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What is Black-Scholes Options Pricing?

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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.

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सूत्र

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

Variable Legend

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प्रतीकनावएककवर्णन
SCurrent stock priceCurrency—
KStrike priceCurrency—
TTime to expirationYears—
rRisk-free interest rateAnnual %—
σVolatilityAnnual %—

How to Black-Scholes Options Pricing

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

Worked Examples

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Example 1
Given:Stock $100, strike $105, 6mo, 5% rate, 20% vol
परिणाम:Call approx $4.08, Put approx $6.65

Real-World Applications

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Pricing European call/put options

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Hedging equity risk

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Valuing executive stock options

Frequently Asked Questions

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Q

What is Black Scholes Calc?

A

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

Q

How accurate is the Black Scholes Calc calculator?

A

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.

Q

What units does the Black Scholes Calc calculator use?

A

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

Q

What formula does the Black Scholes Calc calculator use?

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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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Pro Tip

Black-Scholes assumes constant volatility. Traders use the implied volatility smile for real-world corrections.

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Did you know?

Scholes and Merton won the 1997 Nobel Prize in Economics. Black had passed away in 1995.

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Deep Dive

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Reviewed October 2026
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