I'd like to declare a function that will be part of the equation that I then want to plot. The equation that I want to plot is defined as
\frac{e^{-rT}N'(d_{2})}{S\sigma\sqrt{T}}
The function to be declared is the probability density function
N'\left (x \right )=\frac{1}{\sqrt{2\pi}}e^{-x^2/2}
where x should equal to d_2, and d_2 must also be declared by
d_{2}=\frac{ln(S/K)+(r-\frac{\sigma^2}{2})T}{\sigma\sqrt{T}})
If possible I'd like to be able to define K, r and sigma in advance, so that they can flow into above calculation as fixed values. For the values of S (x axis) and T (y axis) I want to take a different domains, e.g. for S a range 95 to 105, and for T a range 0.01 to 0.3. The overall result should be a surfaceplot where the results of the intial equation are on the z axis. Thanks a million, I hope so much that somebody can help me!
ADDITION: the code that was provided by @percusse works very well but when I try to modify it following the logic of its structure I get an error. Here is the modified code:
\documentclass{article}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}[
declare function={ Nprime(\x) = 1/(sqrt(2*pi))*exp(-0.5*(pow(\x,2)));
d1(\x,\y,\KK,\RR,\SIG) = (ln(\x/\KK)+(\RR+(pow(\SIG,2)/2)*\y))/(\SIG*(sqrt(\y)));
d2(\x,\y,\KK,\RR,\SIG) = (ln(\x/\KK)+(\RR-(pow(\SIG,2)/2)*\y))/(\SIG*(sqrt(\y)));
myfun(\x,\y,\KK,\RR,\SIG) = - (exp(-\RR*\y)*d1*Nprime(d2(\x,\y,\KK,\RR,\SIG))/(\y*(pow(\x,2))*(pow(\SIG,2))));
},
]
\begin{axis}[ y domain=0.01:0.3, domain=95:105,view={25}{20},
]
\addplot3[surf] {myfun(x,y,100,0,0.09)};
\end{axis}
\end{tikzpicture}
\end{document}
What am I doing wrong?
ONE MORE ADDITION: I have tried to swap the \y and \SIG values. Here is the code that does not work
\documentclass{article}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}[
declare function={ Nprime(\x) = 1/(sqrt(2*pi))*exp(-0.5*(pow(\x,2)));
d2(\x,\SIG,\KK,\RR,\y) = (ln(\x/\KK)+(\RR-(pow(\SIG,2)/2)*\y))/(\SIG*(sqrt(\y)));
myfun(\x,\SIG,\KK,\RR,\y) = exp(-\RR*\y)*Nprime(d2(\x,\SIG,\KK,\RR,\y))/(\x*\SIG*sqrt(\y));
},
]
\begin{axis}[
y domain=0.01:0.09, domain=95:105, view={25}{20},
]
\addplot3[surf] {myfun(x,SIG,100,0,0.04)};
\end{axis}
\end{tikzpicture}
\end{document}
What's wrong with it? Thanks a lot!
Best Answer
I don't know what it should look like but from the constants you have provided I get this