Lesson 4: The Volatility Surface

Promise: See how skew and term structure combine into one unified picture, and understand why traders look at the whole surface.

Putting It Together

You now know two ways to slice the vol market:

• Skew (Lesson 2): IV across strikes at one expiry
• Term Structure (Lesson 3): IV across expiries at one strike

The volatility surface (or "vol surface") is what you get when you look at both simultaneously: every strike, every expiry, all at once.

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The vol surface is skew + term structure combined. One 3D picture instead of two 2D slices.

Visualizing the Surface

Think of it as a landscape where:

• X-axis: Strike (or moneyness - distance from ATM)
• Y-axis: Time to expiry
• Z-axis (height): Implied volatility

Explore different market conditions and toggle between 3D and 2D views:

Volatility Surface

Calm markets. Mild put skew, slight contango.

Drag to rotate, scroll to zoom. Click scenarios to see different market conditions.

Anatomy of the Surface

Before diving deeper, let's define the key regions:

The "Wings"

The wings are the OTM regions on either side of ATM. Hover over each region to learn more:

Understanding "Wings"

Hover over a region to learn more. When traders say "wings are elevated," they mean both OTM puts AND OTM calls have higher IV than ATM.

Rows and Columns

On the surface:

• Each row (fixed expiry) is a skew curve
• Each column (fixed strike) is term structure

Why Look at the Whole Surface?

1. Context for Any Single Option

When you're trading a specific option, you're trading a point on this surface. Knowing where it sits relative to neighbors tells you:

• Is this option cheap or expensive vs nearby strikes?
• Is this expiry rich or cheap vs other expiries?
• Am I paying for event premium that's only in near-term?

2. Relative Value

Traders constantly compare:

• "The 90-strike puts look cheap relative to 85-strike"
• "Front-month skew is steeper than back-month"

These are surface comparisons. Without the full picture, you'd miss them.

3. Surface Moves Together

The surface doesn't move randomly. When BTC drops:

• Near-term IV spikes more than far-term (backwardation increases)
• Put skew steepens (more crash fear)
• The whole surface lifts (general uncertainty)

Understanding the surface means understanding these correlated moves.

Reading the Surface

Surface Feature

What You See

What It Means

High near-term, low far-term

Surface slopes down as you go out in time

Event risk priced into near-term (backwardation)

Steep left wing

Surface rises as you go to lower strikes

Demand for downside protection (put skew)

Both wings elevated

U-shape across strikes

Big move expected, direction unknown (smile)

Uniformly elevated

Whole surface is high (60%+ everywhere)

General uncertainty, high-vol regime

Flat and low

Surface is flat around 40-50%

Complacency, low-vol regime

Surface Examples by Regime

Toggle between different market conditions to see how the surface changes:

Surface Examples by Regime

Calm market with mild put skew and mild contango

Strike	7d	30d	90d	180d
OTM Put	62%	58%	54%	52%
ATM	55%	52%	50%	48%
OTM Call	52%	50%	48%	46%

What to notice:

• Mild put skew (top row > bottom row)
• Mild contango (right columns slightly lower)
• Everything relatively calm (40-60% range)

<55%

55-65%

65-80%

80-100%

>100%

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The surface shape tells a story. Learn to read the narrative in the numbers.

Where on the Surface Are You?

Every option you trade is a point on this surface. Consider:

Your Trade	Surface Location	What to Check
ATM 30-day call	Middle of the surface	Is ATM IV elevated vs history?
OTM put (80% strike)	Left wing, steep part of skew	How steep is skew? Are you overpaying?
7-day ATM	Near-term, middle	Is term structure inverted? Event coming?
90-day OTM call	Right wing, far out	Lowest IV on surface usually. Is it elevated?

Interpolation: The Space Between

In reality, you only see prices at specific strikes and expiries. The "surface" is interpolated between these points.

Think of it like a map with a few elevation measurements. We need to estimate the height between measurement points. The method matters because bad interpolation can create pricing errors.

The problem: Markets only quote a handful of strikes and expiries. You need IV at every point for:

• Pricing non-standard strikes
• Greeks calculations
• Risk management

Common methods:

Interpolation Methods Compared

The white dots are the only real market quotes. Everything in between is estimated. Click each method to see its strengths and weaknesses.

What matters for you: The interpolated surface must be "arbitrage-free" - no free money from trading spreads. Professional systems (including Hypercall) use mathematically constrained models that guarantee this.

See SVI Reference for the details.

Common Mistakes

Mistake	Correction
Looking at one option in isolation	Always consider where it sits on the surface
Comparing IV across different surface points	Compare apples to apples: same expiry for skew, same strike for term
Ignoring surface shape when sizing trades	A trade on a steep surface behaves differently than on a flat one
Assuming the surface is static	It moves constantly, and different parts move differently

Test your understanding before moving on.

Q: What are the two dimensions that make up the vol surface?

Q: If the vol surface shows steep backwardation and steep put skew, what is the market pricing?

Q: Why do traders look at the whole surface instead of just individual option IVs?

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

See Also

• Vol Surface Reference - Deep dive with all the details
• SVI Parameterization - How surfaces are mathematically modeled
• Lesson 5: The Smile & Smirk → - Different surface shapes

Navigation: ← Lesson 3: Term Structure | Lesson 5: Smile & Smirk →