Vega Calculator (Options)
This calculator computes Vega — the sensitivity of a European option price to a small change in implied volatility — using the Black‑Scholes closed‑form formula. Vega is commonly used by traders and risk managers to estimate how option prices move as implied volatility changes.
The tool returns intermediate values (d1 and the standard normal probability density at d1) to aid verification and calibration. Results assume continuous compounding and the Black‑Scholes model assumptions described below; use caution for instruments that violate those assumptions.
Governance
Record e9be4f233618 • Reviewed by Fidamen Standards Committee
Inputs
Results
d1 (Black‑Scholes intermediate)
—
Standard normal PDF at d1 (φ(d1))
—
Vega (price change per 1.0 = 100 percentage points of volatility)
—
| Output | Value | Unit |
|---|---|---|
| d1 (Black‑Scholes intermediate) | — | — |
| Standard normal PDF at d1 (φ(d1)) | — | — |
| Vega (price change per 1.0 = 100 percentage points of volatility) | — | — |
Visualization
Methodology
Vega is calculated from the Black‑Scholes model: Vega = S * e^(−qT) * sqrt(T) * φ(d1), where φ is the standard normal probability density and d1 is the usual Black‑Scholes intermediate.
Key assumptions: underlying returns are lognormal, volatility is constant over the remaining life, and option is European (no early exercise). For American options, discrete dividends, or stochastic volatility, model error can be material.
Operational guidance: validate input units (annualized volatility, time in years, decimal rates), perform sensitivity checks around the chosen volatility, and if using outputs for automated trading or reporting, implement regression and unit tests following software engineering and risk-management standards.
Worked examples
Example: S=100, K=100, σ=0.20, T=0.5, r=0.03, q=0.00 → Vega ≈ S * exp(−qT) * sqrt(T) * φ(d1). Use the calculator to compute numeric result and verify by small finite-difference of option price if desired.
Calibration check: if implied vol is low and T is short, Vega will be small; for at-the-money options with longer T, Vega increases roughly with sqrt(T).
F.A.Q.
What unit is Vega expressed in?
Vega here is expressed as price units per 1.0 change in volatility (i.e., per 100 percentage points). To convert to price change per 1 percentage point, divide the Vega value by 100.
Does this work for American options or for options on assets with discrete dividends?
Black‑Scholes is for European options with continuous yields. For American options or discrete dividends, Black‑Scholes may be inaccurate and you should use specialized pricing or numerical methods (binomial, finite difference, or Monte Carlo).
How accurate is this calculator?
The calculator implements the analytical Black‑Scholes formula; numerical rounding and input errors can produce small deviations. Model risk arises from violated assumptions (nonconstant volatility, jumps). Follow testing and validation practices aligned with standards referenced below.
How should I validate outputs before using them in production systems?
Perform unit tests, regression tests, and finite-difference checks (bump volatility by a small delta and recompute option price) to confirm Vega matches numerical derivatives. Maintain change control and logging for inputs and results as part of operational risk controls.
Sources & citations
- International Organization for Standardization (ISO) — https://www.iso.org
- National Institute of Standards and Technology (NIST) — https://www.nist.gov
- Institute of Electrical and Electronics Engineers (IEEE) — https://www.ieee.org
- Occupational Safety and Health Administration (OSHA) — https://www.osha.gov
- OCC — Options Clearing Corporation — https://www.theocc.com/
- CBOE — Options Education — https://www.cboe.com/education/
Further resources
Related tools
Versioning & Change Control
Audit record (versions, QA runs, reviewer sign-off, and evidence).
Record ID: e9be4f233618What changed (latest)
v1.0.0 • 2025-11-03 • MINOR
Initial publication and governance baseline.
Why: Published with reviewed formulas, unit definitions, and UX controls.
Public QA status
PASS — golden 25 + edge 120
Last run: 2026-01-23 • Run: golden-edge-2026-01-23
Versioning & Change Control
Audit record (versions, QA runs, reviewer sign-off, and evidence).
What changed (latest)
v1.0.0 • 2025-11-03 • MINOR
Initial publication and governance baseline.
Why: Published with reviewed formulas, unit definitions, and UX controls.
Public QA status
PASS — golden 25 + edge 120
Last run: 2026-01-23 • Run: golden-edge-2026-01-23
Engine
v1.0.0
Data
Baseline (no external datasets)
Content
v1.0.0
UI
v1.0.0
Governance
Last updated: Nov 3, 2025
Reviewed by: Fidamen Standards Committee (Review board)
Credentials: Internal QA
Risk level: low
Reviewer profile (entity)
Fidamen Standards Committee
Review board
Internal QA
Entity ID: https://fidamen.com/reviewers/fidamen-standards-committee#person
Semantic versioning
- MAJOR: Calculation outputs can change for the same inputs (formula, rounding policy, assumptions).
- MINOR: New features or fields that do not change existing outputs for the same inputs.
- PATCH: Bug fixes, copy edits, or accessibility changes that do not change intended outputs except for previously incorrect cases.
Review protocol
- Verify formulas and unit definitions against primary standards or datasets.
- Run golden-case regression suite and edge-case suite.
- Record reviewer sign-off with credentials and scope.
- Document assumptions, limitations, and jurisdiction applicability.
Assumptions & limitations
- Uses exact unit definitions from the Fidamen conversion library.
- Internal calculations use double precision; display rounding follows the unit's configured decimal places.
- Not a substitute for calibrated instruments in regulated contexts.
- Jurisdiction-specific rules may require official guidance.
Change log
v1.0.0 • 2025-11-03 • MINOR
Initial publication and governance baseline.
Why: Published with reviewed formulas, unit definitions, and UX controls.
Areas: engine, content, ui • Reviewer: Fidamen Standards Committee • Entry ID: 081d027840da