Cernarus

Call Option Calculator

This calculator provides a theoretical European call option price using the Black‑Scholes model plus primary Greeks and an expiration payoff module for scenario analysis. It supports position‑level P&L by specifying contract quantity and size.

Use the Black‑Scholes output for quick theoretical valuations, and the expiration payoff module to understand profit and breakeven at specific future spot scenarios. Enter market premium to compute realized payoff and ROI for your position.

Updated Nov 13, 2025

Computes Black‑Scholes theoretical call price and primary Greeks. Assumes European exercise, constant volatility and continuous dividends.

Inputs

Results

Updates as you type

Theoretical call price (Black‑Scholes)

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Delta

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Gamma

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Vega

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Theta

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Rho

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Position value (theoretical)

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OutputValueUnit
Theoretical call price (Black‑Scholes)—USD
Delta——
Gamma——
Vega——
Theta——
Rho——
Position value (theoretical)—USD
Primary result—

Visualization

Methodology

Black‑Scholes: the calculator implements the standard Black‑Scholes closed‑form formulas for European calls, including d1/d2, cumulative normal functions and analytic Greeks. Assumptions include constant volatility, continuous dividend yield and European exercise.

Numerical and software integrity: calculations are designed with attention to floating‑point stability and traceability. Implementation and testing should follow IEEE 754 for floating‑point handling and established software testing standards.

Security and quality management: implementations that handle user data or trade execution should follow NIST and ISO guidance for system security and operational controls; safety and workplace practices should respect applicable occupational safety standards.

Worked examples

Example: Spot 100, Strike 100, Premium 2.50, Vol 25% annual, Time 0.25 years, Rate 3%: Black‑Scholes outputs a theoretical price and Greeks; expiration payoff at ST=120 shows intrinsic 20.00 per option and profit = (20.00 - 2.50) × quantity × contract_size.

Expert Q&A

How accurate is the Black‑Scholes price compared with market quotes?

Black‑Scholes gives a theoretical price under its assumptions. Market prices reflect supply/demand, discrete dividends, early exercise possibilities, volatility skew and liquidity. Use implied volatility calibrated to observed option prices for closer alignment. Numeric precision follows IEEE floating point conventions; small rounding differences may occur.

Does this tool provide trading advice?

No. This tool is for educational and analytical purposes. It does not constitute financial, investment, tax or legal advice. Always validate results with market quotes and, if needed, a licensed professional.

What are the main limitations I should be aware of?

Key limitations: Black‑Scholes assumes constant volatility and interest rates, continuous dividend yield and European exercise. It does not model early exercise for American options, discrete dividends, complex payoff structures, or transaction costs.

What standards were used to guide development and testing?

Recommended practices referenced include IEEE floating point standard for numeric stability, NIST guidance for system and data security controls, and ISO standards for information security management and quality processes. Occupational safety considerations should follow applicable OSHA guidance where relevant to operations.

How should I calibrate volatility inputs?

Calibrate implied volatility by observing market option prices across strikes and expiries. For consistency check implied volatility against exchange or broker quotes, and consider using the mid‑market premium when available.

Sources & citations