Lesson 5: The Smile and Smirk

Promise: Understand the different shapes volatility takes across strikes, and what each shape reveals about market expectations.

Beyond Simple Skew

In Lesson 2, we focused on the directional tilt: put skew vs call skew. But the full picture is richer. The shape of IV across strikes can be a smile, a smirk, or something else entirely.

The Four Basic Shapes

Toggle between the shapes to see how IV changes across strikes:

Smile and Smirk Shapes

Left wing elevated, right wing low

When you see it: Most common. Crash fear dominates. Hedging demand elevates OTM puts.

25d Risk Reversal

+14

Butterfly

3.0

Quick reference:

Shape	Visual	What It Means
Put Smirk		Crash fear dominates. Most common.
Call Smirk		Upside FOMO. Rare.
Smile		Big move expected, direction unknown.
Flat		Calm market.

The Volatility Smile

A true volatility smile is symmetric: both wings (OTM puts AND OTM calls) have higher IV than ATM.

When You See It

• Currency markets (FX) often show smiles - two-way risk
• Crypto during uncertain, range-bound periods
• Pre-event when direction is truly unknown (ETF decision could go either way)

What It Means

The market expects a large move but doesn't know which direction. Both tails are being bid up because both are seen as valuable insurance.

Example: BTC the day before a major regulatory announcement. It could moon (approval) or dump (rejection). Both OTM puts and OTM calls get bid up, creating a smile.

The Volatility Smirk

A smirk is asymmetric: one wing is elevated more than the other.

Put Smirk (Most Common)

OTM puts have higher IV than OTM calls. The curve "smirks" downward from left to right.

When you see it:

• Most of the time in equities and crypto
• During and after selloffs
• When hedging demand is elevated

What it means: Downside fear dominates. The market is willing to pay more for crash protection than upside lottery tickets.

Call Smirk (Rare)

OTM calls have higher IV than OTM puts. The curve slopes upward from left to right.

When you see it:

• Parabolic rallies (GME, meme coins)
• Speculative frenzies
• When everyone is reaching for upside

What it means: Upside FOMO dominates. People are paying up for lottery tickets. This is often a contrarian warning sign.

💡

Equity markets almost always smirk (puts expensive). Crypto can smile or smirk depending on regime.

Build Your Own Shape

Play with the parameters to see how different market conditions create different 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.

The Curvature: How Steep Are the Wings?

Beyond the tilt (which wing is higher), the curvature matters too:

High Curvature (Steep Wings)

Both OTM puts and calls are significantly elevated above ATM. The curve has a pronounced "U" shape.

Interpretation: High demand for tail hedges on both sides. Expensive to buy wings. The market is pricing significant tail risk.

Low Curvature (Flat Wings)

OTM options aren't much more expensive than ATM. The curve is relatively flat.

Interpretation: Less tail fear priced in. Wings are relatively cheap. The market isn't worried about big moves.

💡

Curvature is often called "butterfly" or "convexity." It measures how much extra you pay to own the tails.

Measuring Smile Shape

25-Delta Butterfly

Measures curvature (how U-shaped the smile is):

25-Delta Butterfly

25d Fly = (IV₂₅ᐩP + IV₂₅ᐩC) / 2 − IV_ATM

Hover to explore:

Hover over a variable above to see its meaning.

Reading

High fly (>5) = wings expensive. Normal (2-5) = typical curvature. Low (<2) = flat smile, wings cheap.

25-Delta Risk Reversal

Measures tilt (which wing is higher):

25-Delta Risk Reversal

25d RR = IV₂₅ᐩP − IV₂₅ᐩC

Hover to explore:

Hover over a variable above to see its meaning.

Reading

Positive = put smirk (normal). Negative = call smirk (unusual, FOMO). Near zero = symmetric smile.

Together, RR and Fly give you a complete picture of the smile.

Smile Dynamics: How It Changes

The smile shape responds to market conditions:

Market Event

Effect on Shape

Why

Sharp selloff

Put smirk steepens, curvature increases

Hedging demand spikes, tail fear rises

Slow grind up

Put smirk flattens, curvature decreases

Fear subsides, put sellers emerge

Parabolic rally

May flip to call smirk

FOMO, speculative call buying

Range-bound chop

Smile becomes more symmetric

Direction unclear, both sides bid

Pre-binary event

Both wings elevate (smile steepens)

Uncertainty about direction

Crypto vs Equity Smile Patterns

Aspect

Equities (SPX)

Crypto (BTC)

Dominant shape

Persistent put smirk

Varies by regime

Call smirk

Almost never

Happens in bull runs

Symmetry

Rare

More common

Speed of change

Slow

Fast - can flip in days

Trading the Smile

Understanding smile shape helps with strategy selection:

If You Think...	Consider...	Risk
Wings are too expensive	Selling strangles (short both tails)	Blow-up if tails hit
Wings are too cheap	Buying strangles (long both tails)	Theta decay
Put skew is too steep	Risk reversals (sell puts, buy calls)	Crash happens
Call skew is unusual	Fade it (sell calls, buy puts)	Rally continues

warning

Trading the smile directly is advanced. You're betting on shape changes, not just direction or vol level.

Common Mistakes

Mistake	Correction
Ignoring smile when buying OTM options	You're paying smile premium. Know how much.
Assuming equity smile applies to crypto	Crypto smiles are different and more variable.
Only looking at skew, ignoring curvature	Both RR and Fly matter for the full picture.
Treating smile as static	It changes with market conditions. Monitor it.

The SVI (Stochastic Volatility Inspired) model captures smile shape with 5 parameters:

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

Where $w$ is total variance and $k$ is log-moneyness.

• $a$: Overall variance level
• $b$: Slope magnitude
• $\rho$: Skew direction (negative = put smirk)
• $m$: Center point shift
• $\sigma$: Curvature (butterfly)

This compact representation is widely used for interpolating smiles and computing Greeks.

Test your understanding before moving on.

Q: What's the difference between a volatility smile and a smirk?

Q: What does a high 25-delta butterfly indicate?

Q: When might you see a call smirk instead of a put smirk?

💡 Tip: Try answering each question yourself before revealing the answer.

See Also

• Skew Reference - More metrics and detail
• Lesson 2: Skew - The basics
• Lesson 6: Vol Regimes → - How overall vol levels matter

Navigation: ← Lesson 4: The Vol Surface | Lesson 6: Vol Regimes →