Black-Scholes model
The Black-Scholes formula prices European options using spot (S), strike (K), time to expiry (T), risk-free rate (r), volatility (σ), and optional dividend yield (q):
- d₁ = [ln(S/K) + (r − q + σ²/2)T] / (σ√T)
- d₂ = d₁ − σ√T
- Call = S·e⁻qT·N(d₁) − K·e⁻rT·N(d₂)
- Put = K·e⁻rT·N(−d₂) − S·e⁻qT·N(−d₁)
Indian index options (Nifty, Bank Nifty, Sensex) are European-style—exercisable only at expiry—so this model is commonly used for theoretical pricing and Greeks. Theta is per day; Vega and Rho are per 1% change in volatility and interest rate.
Greeks
Delta: sensitivity to ₹1 move in spot. Gamma: rate of change of delta. Theta: time decay per day. Vega: sensitivity to 1% change in implied volatility. Rho: sensitivity to 1% change in interest rate.