Cfrgtkky

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})}{Ssigmasqrt{T}}

The function to be declared is the probability density function

N'left (x  right )=frac{1}{sqrt{2pi}}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}{sigmasqrt{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!

I don't know what it should look like but from the constants you have provided I get this

documentclass{article}

usepackage{pgfplots}

begin{document}



begin{tikzpicture}[

declare function={ Nprime(x)                 = 1/(sqrt(2*pi))*exp(-0.5*(pow(x,2))); 

                   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)*Nprime(d2(x,y,KK,RR,SIG))/(x*SIG*sqrt(y));

                 },

]

begin{axis}[y domain=0.01:0.3,domain=95:105,view={150}{20}]

addplot3[surf] {myfun(x,y,100,0,0.09)};

end{axis}

end{tikzpicture}





end{document}