European Option Black-Scholes Calculator
Price a European call or put with the Black-Scholes-Merton model using continuous rates and dividend yield; the model assumes constant volatility and exercise only at expiration.
Description
Price a European call or put with the Black-Scholes-Merton model using continuous rates and dividend yield; the model assumes constant volatility and exercise only at expiration.
European Option Black-Scholes Calculator: Price a European call or put with the Black-Scholes-Merton model using continuous rates and dividend yield; the model assumes constant volatility and exercise only at expiration.
When to use European Option Black-Scholes
Use this financial calculation for a transparent scenario, ratio, valuation, pricing, or cash-flow estimate when all amounts, dates, rates, and compounding conventions are defined consistently.
- Spot price
- Required number input.
- Strike price
- Required number input.
- Time to expiration (years)
- Required number input.
- Continuously compounded risk-free rate (%)
- Required number input.
- Continuous dividend yield (%)
- Required number input.
- Annualized volatility (%)
- Required number input.
- Option type
- Required string input.
How European Option Black-Scholes works
Price a European call or put with the Black-Scholes-Merton model using continuous rates and dividend yield; the model assumes constant volatility and exercise only at expiration. The tool evaluates the supplied inputs together and returns the named outputs below; it does not infer omitted operating conditions or change the units shown.1
- Option price
- The resulting option price returned as a number.
- d1
- The resulting d1 returned as a number.
- d2
- The resulting d2 returned as a number.
Limitations and assumptions
- Option values depend on contract terms and model assumptions for volatility, rates, dividends, exercise, barriers, monitoring, discretization, and underlying dynamics. Black–Scholes and small trees can misprice early exercise, jumps, smiles, path dependence, and illiquid contracts.
- Use finite inputs in the displayed units and preserve more precision than the final presentation requires. Independently verify safety-critical, financial, compliance, or production decisions.
Alternative or Complementary approaches
Test multiple scenarios, reconcile rates and cash-flow dates, retain full precision, and verify contractual, tax, market, and accounting inputs with current primary documents or qualified advice.
References
-
Option (finance) — Wikipedia contributors
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