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Option vega

Vega measures the local change in an option's value with respect to the implied-volatility input used by its model. Scale, surface, expiry and position sign are part of the measure.

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Who this page is for — Anyone measuring how an option's value reacts locally to implied volatility while separating that effect from the underlying move and the passage of time.

Vega is the sensitivity of an option's theoretical value to the model's volatility input:

Vega = ∂V / ∂σ

V is option value and σ is implied volatility under the selected convention. Vega is not the volatility level and does not directly measure how far the underlying will move. It describes the local change in model value when σ changes and other inputs are held fixed.

Option Greeks: local sensitivities and coordinates Delta, gamma, vega and theta describe different changes in the same value. Vanilla-option map: model, inputs, units and sign conventions must be stated. Option Greeks: local sensitivities and coordinates Delta, gamma, vega and theta describe different changes in the same value Vanilla-option map: model, inputs, units and sign conventions must be stated. ● Delta Local slope of optionvalue with respect tothe underlying price. ◆ Gamma Local change in deltawhen the underlyingprice changes. ■ Vega Local response to aconventional change inimplied volatility. ▲ Theta Local response to thepassage of time under astated convention. ◎ Model Greeks depend on themodel and inputs used tocalculate them. ● Units Per contract, per pointand per 1% are notinterchangeable scales. ◆ Nonlinearity A local approximationloses precision as themovement grows. ■ Joint changes Underlying price, IV andtime can move togetherand interact. Cyclepedia · teaching example, not a quote or forecast
The illustrative curve represents a vanilla long call. Vega observes an implied-volatility shock; gamma and theta respond to other coordinates, and the profile is not universal.

Scale: 1% is not 1.00

Volatility may be written as 20%, 0.20 or “20 vol”. That creates an essential scale distinction:

  • some systems quote vega for one volatility point, such as a move from 20% to 21%;
  • others calculate the derivative for a unit change in σ, from 0.20 to 1.20;
  • portfolio reports may already include quantity, multiplier and currency.

If mathematical vega for Δσ = 1.00 is 12, vega for one volatility point, Δσ = 0.01, is approximately 0.12. Missing the conversion causes a factor of 100 error.

An operational statement should say, for example, “USD 4,500 per one-point increase in implied volatility”, not just “vega 4,500”. Date, model, underlying, strike, expiry and surface complete the coordinate.

Position sign

For a long vanilla call or put, vega is normally positive when other model inputs are fixed: more model volatility raises the value of the optionality. Selling the same option reverses position sign. Multi-leg spreads may have positive, negative or near-zero vega depending on quantities, strikes and expiries.

This relationship should not be imposed on every product. Barriers, exotics, stochastic-volatility structures and multi-underlying payoffs may behave differently. Sign and magnitude need to be computed from the actual payoff.

“Long vega” does not guarantee profit when observed volatility rises. Value depends on the implied volatility relevant to the position, while the underlying, time, rates, dividends, smile and liquidity may move together. Executable quotes can also diverge from theoretical value.

A surface, not one number

Options on the same underlying can have different implied volatilities across strike and expiry. The portfolio is exposed to a surface:

  • a parallel move in all implied volatilities;
  • a change in skew across strikes;
  • a change in term structure across expiries;
  • a local move in one region;
  • joint movement of the underlying and smile.

Adding vega as though one input moved in parallel can conceal volatility basis. A professional report retains at least expiry buckets and, where material, strike or moneyness buckets. The Basel MAR21 framework provides an institutional example: regulatory vega sensitivities are organised by factors and maturities before aggregation. Its parameters are not universal rules for every portfolio, but the structure shows why the factor perimeter matters.

Vega, gamma and theta interact

A local P&L approximation may contain:

ΔV ≈ Delta × ΔS + ½ × Gamma × (ΔS)² + Vega × Δσ + Theta × Δt

The terms are not independent in observed markets. An underlying move may change implied volatility; time changes vega and gamma; a shock can reshape the surface. Cross-sensitivities such as vanna and volga can refine local explanation, but extra labels do not replace joint revaluation in material scenarios.

For standard vanilla options, vega is often larger near at-the-money and with more time to expiry. This is model-conditioned, not a universal threshold. Near expiry, vanilla vega may diminish while gamma concentrates, so the risk profile can change quickly.

Aggregation and hedging

Vega aggregation requires at least:

  1. the same volatility-point definition;
  2. coherent currency and multipliers;
  3. signed positions;
  4. underlying, strike and expiry buckets;
  5. the same valuation time, model and surface.

A position that is “vega-neutral” to a parallel shock can remain exposed to skew, term structure, jumps, realised volatility and liquidity. Hedging with another option creates basis between contracts and changes delta, gamma and theta. Neutrality is a local coordinate, not absence of risk.

For multi-currency books, converting vega to a reporting currency adds FX risk. For index and single-name options, a vega offset may fail when correlation or dispersion changes. Gross and net views should therefore be retained alongside scenarios.

Common mistake — Multiplying vega quoted per volatility point by a decimal volatility change, or the reverse. Establish whether the shock is `1`, `1%` or `0.01` before calculation.

Checklist

  1. Is vega quoted for Δσ = 0.01 or Δσ = 1.00?
  2. Is the figure unit, per contract or position-level?
  3. Which currency, quantity and multiplier does it include?
  4. Which strike, expiry and surface node does it represent?
  5. Which model and observed price produce implied volatility?
  6. Is the scenario parallel or does it change skew and term structure?
  7. Which delta, gamma, theta, basis and execution costs remain after hedging?

Sources

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