Wing model from zero
1/4What is the wing model?
A volatility smile is the curve of implied volatility across strikes. The wing model (ORC Wing) parameterizes that curve in pieces: one piece for the left side, one for the right side, with a smooth join at the money.
Most parameterizations try to describe the entire smile with a single formula. SVI, for example, uses five mathematical parameters (a, b, rho, m, sigma) that blend into one smooth curve. That is elegant for fitting, but opaque if you want to adjust just one wing.
The wing model takes a different approach: split the smile at ATM. The left side (puts, strikes below spot) gets its own slope and curvature. The right side (calls, strikes above spot) gets its own. A smoothing region around ATM blends them together.
This is not a different model of how volatility works. It is a different control surface for the same smile shape. Where SVI gives you dials that each twist the whole curve, wing gives you dials that control each side independently.
Piecewise structure: left wing, ATM, right wing
Think of a car's suspension. SVI is like a single knob that adjusts firmness for the whole car. Wing is like separate controls for front and rear -- you can soften the front (left/put wing) without touching the rear (right/call wing). Same car, same road, but much more direct control.
The parameters
Six knobs, each with a clear visual effect. Move each slider below and watch exactly what changes on the smile.
The wing model has three layers of control:
Adjust each parameter
Key insight: each parameter changes one visible feature of the smile. Compare this with raw SVI, where changingrho moves the skew and changes the wing balance and shifts the minimum. In wing, one knob = one visual effect.
Left wing vs right wing
The left wing is the put side. The right wing is the call side. Their relative steepness tells you the market's directional fear.
Left wing (sr, vc) controls OTM put implied volatility. When the market fears a crash, traders bid up downside protection. That demand steepens the left wing. This is the famous "skew" or "smirk" that dominates equity and crypto markets.
Right wing (pr, pc) controls OTM call implied volatility. When the market expects a parabolic rally or a short squeeze, upside calls get bid. That steepens the right wing. This is rare in equities but happens in crypto during euphoric phases.
Adjust the sliders below. Make the left wing steep and the right wing flat -- that is a normal market. Now flip them. That is euphoria. Make them equal -- that is a pre-binary-event smile.
Left vs right: adjust each side independently
Reading the wings:
sr >> pr -- Market fears downside more than upside. Normal for equities and crypto.
sr = pr -- Symmetric risk. Pre-binary event where direction is unknown.
pr >> sr -- Market fears upside more than downside. Meme coins, short-squeeze territory.
Before a major crypto hack or regulatory announcement, you often see the left wing spike as traders scramble for puts. If BTC is running into a new ATH with heavy call buying, the right wing steepens instead. The wing model makes this asymmetry immediately visible and independently adjustable.
When to use wing vs SVI
Wing is a trader's tool. SVI is a quant's tool. They can express the same smile, but they optimize for different workflows.
Use wing when: a trader needs to manually adjust the smile. "Steepen the put wing by 2 points" maps to increasingsr by 0.02. One parameter, one change, done.
Use SVI when: you are fitting market data algorithmically or need analytical properties (variance is linear in the wings, which guarantees well-defined moment explosions). SVI is designed for optimization, not for human knob-twiddling.
Toggle the SVI overlay below to see how the same smile looks in both parameterizations. The dashed yellow line is an SVI fit. Notice how the two can approximate each other closely.
Wing (green) vs SVI (yellow dashed)
The tradeoff in practice:
Most institutional vol desks expose wing-style knobs to traders (ORC, Bloomberg OVML) even if the underlying fitting engine uses SVI or SSVI. The conversion between wing and raw SVI is mechanical -- so systems translate in both directions on the fly.
Think of it like temperature: Celsius and Fahrenheit measure the same thing. You pick whichever is natural for the task. Fitting an optimization? SVI. Talking to a trader? Wing.
Where to go next:
SVI parameterization -- the raw (a, b, rho, m, sigma) form
SSVI -- SVI extended across the full surface
Skew -- understanding strike structure in depth
How surfaces are built -- the full pipeline