Derivatives & Options
Black-Scholes pricing, option Greeks (Delta, Gamma, Theta, Vega, Rho), put-call parity, and futures margin.
Black-Scholes Pricing
d₁, d₂
d₁ = [ln(S/K) + (r + σ²/2)T] / (σ√T) d₂ = d₁ − σ√T
- S — Spot (₹)
- K — Strike (₹)
- r — Risk-free rate (decimal)
- σ — Volatility (decimal)
- T — Time to expiry (years)
Call
C = S·N(d₁) − K·e⁻ʳᵀ·N(d₂)
Put
P = K·e⁻ʳᵀ·N(−d₂) − S·N(−d₁)
Put-Call Parity
C − P = S − K·e⁻ʳᵀ
Option Greeks
| Greek | Call | Put |
|---|---|---|
| Delta (Δ) | N(d₁) | N(d₁) − 1 |
| Gamma (Γ) | φ(d₁) / (S·σ·√T) | Same as call |
| Theta (Θ) | −S·φ(d₁)·σ/(2√T) − rK·e⁻ʳᵀ·N(d₂) | −S·φ(d₁)·σ/(2√T) + rK·e⁻ʳᵀ·N(−d₂) |
| Vega (V) | S·φ(d₁)·√T | Same as call |
| Rho (ρ) | K·T·e⁻ʳᵀ·N(d₂) | −K·T·e⁻ʳᵀ·N(−d₂) |
Related calculator
Option Greeks
Compute Black-Scholes Delta, Gamma, Theta, Vega, and Rho for equity options.
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