Greeks Calculator
Black-Scholes pricing with real-time Greeks — NSE/BSE options
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Last calc: 17:41:22 IST
Input Parameters
Premium Analysis
NIFTY 24900 CE · 19-Jun-2026BS Fair Value
₹191.84
Market Price
₹187.30
Intrinsic
₹0.00
Time Value
₹187.30
Mispricing:₹-4.54(-2.37%)Market trading below BS value — potential buy
Moneyness
OTMOut of the Money
Distance₹52.5 (0.21%)
Deep ITMATMDeep OTM
Options Greeks
Delta Impact on Your Position
+₹36.17 per lot per ₹1 move
NIFTY needs to move +52.5 pts to offset overnight Theta decay
Premium Impact at Spot Levels
Step 1 — Input Variables
S
Spot Price
₹24,847.50
K
Strike Price
₹24,900.00
T
Time to Expiry
8d = 0.02192 yr
r
Risk-Free Rate
6.50% p.a.
σ
Implied Vol
14.85% p.a.
Step 2 — Compute d₁ and d₂
d₁ Formula
d₁ = [ln(S/K) + (r + σ²/2) · T] / (σ · √T)
= [ln(24847.5/24900) + (0.0650 + 0.01103) × 0.02192]
/ (0.1485 × √0.02192)
= [ln(0.99789) + 0.001666]
/ 0.02198
= [-0.00211 + 0.001666] / 0.02198
d₁ = -0.0202
d₂ Formula
d₂ = d₁ − σ · √T
= -0.0202 − 0.1485 × √0.02192
= -0.0202 − 0.02198
d₂ = -0.0422
Normal CDF values:
N(d₁) = N(-0.0202) = 0.4886
N(d₂) = N(-0.0422) = 0.4762
N(−d₁) = 0.5114 N(−d₂) = 0.5238
Step 3 — Black-Scholes Option Price
Call Price (C)
ActiveC = S · N(d₁) − K · e^(−rT) · N(d₂)
= 24847.5 × 0.4886 − 24900 × e^(−0.0650×0.02192) × 0.4762
= 12140.46 − 24900 × 0.99858 × 0.4762
= 12140.46 − 11840.69
C = ₹299.77
Put Price (P)
P = K · e^(−rT) · N(−d₂) − S · N(−d₁)
= 24900 × 0.99858 × 0.5238 − 24847.5 × 0.5114
= 13023.86 − 12707.04
P = ₹316.82
Put-Call Parity: C − P = S − K·e^(−rT) = -17.05
Step 4 — Greeks Derivation
Δ
Delta
∂C/∂SΔ Call = N(d₁)
Δ Put = N(d₁) − 1
N(d₁) = N(-0.0202) = 0.4886
Δ Call = 0.4886
Δ Put = -0.5114
₹1 move in spot → premium changes by Δ. Call Δ ∈ [0,1], Put Δ ∈ [−1,0].
Γ
Gamma
∂²C/∂S²Γ = φ(d₁) / (S · σ · √T)
φ(d₁) = φ(-0.0202) = 0.39886
= 0.39886 / (24847.5 × 0.1485 × √0.02192)
= 0.39886 / 546.2705
Γ = 0.000730
Rate of Delta change per ₹1 move. Same for Call & Put.
Θ
Theta
∂C/∂TΘ = −[S·φ(d₁)·σ/(2√T) + r·K·e^(−rT)·N(d₂)] / 365
Part A = 24847.5×0.39886×0.1485 / (2×√0.02192)
= 4970.5216
Part B = 0.0650×24900×0.99858×0.4762
= 769.6448
Θ Call = -15.7265/day
Θ Put = -11.2985/day
Daily time decay. Negative for long options — premium erodes each day.
ν
Vega
∂C/∂σν = S · φ(d₁) · √T / 100
= 24847.5 × 0.39886 × √0.02192 / 100
= 24847.5 × 0.39886 × 0.14805 / 100
= 1467.2450 / 100
ν = 14.6724
Premium change per 1% IV move. Same for Call & Put.