Black-Scholes Model
★★★★★Graduate+
📖Definition
Black-Scholes model calculates theoretical prices of European options. Based on stochastic calculus.
📐Formulas
C = S₀ N(d₁) - Ke^-rTN(d₂)
Call option price
d₁ = (ln(S₀/K) + (r + σ²/2)T)/(σ√T)
d₁ calculation
d₂ = d₁ - σ√T
d₂ calculation
(∂ V)/(∂ t) + (1)/(2)σ² S² (∂² V)/(∂ S²) + rS(∂ V)/(∂ S) - rV = 0
Black-Scholes PDE
✏️Examples
예제 1
S=100, K=100, r=5%, σ=20%, T=1. Call price?
📜History
Discovered by: Fischer Black, Myron Scholes (1973)
Scholes and Merton won 1997 Nobel Prize in Economics.
⚡Applications
Derivatives
Option pricing
Risk Management
Greeks calculation
Volatility
Implied volatility estimation
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