EQUITY OPTIONS / RISK ANALYTICS

Option Risk Explain.

Daily P&L attribution for equity-option portfolios.

Break down an option desk’s daily change into Delta, Gamma, Vega, Theta, rates and valuation residuals. Inspect the contracts behind each exception.

Explore the demo Install Python package

Python API · CLI · Interactive report Synthetic data

DESK / SELECTED SCENARIO

Daily desk review

−$1,152 OBSERVED P&L · USD

POSITIONS05

EXCEPTIONS02

RECONCILIATION$0.00

View attribution

Choose a risk scenario

Switch between market moves and valuation checks.

MIXED EXPOSURES

Which factors explain the daily change?

SPY -0.9%, AAPL +1.2%

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SYNTHETIC DATA

Portfolio P&L

—

Observed P&L—

Positions—

Exceptions—

Reconciliation error—

P&L by risk factor

Negative contributions to the left; positive to the right

Reading the attribution

Greeks: opening sensitivities applied to the change in spot, implied volatility, rates and time.
Approximation residual: full BSM repricing less the Greek estimate. Includes higher-order effects.
Market/model basis: mark-to-market P&L less BSM repricing. Check valuation inputs and timestamps.
Coverage: fixed contract quantities and European BSM pricing. Exercise, settlements and trades are excluded.

Contract-level attribution

Contract	Contracts	Observed P&L	Greek explain	Approx. residual	Market/model basis	Flags

Exceptions

User-selected threshold

Contract	Check	Amount / action

The model assumes European exercise and unchanged positions. The regulatory FRTB P&L attribution test is outside its scope.

Custom portfolio analysisLocal Python server required

Upload two position snapshots to calculate a report for your own book. Contract identities, quantities and multipliers must match across both dates.

PYTHON / LOCAL-FIRST

Use the same engine in your own workflow.

Analyze fixed-position snapshots from Python, the CLI or the local browser.

Installation guide View source

OPTION PRICING

Black–Scholes model

Call and put prices, Greeks and spot-price sensitivity. Inputs stay in the browser.

CALL / MODEL PRICE C

—European call · per share

PUT / MODEL PRICE P

—European put · per share

MODEL SENSITIVITY / SPOT

Premium against spot

Call Put

The horizontal axis varies spot; all other parameters remain fixed. Curves are theoretical model values, not market prices.

FIRST- AND SECOND-ORDER RISK

Option Greeks

per share

Measure	Call	Put
Delta per 1-unit spot change	—	—
Gamma per unit of spot²	—	—
Vega per +1 vol. point	—	—
Theta per calendar day	—	—
Rho per +1 rate point	—	—

Greeks are unavailable at expiration or zero volatility, where standard smooth derivatives break down.

MARKET DATA

Yahoo option chains

Calls, puts, bid/ask, implied volatility and open interest from Yahoo Finance. Available when the Python server runs locally.

DATA PROVIDER / YAHOO FINANCE VIA YFINANCEChecking local data adapter…

Choose a symbol to retrieve its quote and expiration dates.

Yahoo data may be delayed or incomplete. Retrieval time is separate from the exchange quote timestamp.

For option-chain data, run python -m option_lab serve and open http://127.0.0.1:8765/. Static hosting supports the pricing model and four saved portfolio scenarios.

METHODOLOGY

Model assumptions

European option prices with continuous dividends. Scenario attribution uses opening Greeks and full model repricing.

BLACK–SCHOLES–MERTON

Closed-form pricing with continuous dividends

S is the underlying spot, K the exercise price, T the time in years, r the risk-free rate, q the dividend yield and σ the annualized volatility.

C = S e^−qT N(d₁) − K e^−rT N(d₂)

P = K e^−rT N(−d₂) − S e^−qT N(−d₁)

d₁ = [ln(S/K) + (r − q + σ²/2)T] / (σ√T); d₂ = d₁ − σ√T.

01 / EXERCISE

European contracts

Options are assumed exercisable only at expiration. This model does not include American early exercise.

02 / DATA BOUNDARY

Yahoo through the local API

The Streamlit-free Python adapter retrieves market quotes, listed expiration dates and call/put chains through yfinance. The public static GitHub Pages site is limited to theoretical pricing.

03 / INTERPRETATION

Theoretical prices

Constant volatility and rates, no transaction costs. Outputs are educational and are neither executable quotes nor trading recommendations.