Fidamen

Rho Calculator (Options)

This calculator computes the Rho of a European option under the Black‑Scholes framework. Rho is the partial derivative of the option price with respect to the continuously compounded risk‑free interest rate and expresses how the option price changes when rates move.

The tool returns the Black‑Scholes call price and both call and put Rho values expressed per unit change in the annual rate (i.e. per 1.0 = 100 percentage points) and per one percentage point change (multiply per unit by 0.01). Use inputs for underlying price, strike, days to expiry, annual volatility, risk‑free rate and dividend yield.

Updated Nov 25, 2025QA PASS — golden 25 / edge 120Run golden-edge-2026-01-23

Governance

Record 86f89b471886 • Reviewed by Fidamen Standards Committee

Inputs

Results

Updates as you type

Black‑Scholes call price

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Call Rho (change in price per 1.0 = 100% point change in r)

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Call Rho (per 1 percentage point change in r)

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Put Rho (change in price per 1.0 = 100% point change in r)

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Put Rho (per 1 percentage point change in r)

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OutputValueUnit
Black‑Scholes call price—USD
Call Rho (change in price per 1.0 = 100% point change in r)—USD
Call Rho (per 1 percentage point change in r)—USD
Put Rho (change in price per 1.0 = 100% point change in r)—USD
Put Rho (per 1 percentage point change in r)—USD
Primary result—

Visualization

Methodology

Calculations use the Black‑Scholes closed‑form expressions for European options. Key assumptions: lognormal asset returns, constant volatility and interest rates, continuous dividend yield, and European exercise (no early exercise).

Rho is calculated analytically from the Black‑Scholes formula: for a call C, rho = ∂C/∂r = K * T * exp(-rT) * N(d2). For a put P, rho = ∂P/∂r = -K * T * exp(-rT) * N(-d2). The calculator exposes both the per‑unit and per‑one‑percentage‑point versions.

F.A.Q.

Is this Rho valid for American options or options on futures?

No. The formula implemented is the Black‑Scholes closed form for European options on underlying assets with continuous dividend yield. American options and certain futures options require different models (binomial, finite difference, or Black 76). Use models appropriate to exercise style and underlying.

What are the main limitations of the Black‑Scholes Rho?

It assumes constant volatility and interest rates and no early exercise; Rho reflects sensitivity for small instantaneous changes in the risk‑free rate under those assumptions. Large rate moves, stochastic rates, discrete dividends, or volatility skew will make results approximate.

How should I interpret Rho per percentage point versus per unit?

Rho per unit is the derivative ∂price/∂r when r is expressed as a decimal (e.g., change per 1.0 = 100 percentage points). Rho per 1 percentage point multiplies that derivative by 0.01 and shows the expected price change for a 1 percentage‑point (100 basis points) change in the annual rate.

How can I improve accuracy for traded instruments?

Calibrate implied volatility from market option prices for matching strike and tenor, use market yields for the risk‑free curve and account for discrete dividends if material. Consider Monte Carlo or local volatility models when path‑dependent or early exercise features are present.

Are results guaranteed to be exact?

No. Results are mathematically correct under Black‑Scholes assumptions but subject to input quality, numerical precision, and model limitations. See accuracy and compliance notes below.

Sources & citations

Further resources

Versioning & Change Control

Audit record (versions, QA runs, reviewer sign-off, and evidence).

Record ID: 86f89b471886

What changed (latest)

v1.0.0 • 2025-11-25 • 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 25, 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 • 2025-11-25 • 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: a879c58e00e7