Option Pricing Calculator

Estimate call and put option value, delta, gamma, and vega from market and volatility assumptions.

Black-Scholes inputs

Estimate European call and put value from price, strike, time, volatility, rates, and dividends.

Call value

$5.5482

Put value

$8.9678

Call delta

0.4568

Put delta

-0.5382

Gamma

0.022337

Vega

0.2792

Price change for one volatility point.

Call time value

$5.5482

Put time value

$3.9678

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What is the option pricing calculator?

This calculator prices European call and put options with the Black-Scholes model and reports Greeks for sensitivity analysis. It can be used for stocks, equity indexes, and commodities, including KOSPI200-style option analysis.

Black-Scholes model

Model background and assumptions

  • Black-Scholes was developed by Fischer Black and Myron Scholes in 1973.
  • Scholes later received the 1997 Nobel Prize in Economics for this work; Black had died before the award.
  • The model assumes geometric Brownian motion, constant volatility, constant risk-free rate, no transaction cost or tax, unrestricted short selling, and no arbitrage.
  • It is designed for European options. American options require adjustment because early exercise can matter.

Core formulas

  • Call price = S x e^(-qT) x N(d1) - K x e^(-rT) x N(d2).
  • Put price = K x e^(-rT) x N(-d2) - S x e^(-qT) x N(-d1).
  • S is underlying price, K is strike, T is time to maturity, r is risk-free rate, q is dividend yield, sigma is volatility, and N(x) is the standard normal cumulative distribution.
  • Implied volatility reverses the formula from a market option price, and the Korean source notes Newton-Raphson as the numerical method.

Greeks and strategies

Greeks

  • Delta shows option-price change for a 1 unit underlying move. Call delta runs from 0 to 1, while put delta runs from -1 to 0.
  • Gamma measures how delta changes as the underlying moves and is highest near at-the-money options, especially near expiry.
  • Theta measures time decay per day and is usually a cost for option buyers.
  • Vega measures the impact of a 1 percentage point implied-volatility move and is largest for at-the-money and longer-dated options.
  • Rho measures the impact of a 1 percentage point risk-free-rate move and matters more for longer maturities.

KOSPI200 market references

  • KOSPI200 option volatility is described as commonly around 15% to 30%, but it changes sharply with market stress.
  • KOSPI200 dividend yield is referenced around 2% in 2026, which lowers call value and raises put value relative to a no-dividend model.
  • KOSPI200 option contract multiplier is KRW 250,000, minimum tick is 0.01 point, tick value is KRW 2,500, regular trading is 09:00 to 15:45, and expiry-day trading ends at 15:20.
  • Long call has max loss equal to premium and unlimited upside. Long put has max loss equal to premium and max profit equal to strike minus premium. Covered call caps upside, and straddle needs a large move to cover both premiums.