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The Black-Scholes model is a mathematical formula for pricing European-style options. It calculates a theoretical fair value based on stock price, strike price, time to expiry, volatility, and risk-free rate.

公式

C = S×N(d₁) − K×e^(−rT)×N(d₂) | d₁=(ln(S/K)+(r+σ²/2)T)/(σ√T)

S: Current stock price (Currency)
K: Strike price (Currency)
T: Time to expiration (Years)
r: Risk-free interest rate (Annual %)
σ: Volatility (Annual %)

ステップバイステップガイド

1Call = S·N(d1) - K·e^(-rT)·N(d2)
2d1 = [ln(S/K) + (r + sigma^2/2)T] / (sigma*sqrt(T))
3d2 = d1 - sigma*sqrt(T)
4N() is the cumulative standard normal distribution

解いた例

入力

Stock $100, strike $105, 6mo, 5% rate, 20% vol

結果

Call approx $4.08, Put approx $6.65

よくある質問

What is Black Scholes Calc?

How accurate is the Black Scholes Calc calculator?

The calculator uses the standard published formula for black scholes calc. Results are accurate to the precision of the inputs you provide. For financial, medical, or legal decisions, always verify with a qualified professional.

What units does the Black Scholes Calc calculator use?

This calculator works with inches. You can enter values in the units shown — the calculator handles all conversions internally.

What formula does the Black Scholes Calc calculator use?

The core formula is: Call = S·N(d1) - K·e^(-rT)·N(d2). Each step in the calculation is shown so you can verify the result manually.

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