Option Greeks Live Prediction
Black-ScholesAll 5 Greeks with formulas, step-by-step derivation, and live sensitivity predictions
Live Inputs
Δ
Delta
0.4886
CE
Γ
Gamma
0.000730
CE
Θ
Theta
-15.7265
CE
ν
Vega
14.6724
CE
ρ
Rho
2.5952
CE
Δ Call = N(d₁) | Δ Put = N(d₁) − 1
Rate of change of option price per ₹1 move in underlying. Call Δ ∈ [0,1], Put Δ ∈ [−1,0].
Step-by-Step Calculation
1.d₁ = -0.0202
2.N(d₁) = N(-0.0202) = 0.4886
3.Δ Call = 0.4886 → ₹1 spot move ≈ ₹0.49 premium change
4.Δ Put = -0.5114 → ₹1 spot move ≈ ₹-0.51 premium change
Live Prediction: ₹1 spot move → premium +0.49
| Spot | Δ Spot | Call Price | Put Price | Delta (Δ) | Gamma (Γ) | Theta (Θ)/day | Vega (ν)/1% |
|---|---|---|---|---|---|---|---|
| 24647.5 | -200 | ₹199.74 | ₹416.79 | 0.2917 | 0.000683 | -13.7770 | 13.5028 |
| 24697.5 | -150 | ₹224.27 | ₹391.33 | 0.3379 | 0.000703 | -14.4059 | 13.9631 |
| 24747.5 | -100 | ₹249.25 | ₹366.31 | 0.3867 | 0.000718 | -14.9472 | 14.3164 |
| 24797.5 | -50 | ₹274.47 | ₹341.52 | 0.4372 | 0.000727 | -15.3902 | 14.5546 |
| 24847.5 | Current | ₹299.77 | ₹316.82 | 0.4886 | 0.000730 | -15.7265 | 14.6724 |
| 24897.5 | +50 | ₹325.08 | ₹292.13 | 0.5401 | 0.000727 | -15.9504 | 14.6677 |
| 24947.5 | +100 | ₹350.41 | ₹267.47 | 0.5909 | 0.000718 | -16.0588 | 14.5413 |
| 24997.5 | +150 | ₹375.87 | ₹242.92 | 0.6400 | 0.000703 | -16.0517 | 14.2970 |
| 25047.5 | +200 | ₹401.62 | ₹218.67 | 0.6869 | 0.000683 | -15.9319 | 13.9415 |
* Highlighted row = current spot. All Greeks recalculated at each spot level using Black-Scholes.
Greeks Summary — All Values
| Greek | Symbol | Formula | Call Value | Put Value | Interpretation |
|---|---|---|---|---|---|
| Delta | Δ | N(d₁) / N(d₁)−1 | 0.4886 | -0.5114 | ₹1 spot → ₹0.49 call / ₹-0.51 put |
| Gamma | Γ | φ(d₁)/(S·σ·√T) | 0.000730 | 0.000730 | Δ changes by 0.000730 per ₹1 |
| Theta | Θ | [−S·φ·σ/(2√T)−rKe^(−rT)N(d₂)]/365 | -15.7265 | -11.2985 | ₹15.73/day call decay |
| Vega | ν | S·φ(d₁)·√T/100 | 14.6724 | 14.6724 | ₹14.67 per 1% IV change |
| Rho | ρ | K·T·e^(−rT)·N(d₂)/100 | 2.5952 | -2.8545 | ₹2.5952 per 1% rate change |