Trading glossary
Vega
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Vega measures how much an option's price changes when the volatility implied by the market rises or falls by one percentage point, with everything else about the option held still.
One of the sensitivities collectively called the Greeks, alongside delta and gamma, although vega is not a Greek letter and is a trading floor coinage rather than a mathematical convention. It states the change in an option's theoretical price for a one point change in implied volatility. Held options carry positive vega whichever way they point, because a wider expected range makes finishing beyond the strike more likely for a call and for a put alike, and written options carry it negatively.
The figure comes out of the same pricing model that produced the premium, as the rate of change of price with respect to volatility, and it is quoted per one point of volatility in the currency the premium is quoted in, scaled by the contract multiplier. It is largest for options struck near the current price and grows with the time left to expiry, since a long dated contract has more room for a change in expectations to matter. It shrinks towards nothing as expiry approaches and as the strike moves far from the market.
Two limits are commonly missed. Vega is a first order estimate taken at one set of inputs, and it changes as those inputs change, so it describes a small move accurately and a large one only loosely. More awkwardly, implied volatility is not a single number but a surface across strikes and maturities, and it rarely shifts by the same amount everywhere at once, so a single vega figure prices a parallel shift that the market seldom delivers. Desks disagree about which model and which surface an exposure should be measured against, which is why two firms can report different vega for the same position.
How it is calculated
Vega is the change in an option's theoretical price for a one percentage point change in implied volatility, with the underlying price, the time remaining and interest rates unchanged.
A one point move in implied volatility
- Option premium
- 2.40
- Vega, per one point of volatility
- 0.12
- Implied volatility assumed to rise
- 18% to 20%
- Estimated premium after the rise
- 2.40 + (0.12 × 2) = 2.64
- Estimated premium on the same fall instead
- 2.40 less (0.12 × 2) = 2.16
Illustrative arithmetic. Every figure is an assumption chosen to keep the calculation legible and none is a quote. The estimate holds only for small moves, because vega itself changes as volatility, the underlying price and the time remaining change.
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