Black Scholes Calculator
Graph 2D 3D
Option Call Put
Nb steps (x, y)
x y input min max
Spot = \(S\) from to
Strike = \(K\) from to
Mat (y) = \(T\) from to
Vol (%) = \(\sigma\) from to
Rate (%) = \(r\) from to
Div (%) = \(q\) from to

Status: Missing input

z axis output
\(d_1\) =
\(N(d_1)\) =
\(N(-d_1)\) =
\(N'(d_1)\) =
\(d_2\) =
\(N(d_2)\) =
\(N(-d_2)\) =
\(N'(d_2)\) =
\(e^{-rT}\) =
\(e^{-rT}K\) =
\(V\) =
\(\Delta\) =
\(\Gamma\) =
\(\nu\) =
\(\Theta\) =
\(\rho\) =
\(voma\) =
\(Payoff\) =
\(e^{-rT}Payoff\) =



Reference
\[Option\] \[Call\] \[Put\]
\[Payoff\] \[Max(0, S-K)\] \[Max(0, K-S)\]
\[Value=V\] \[Se^{-qT}N(d_1)-Ke^{-rT}N(d_2)\] \[Ke^{-rT}N(-d_2)-Se^{-qT}N(-d_1)\]
\[\Delta=\frac{\partial V}{\partial S}\] \[e^{-qT}N(d_1)\] \[-e^{-qT}N(-d_1)\]
\[\Gamma=\frac{\partial \Delta}{\partial S}\] \[e^{-qT}\frac{N'(d_1)}{S\sigma\sqrt{T}}\]
\[\nu=\frac{\partial V}{\partial \sigma}\] \[Se^{-qT}N'(d_1)\sqrt{T}=Ke^{-rT}N'(d_2)\sqrt{T}\]
\[\Theta=-\frac{\partial V}{\partial T}\] \[-e^{-qT}\frac{SN'(d_1)\sigma}{2\sqrt{T}}-rKe^{-rT}N(d_2)+qSe^{-qT}N(d_1)\] \[-e^{-qT}\frac{SN'(d_1)\sigma}{2\sqrt{T}}+rKe^{-rT}N(-d_2)-qSe^{-qT}N(-d_1)\]
\[\rho=\frac{\partial V}{\partial r}\] \[KTe^{-rT}N(d_2)\] \[-KTe^{-rT}N(-d_2)\]
\[Voma=\frac{\partial \nu}{\partial \sigma}\] \[Se^{-qT}N'(d_1)\sqrt{T}\frac{d_1 d_2}{\sigma}\]
\[\frac{\partial V}{\partial t} + rS\frac{\partial V}{\partial S} + \frac{1}{2}\sigma^2S^2\frac{\partial^2 V}{\partial S^2}=rV\]
\[d_1=\frac{\log(S/K) + (r-q +\sigma^2/2)T}{\sigma \sqrt{T}}\]
\[d_2=\frac{\log(S/K) + (r-q -\sigma^2/2)T}{\sigma \sqrt{T}}=d_1 - \sigma \sqrt{T}\]
\[N(x)=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{x} e^{-\frac{t^{2}}{2}}dt\]
\[N'(x)=\frac{1}{\sqrt{2\pi}}e^{-\frac{x^{2}}{2}}\]