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ORC Wing (Jump-Wing)

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This page covers the Jump-Wing parameterization of SVI. For the raw SVI parameterization, see SVI. For context on how it fits into the vol surface pipeline, see How Surfaces Are Built.

Jump-Wing (JW), also called ORC Wing after the ORC trading system that popularized it, is an alternative way to express the same SVI smile using parameters that match how traders think.

Raw SVI uses five mathematical parameters (a,b,ρ,m,σ)(a, b, \rho, m, \sigma) that control variance level, slope, skew, shift, and curvature. These are clean for fitting but opaque for intuition. Jump-Wing replaces them with five quantities a trader can read directly off the smile.

Explore the Parameters

Adjust each Jump-Wing parameter to see how it shapes the smile. Toggle "Show raw SVI" to see the equivalent raw parameters.

Jump-Wing Parameter Explorer

Typical put skew. Put wing steeper than call wing.
61%80%100%49.3%100%63%put wingcall wing-0.2-0.1ATM0.10.2Log-moneyness (k)Implied Vol (%)
ATM Variance0.25
Overall vol level (annualized variance)
ATM Skew-0.15
Slope at ATM. Negative = put skew.
Put Wing Slope0.30
How steeply the left wing rises
Call Wing Slope0.10
How steeply the right wing rises
Minimum Variance0.22
Floor of the smile (lowest variance)
ATM IV
49.3%
25d Risk Reversal
37.2
Butterfly
32.3

Dashed lines show the asymptotic wing slopes. Click "Show raw SVI" to see the equivalent (a, b, ρ, m, σ) parameters.

The Five Parameters

JW ParameterSymbolWhat it means
ATM Variancevtv_tThe variance (IV squared) at the money. Controls the overall level of the smile.
ATM Skewψt\psi_tThe slope of the smile at ATM. Negative means the smile tilts down to the right (put skew).
Put Wing Slopeptp_tThe asymptotic slope of the left wing. Higher = steeper OTM put premiums.
Call Wing Slopectc_tThe asymptotic slope of the right wing. Higher = steeper OTM call premiums.
Minimum Variancev~t\tilde{v}_tThe lowest point on the smile. The variance floor. Must be positive.

Why these parameters matter

A trader looking at a smile cares about:

  1. Where is ATM? That is vtv_t, immediately readable.
  2. Which way does it tilt? That is ψt\psi_t. A quick check: is the skew normal (negative) or inverted (positive)?
  3. How expensive are OTM puts? That is ptp_t. The steeper the put wing, the more the market is paying for crash protection.
  4. How expensive are OTM calls? That is ctc_t. A steep call wing means upside is being bid (rare, signals euphoria or event risk).
  5. What is the floor? That is v~t\tilde{v}_t. How low can vol go even in the cheapest part of the smile?

These map directly to observable features. Compare with raw SVI: "a = 0.04, b = 0.25, rho = -0.4" tells you nothing at a glance. "ATM vol = 50%, put wing slope = 0.30, call wing slope = 0.10" tells you the market is pricing significant downside risk with mild upside premium.

Reading Market Conditions from JW Parameters

ConditionATM VarATM SkewPut WingCall Wing
Calm marketLowSlightly negativeModerateLow
Pre-eventElevatedNear zeroHighHigh
CrisisVery highStrongly negativeVery highLow
EuphoriaModeratePositiveLowHigh

The relationship between put and call wing slopes tells you the market's directional bias:

  • ptctp_t \gg c_t: The market fears downside more than upside (normal for equities/crypto)
  • ptctp_t \approx c_t: Symmetric risk (pre-binary event, direction unknown)
  • ctptc_t \gg p_t: The market fears upside more (rare, meme-stock/parabolic rally territory)

Converting Between JW and Raw SVI

The two parameterizations describe the same smile. You can convert between them.

Why JW Exists

Raw SVI was designed for fitting. The five parameters (a,b,ρ,m,σ)(a, b, \rho, m, \sigma) are numerically convenient but hard to interpret. When a trader on a vol desk says "steepen the put wing by 2 points," they mean increase ptp_t. In raw SVI, that same change requires coordinated adjustments to bb and ρ\rho (and possibly mm and σ\sigma to keep the fit stable).

JW makes the smile editable by hand. A trader can:

  • Bump ATM vol by 1 point (increase vtv_t)
  • Steepen the put wing (increase ptp_t)
  • Flatten the call wing (decrease ctc_t)

Each change maps to a single parameter. In raw SVI, every intuitive change touches multiple parameters.

Where you see JW in practice

  • ORC (now part of Itiviti/Broadridge): The trading system that originated the JW form. Used on many institutional vol desks.
  • Bloomberg OVML: Uses a JW-like parameterization for its vol surface editor.
  • Internal vol surface editors: Most banks and crypto market makers expose JW-style knobs to traders, even if the underlying model is raw SVI or SSVI.
  • Deribit: Their vol surface output can be interpreted in JW terms.

Arbitrage Constraints in JW

The no-arbitrage constraints from raw SVI translate to simple conditions on JW parameters:

  • pt0p_t \geq 0 and ct0c_t \geq 0 (wing slopes are non-negative)
  • v~t>0\tilde{v}_t > 0 (minimum variance is positive)
  • v~tvt\tilde{v}_t \leq v_t (the minimum is below ATM)
  • (pt+ct)(1+ρ)4T(p_t + c_t)(1 + |\rho|) \leq \frac{4}{T} where ρ=12pt/(pt+ct)\rho = 1 - 2p_t/(p_t + c_t) (butterfly constraint from raw SVI)

The first three are easy to enforce with slider bounds. The butterfly constraint can be checked after conversion to raw SVI.


See also: