What is Vega?
By EC Assets Research Team, Volatility & Derivatives Desk · Published · Updated
Vega: Vega is how much an option's price changes for a one-point move in implied volatility: vega 0.12 means the option gains 0.12 when implied volatility rises from 20 to 21. It peaks at the money and grows with the square root of time to expiration.
What Vega Measures
Vega is the sensitivity of an option's value to a change in implied volatility. It is usually quoted per volatility point: an option with a vega of 0.20 gains about 0.20 if implied volatility rises from 20 to 21 percent. Long options, calls and puts alike, have positive vega; short options have negative vega.
Vega sits awkwardly inside the model that defines it. The Black-Scholes model assumes volatility is constant, yet vega measures what happens when it changes. Practitioners accept the inconsistency because the market quotes options in implied volatility, and vega translates a change in that quote into money. It is the Greek that measures exposure to the price of volatility rather than to the underlying.
How It Works
$$\nu = S,e^{-qT},\varphi(d_1),\sqrt{T}$$
Divided by 100, this gives the value of one volatility point. Three properties follow from the formula:
| Property | Reason | Consequence |
|---|---|---|
| Same for calls and puts | Put-call parity links them through instruments with no volatility exposure | Hedging vega does not depend on the option type |
| Peaks near the money | φ(d1) is largest when d1 is near zero | Vega is concentrated around the current price |
| Grows with √T | Volatility acts over the whole remaining life | Long-dated options carry most of a book's vega |
Vega per unit of premium is highest for long-dated at-the-money options, which is why they are the instrument of choice for trading volatility outright.
The second-order terms matter for large moves. Volga measures how vega changes with volatility and vanna how vega changes with spot; together they explain why a book that is vega-neutral at today's prices can gain or lose on a large shock.
Worked Example
An index call with spot 5,000, strike 5,000, 30 days to expiry, a 5 percent rate, a 1.5 percent dividend yield and 15 percent implied volatility has d1 = 0.088 and φ(d1) = 0.397. Vega is 5,000 × e^(-0.015 × 0.082) × 0.397 × 0.287 = 569 per unit of volatility, or 5.69 per volatility point. With a multiplier of 100 one contract gains about 569 dollars if implied volatility rises from 15 to 16 percent.
| Strike | Days to expiry | Vega per contract, dollars per volatility point |
|---|---|---|
| 4,800 | 30 | 333 |
| 4,900 | 30 | 489 |
| 5,000 | 30 | 569 |
| 5,100 | 30 | 533 |
| 5,200 | 30 | 407 |
| 5,000 | 7 | 276 |
| 5,000 | 90 | 975 |
| 5,000 | 180 | 1,358 |
| 5,000 | 365 | 1,874 |
Black-Scholes values for the inputs above; vega rises with maturity roughly as the square root of time.
Now shock implied volatility by ten points, from 15 to 25 percent. The at-the-money contract gains 5,693 dollars against a linear vega estimate of 5,689: at the money, vega is almost constant. The 5,200 call gains 4,702 dollars against a linear estimate of 4,069, 16 percent more, because its vega rises as volatility pushes it towards the money. That convexity is volga, and it is why out-of-the-money options are the cheaper way to own a large volatility spike.
When It Applies (and Limitations)
It assumes a parallel move. A single vega number assumes every strike and maturity moves by the same amount. Real surfaces steepen, flatten and twist: short-dated volatility moves more than long-dated, and downside strikes move more than upside ones in a sell-off. Books therefore report vega by maturity bucket along the term structure of volatility and by strike across the volatility surface.
Offsetting vega is not hedged vega. Long one-month vega against short one-year vega can net to zero and still lose heavily if the front of the curve jumps while the back stays put. Weighting buckets by how much each typically moves gives a more honest aggregate.
It is model-dependent. Local-volatility and stochastic-volatility models attribute volatility changes differently and produce different vegas. Black-Scholes vega is the quoting convention; hedging often relies on model-specific sensitivities.
It decays with time. Short-dated options carry little vega and are dominated by gamma. A position meant to express a view on volatility should hold the maturity where vega, not gamma, dominates.
Why It Matters for Institutional Investors
It is the second line of every options risk report. After delta, net vega in currency per volatility point shows how a book will move on a change in implied volatility independent of the underlying. Vega limits, often per underlying and maturity bucket, are the main risk budget of volatility funds.
It drives structured product hedging. Issuers of autocallables, reverse convertibles and other notes are left with embedded option positions, typically short long-dated vega. Their hedging programmes are a major source of flow in listed and over-the-counter options and influence the shape of long-dated volatility.
Long-term guarantees carry it. Variable annuities and pension guarantees behave like long-dated puts. A rise in implied volatility raises the cost of those guarantees, which is why insurers run vega hedges with long-dated index options.
It separates two sources of profit and loss. Attribution that splits returns into delta, gamma, vega and theta tells a manager whether a surprise came from the underlying moving more than implied (gamma) or from the market repricing volatility itself (vega). The two call for different responses.
References
- Black, F., & Scholes, M. (1973). The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81(3), 637-654.
- Gatheral, J. (2006). The Volatility Surface: A Practitioner's Guide. Wiley.
- Natenberg, S. (2015). Option Volatility and Pricing (2nd ed.). McGraw-Hill.
- Hull, J. C. (2022). Options, Futures, and Other Derivatives (11th ed.). Pearson.
Frequently asked questions
Is vega the same for calls and puts?
Yes, for European options with the same strike and expiry. Put-call parity ties the call and the put together through the stock and a bond, neither of which depends on volatility, so any change in implied volatility moves both options by the same amount.
Why does vega peak at the money?
Because volatility matters most where the outcome is most uncertain. A deep in-the-money option behaves like the stock and a far out-of-the-money option is nearly worthless under most volatility assumptions; an at-the-money option's value depends almost entirely on how far the underlying might travel.
How is vega quoted in practice?
As the change in option value for a one-point move in implied volatility, for example from 15 to 16 percent, usually multiplied by the contract multiplier to give a money amount per contract. Books aggregate it in currency per volatility point, often by maturity bucket.
What is the difference between vega and volga?
Vega is the first-order sensitivity of price to volatility; volga, also called vomma, is how vega itself changes as volatility moves. Volga is close to zero at the money and largest for out-of-the-money options, which is why their prices react more than vega alone predicts to a large volatility shock.
How does vega change as expiry approaches?
It falls roughly with the square root of the time remaining. A 7-day at-the-money option carries less than half the vega of a 30-day option, and very short-dated options are driven almost entirely by gamma rather than by changes in implied volatility.
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