The core idea
A volatility smile is implied volatility across strikes for one expiry.
Start with implied volatility for each option. Keep the expiry fixed. Plot IV against strike, moneyness, or delta. The resulting curve is the volatility smile.
Convert prices into IV
Each option price is converted into implied volatility so strikes can be compared on the same scale.
Plot one expiry across strikes
For a single maturity, IV by strike, moneyness, or delta forms the smile.
Fit and extract risk nodes
A smooth smile fit supports risk reversals, flies, interpolation, and surface construction.
A volatility surfaceis the connected set of many expiry smiles. The surface is what lets a desk compare front-end skew, longer-dated wings, and live quote quality in one market state.
Formula
The smile is a one-expiry function of strike or moneyness.
The raw smile is a set of market IV points. Production systems usually fit those points with a controlled curve so the dashboard can interpolate between strikes and extract stable risk nodes.
Smile parts
Traders read the body, wings, skew, and curvature.
The shape matters because it captures how the market prices different parts of the payoff distribution. In crypto options, sparse strikes and fast-moving forwards make it especially important to keep smile points tied to live venue context.
ATM level
The body of the smile near the forward or ATM strike. Desks often track this as the headline volatility for an expiry.
Put wing
The downside side of the smile. In BTC and crypto options, this wing is often important for crash protection and skew monitoring.
Call wing
The upside side of the smile. It helps show whether convex upside demand is rich or cheap against downside protection.
Curvature
The bend from ATM into the wings. Flies summarize this curvature in a compact trader-facing number.
SVI fitting
SVI gives the smile a stable total-variance shape.
A raw smile can be noisy, sparse, or inconsistent. SVI fits total implied variance across log-moneyness for one expiry, producing a smoother curve for interpolation, surface construction, and diagnostics.
Read the SVI formula guideRisk nodes
Risk reversals and flies summarize the smile.
A risk reversal compares same-delta call and put IV to read signed skew. A fly compares the average wing IV with ATM IV to read curvature. Both are compact ways to monitor a fitted smile across expiries.
Topical path
Move from one smile into the full surface workflow.
FAQ
Common questions about volatility smiles.
What is a volatility smile?
A volatility smile is the curve of implied volatility across strikes, moneyness, or delta for one option expiry.
How is a volatility smile different from a volatility surface?
A smile is one expiry slice. A volatility surface connects many smiles across expiries so traders can inspect both strike shape and term structure.
Why is it called a smile?
In many markets, out-of-the-money puts and calls trade at higher implied volatility than ATM options, making the curve bend upward at the wings.
Where does SVI fit into a smile?
SVI fits total implied variance across log-moneyness for one expiry, giving the smile a stable mathematical shape before it is used inside a surface.
References