Quantitative Derivatives
Pure Edge Computation
Black-Scholes European Option Valuation & Greeks Calculator
Models European options contract pricing and sensitivities (Delta, Gamma, Vega, Theta, Rho) under the Black-Scholes continuous differential framework.
Formula:
C = S * e^(-q*T) * N(d1) - K * e^(-r*T) * N(d2); Delta = e^(-q*T) * N(d1); Gamma = e^(-q*T) * phi(d1) / (S * sigma * sqrt(T))
Model Parameters
Outputs & Underwriting Summary
Calculation Status
ANALYTIC GREEKS RESOLVED
Verified Model
European Call Premium
$10.45
Call Delta: 0.637 | Daily Theta: $-0.018/day
European Put Premium
$5.57
Put Delta: -0.363 | Gamma: 0.0188 | Vega: $0.375/1% vol
European Option (S=$100.00, K=$100.00, T=1.0y, vol=20%): Call = $10.45 (Delta +0.637), Put = $5.57 (Delta -0.363). Gamma is 0.0188, Vega is $0.38 per 1% vol, Daily Theta decay is $-0.018/day.
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