What does vega measure?

Vega measures the change in an option's theoretical price for a 1 percentage point (1%) increase in implied volatility. A vega of 0.08 means the option gains $0.08 in value if IV rises from, say, 25% to 26%.

Is vega the same for calls and puts?

Yes. Under Black-Scholes, European calls and puts with the same underlying, strike, expiry, and volatility have identical vega. Vega depends only on d1 and the stock price, not on whether the option is a call or a put.

Why is vega highest for at-the-money options?

Vega peaks when the option is at-the-money (stock price ≈ strike). Deep in-the-money or deep out-of-the-money options have lower vega because a volatility change has less incremental effect on their probability of finishing in-the-money.

What is the Black-Scholes vega formula?

Vega = S × N'(d1) × √T, where S is the stock price, T is time to expiration in years, N'(d1) is the standard normal probability density function evaluated at d1, and d1 = [ln(S/K) + (r + σ²/2)×T] / (σ×√T). The result gives the dollar vega per 1-point (100%) vol move; divide by 100 for per-1% sensitivity.

Does vega apply to American options?

The Black-Scholes vega formula strictly applies to European options. American options can be early-exercised, so their vega is usually computed numerically (e.g. with a binomial tree). For options on non-dividend stocks, the Black-Scholes value still serves as a useful approximation.

Option Vega Calculator

Name: Option Vega Calculator
Availability: InStock
Author: Nham Vu

Enter stock price, strike, time to expiry, volatility, and risk-free rate to compute the Black-Scholes vega of a European call or put option.

Black-Scholes Inputs

Stock Price (S)

Strike Price (K)

Time to Expiration (T, years)

e.g. 0.5 = 6 months, 0.25 = 3 months

Implied Volatility (σ, %)

Risk-Free Rate (r, %)

Vega Result

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per 1% vol move

A 1 percentage point rise in implied volatility changes the option price by the vega amount (in dollars, per share).

Black-Scholes Intermediates

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N'(d1) — PDF

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S × √T

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Raw Vega (per 100%)

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Vega by Volatility Shift

Vol Shift	New IV	Price Change ($)
Enter values to see table

Formula Reference

d1 = [ln(S/K) + (r + σ²/2) × T] / (σ × √T)

N'(d1) = (1/√(2π)) × e^-d1²/2

Vega = S × N'(d1) × √T ÷ 100

Dividing by 100 converts raw vega to per-1% volatility sensitivity.

Summary

Enter stock price, strike, time to expiry, volatility, and risk-free rate to compute the Black-Scholes vega of a European call or put option.

How it works

Enter the current stock (or underlying) price.
Enter the option strike price and time to expiration in years.
Set the annualized implied volatility (e.g. 0.25 for 25%) and risk-free rate.
The calculator computes d1 using the Black-Scholes formula.
Vega is derived from the standard normal PDF evaluated at d1, multiplied by the stock price and square root of time.
Results update instantly — no submit button needed.

Use cases

Estimating how much an option premium will change when implied volatility shifts.
Constructing vega-neutral hedges by matching vega exposure across positions.
Comparing vega across strikes to identify which options are most vol-sensitive.
Stress-testing a portfolio by applying a volatility shock and multiplying by total vega.
Teaching or studying the Black-Scholes Greeks in a finance course.
Cross-checking option pricing software outputs for European-style contracts.

Frequently Asked Questions

Last updated: 2026-07-24 · Reviewed by Nham Vu