret:

25d RR Value	Interpretation
+15 or more	Extreme put skew - panic mode
+5 to +15	Elevated put skew - nervous market
0 to +5	Mild put skew - normal conditions
-5 to 0	Flat - no strong directional fear
Below -5	Call skew - upside FOMO (rare)

If 25d Risk Reversal = +12, it means:

• 25-delta puts have IV 12 points higher than 25-delta calls
• Example: if ATM IV is 50%, 25d puts might be at 62%, 25d calls at 50%
• The market is paying a significant premium for downside protection
• This is elevated but not panic-level

25-Delta Butterfly

Measures how much both wings are elevated vs ATM (the "curvature" of the smile):

$$\text{25d Fly} = \frac{\text{IV}_{25\Delta P} + \text{IV}_{25\Delta C}}{2} - \text{IV}_{\text{ATM}}$$

• High butterfly = Wings expensive = expecting big moves in either direction
• Low butterfly = Wings cheap = complacency

ATM-Wing Spread

Simple comparison of wing IV to ATM:

$$\text{Put Wing} = \text{IV}_{25\Delta \text{ Put}} - \text{IV}_{\text{ATM}}$$ $$\text{Call Wing} = \text{IV}_{25\Delta \text{ Call}} - \text{IV}_{\text{ATM}}$$

Problem with absolute strikes: A $90k put is very different on different days. If BTC is at$100k, that's 10% OTM. If BTC is at $95k, it's only 5% OTM.

Solution: Delta standardizes moneyness. A 25-delta option is always roughly the same "distance" from ATM in probability terms, regardless of spot price.

This makes it possible to:

• Compare skew across different time periods
• Compare skew across different assets
• Track how skew evolves as spot moves

Delta-to-strike mapping:

The strike for a given delta depends on spot, IV, and time. A 25-delta put at 60% IV and 30 DTE might be at 85% of spot, while at 30% IV it might be at 92% of spot.

Skew Dynamics

Skew isn't static. It responds to market conditions:

Market Event

Effect on Skew

Why

Sharp selloff

Put skew steepens

Hedging demand spikes, fear increases

Slow grind up

Put skew flattens

Fear subsides, put sellers emerge

Parabolic rally

May flip to call skew

FOMO, speculative call buying

Pre-event (FOMC, etc)

Both wings elevate (smile)

Uncertainty about direction

Post-event

Wings collapse, skew normalizes

Uncertainty resolved

Crypto vs Traditional Markets

Crypto skew behaves differently:

Aspect	Equities (SPX)	Crypto (BTC/ETH)
Baseline skew	Strong, persistent put skew	Variable, can be mild
Call skew	Almost never	Happens in bull runs
Speed of change	Slow	Fast - can flip in days
Mean reversion	Weeks to months	Days to weeks

Crypto is younger, more speculative, and has different participants. Skew can flip from put-heavy to call-heavy within a single regime change.

Trading Implications

If You're Buying Options

• Buying OTM puts is expensive due to skew premium
• Buying OTM calls may be relatively cheap (in normal conditions)
• Consider how much you're paying for skew premium vs "fair" value

If You're Selling Options

• Selling OTM puts collects skew premium but you're short crash insurance
• Selling OTM calls offers less premium but less tail risk
• The premium is there for a reason - crashes hurt

Trading Skew Directly

Some traders trade skew itself:

Strategy	What You Do	Bet
Risk Reversal	Sell puts, buy calls (or vice versa)	Skew will flatten/steepen
Ratio Spread	Different quantities at different strikes	Skew shape will change
Butterfly	Buy wings, sell ATM (or vice versa)	Curvature will change

Skew is often modeled using SVI (Stochastic Volatility Inspired):

$$w(k) = a + b \left( \rho(k - m) + \sqrt{(k - m)^2 + \sigma^2} \right)$$

Where:

• $w(k)$ = total implied variance at log-moneyness $k$
• $\rho$ = skew parameter (negative = put skew)
• $\sigma$ = curvature parameter (higher = more smile)

The $\rho$ parameter primarily controls skew direction and steepness. Professional systems fit these parameters to market data to create arbitrage-free surfaces.

See SVI Reference for the full mathematical treatment.

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Related:

• Vol Surface - The complete picture
• Term Structure - The other dimension
• Reading Volatility: Skew Lesson - Full course lesson