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TL;DR

The sensitivity of option price to volatility: \( \mathcal{V} = \frac{\partial V}{\partial \sigma} \). Vega is highest for ATM options and increases with time to expiration.

By Valenke Exam Prep Team·Last updated 2026-06-03

Vega (Greek)

The sensitivity of option price to volatility: \( \mathcal{V} = \frac{\partial V}{\partial \sigma} \). Vega is highest for ATM options and increases with time to expiration.

Why it matters for interviews

Vega exposure determines P&L from volatility changes. Understanding vega is essential for volatility trading, which is a major activity at options desks. Vega is also the denominator in Newton's method for implied volatility.

Definition and Mathematical Foundation

The sensitivity of option price to volatility: \( \mathcal{V} = \frac{\partial V}{\partial \sigma} \). Vega is highest for ATM options and increases with time to expiration.

Application in Quantitative Finance

Vega exposure determines P&L from volatility changes. Understanding vega is essential for volatility trading, which is a major activity at options desks. Vega is also the denominator in Newton's method for implied volatility.

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Frequently Asked Questions

Why is vega not actually a Greek letter?▼
It is not -- the name was invented by analogy with delta, gamma, theta. Some textbooks use kappa instead. Despite not being Greek, 'vega' is universally used in practice.
How does vega change with time to expiration?▼
Vega increases with \( \sqrt{T} \). Longer-dated options have higher vega because there is more time for volatility to affect the outcome. This is why term structure trades (calendar spreads) are vega plays.
What is vega convexity (volga)?▼
The second derivative of price with respect to volatility: \( \frac{\partial^2 V}{\partial \sigma^2} \). It measures how vega itself changes with volatility, important for pricing and risk management of volatility derivatives.