Vol Surface

The volatility surface is a 3D map showing implied volatility across all strikes and expiries. It's the complete picture of how the market prices risk.

Definition

The vol surface shows IV for every option (strike x expiry combination) on an underlying. Think of it as a landscape where height = IV.

Key Points

• Each option has its own IV - the surface captures all of them
• The surface is not flat - IV varies by strike (skew) and by expiry (term structure)
• The shape tells a story - fear, events, euphoria all create distinct patterns

See It In Action

Explore how the surface changes under different market conditions. 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.

The Two Dimensions

The vol surface combines two concepts:

Strike Dimension: Skew

At any single expiry, IV varies across strikes. This is called skew:

• Put skew (most common): OTM puts have higher IV than OTM calls
• Call skew (rare): OTM calls are more expensive - upside FOMO
• Smile: Both wings elevated - expecting a big move, direction uncertain

Time Dimension: Term Structure

At any single strike, IV varies across expiries. This is called term structure:

Shape

What It Looks Like

What It Means

Contango

Far-term IV > Near-term IV

Normal state. Uncertainty accumulates over time.

Backwardation

Near-term IV > Far-term IV

Event risk. Something is happening soon.

Flat

IV roughly equal across expiries

No strong view on timing of risk.

Backwardation = Event Risk

When you see near-term IV much higher than far-term, the market is pricing in something specific happening soon. After the event passes, expect the term structure to normalize (near-term IV will crash).

How to Read a Vol Surface

When looking at a surface, ask yourself:

Question	Where to Look	What It Tells You
How expensive are options overall?	ATM IV level	General vol regime (high/low/normal)
Is there crash fear?	Compare OTM put IV to ATM	Put skew steepness = downside concern
Is there event risk?	Compare 7d to 30d IV	Backwardation = near-term event priced in
Is there upside FOMO?	Compare OTM call IV to ATM	Elevated = speculative call buying

Example: If you see 7d ATM at 85% but 30d ATM at 55%, that 30-point backwardation screams "event in the next week."

How the Surface is Built

Here's what happens behind the scenes at exchanges and market makers:

1. Raw Market Data

Exchanges publish option prices, but only where there's trading activity:

Strike	7 DTE	30 DTE	90 DTE
$85k	$342	$1,240	--
$90k	$890	$2,100	$3,800
$95k	$2,100	--	$5,200
$100k	$4,500	$6,200	$7,800

Notice the gaps (--). Not every strike trades at every expiry.

2. Convert Prices to IV

For each traded option, solve for the volatility that makes Black-Scholes match the market price.

3. Interpolation: Filling the Gaps

The market doesn't quote every point. Interpolation fills the blanks.

Imagine you want to trade a $97k call, but only$95k and $100k are quoted. The exchange needs to give you a price. Interpolation determines what IV (and therefore price) you'll see.

Bad interpolation can create arbitrage opportunities - if you can buy cheap and sell expensive with no risk, something is broken.

Common methods:

Method	How it works	Trade-off
Linear	Draw straight lines between points	Simple but can create arbitrage
Spline	Smooth curves through points	Prettier but can oscillate wildly
SVI	Parametric model with 5 parameters	Arbitrage-free, industry standard

Most professional systems (including Hypercall) use SVI or similar parametric models that are mathematically guaranteed to be arbitrage-free.

4. Extrapolation: The Wings

What about deep OTM options with no trading? Extrapolation extends the surface beyond market data.

This is harder and more uncertain. Systems typically:

• Use the fitted model parameters to extend smoothly
• Cap how far they'll extrapolate
• Add uncertainty buffers for very deep OTM quotes

Reading the Surface: Quick Reference

Surface Feature

What You See

What It Means

Steep put skew

Left side much higher than right

Crash fear, hedging demand

Backwardation

Near-term rows higher than far-term

Event risk priced in

Smile shape

Both wings elevated (U-shape)

Big move expected, direction unknown

Uniformly elevated

Everything 80%+

Crisis mode, high uncertainty

Flat and low

40-50% everywhere, minimal variation

Calm markets, complacency

Surface Dynamics

The surface doesn't just move up and down. It moves in several modes:

• Parallel shift: Whole surface rises/falls together (general vol change)
• Skew rotation: Put wing steepens/flattens relative to calls
• Term rotation: Near-term rises relative to far-term (or vice versa)
• Smile change: Wings become more/less elevated vs ATM

These modes often correlate with spot moves. See Surface Dynamics Lesson for how to anticipate them.

No-Arbitrage Constraints

A valid vol surface must follow certain rules. If violated, traders could extract free money.

No-arbitrage ensures the surface is internally consistent. The most fundamental no-arbitrage condition is put-call parity.

1. Calendar Spread Constraint

Rule: Total variance must increase with time.

$$\sigma(K, T_1)^2 \cdot T_1 \leq \sigma(K, T_2)^2 \cdot T_2 \quad \text{for } T_1 < T_2$$

In plain English: You can't have a situation where buying a longer-dated option and selling a shorter-dated option at the same strike gives you free money.

Example violation: If 30-day $100k IV is 80$100k IV is 40%, the calendar spread is mispriced. You'd buy the 60-day (cheap variance) and sell the 30-day (expensive variance).

2. Butterfly Constraint

Rule: The smile must be convex (curved upward at the wings).

$$\frac{\partial^2 C}{\partial K^2} \geq 0$$

In plain English: Call prices must decrease at a decreasing rate as strike increases. Otherwise, a butterfly spread would have negative cost (free money).

3. Call Spread Constraint

Rule: Call prices must decrease with strike.

$$\frac{\partial C}{\partial K} \leq 0$$

In plain English: A $90k call must be worth more than a$100k call. If not, you could buy the higher strike and sell the lower strike for profit at any outcome.

Typical Surface Shapes by Market

Market	Put Skew	Term Structure	Typical ATM IV
BTC (calm)	Moderate	Slight contango	45-60%
BTC (stressed)	Steep	Backwardated	80-150%
ETH	Similar to BTC	Often steeper	50-70%
SPX (equities)	Strong, persistent	Usually contango	12-25%

Crypto surfaces are more variable than equity surfaces. Skew can flip from put-heavy to call-heavy within weeks during regime changes.

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Related:

• Reading Volatility Course - Full lesson on the vol surface
• Skew - Deep dive on the strike dimension
• Term Structure - Deep dive on the time dimension
• SVI Parameterization - How surfaces are mathematically modeled
• Vol Indices - Single numbers that summarize the surface