📊 Black‑Scholes Option Calculator

European options · Greeks · Sensitivity · Price curve
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📉 Sensitivity Analysis
Call Option Price $6.80

Option price vs underlying price (S).

📘 Quick Interpretation
  • Delta: Hedge ratio. Call delta ∈ (0,1), Put ∈ (-1,0).
  • Gamma: Delta's sensitivity. Highest near ATM.
  • Theta: Daily time decay (value / 365).
  • Vega: Impact of 1% vol change (value / 100).
  • Rho: Impact of 1% rate change (value / 100).
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📘 What is the Black‑Scholes Model?

The Black‑Scholes model provides a theoretical estimate of the price of European‑style options. It assumes constant volatility and risk‑free rate. Use this calculator to understand how option prices and Greeks change with underlying price, volatility, and time.

❓ Frequently Asked Questions

What are the Greeks used for?

Delta measures directional risk, Gamma measures delta stability, Theta measures time decay, Vega measures volatility sensitivity, Rho measures interest rate exposure.

Why does Theta appear negative?

Options lose value as expiration approaches (time decay). Theta is typically negative for long option positions.

What is a reasonable volatility input?

For stocks, 15‑40% is common. For indices, 10‑25%. Use implied volatility from the market for accurate pricing.

Does this model work for American options?

The Black‑Scholes model is designed for European options. American options may have slightly higher values due to early exercise premium.