Mrthfx

I found this image on a presentation.

I am working on MWE but I was wondering if you had ever come through that type of representation with a projection on the 3d graph ?
It could look quite like TeXexample but impossible to adapt to real data so far. MWE to follow.
The green graph is projected on the 3D graph (transformation) and projected on the axis below.

Following @marmot answer, I adapted the code with the correct 3D functions (Call).

    documentclass[tikz,border=3.14mm]{standalone}

usepackage{pgfplots}

pgfplotsset{compat=1.12}



%--------  Brownian motion in 2D only--------------------------

newcommand{BM}[5]{

    % points, advance, rand factor, options, end label

    draw[#4] (0,0)

    foreach x in {1,...,#1}

    {   -- ++(#2,rand*#3) coordinate (aux-x) % <- added coordinate names

}

node[right] {#5};

   }



   begin{document}

   begin{tikzpicture}[scale=1.8,   declare function={ 

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

    normcdf(x,m,SIG) = 1/(1 + exp(-0.07056*((x-m)/SIG)^3 - 1.5976*(x-m)/SIG));

    d2(x,y,KK,RR,SIG) = (ln(x/KK)+(RR-(pow(SIG,2)/2)*y))/(SIG*(sqrt(y)));

    d1(x,y,KK,RR,SIG) = d2(x,y,KK,RR,SIG) + (SIG*(sqrt(y)));

    Call(x,y,KK,RR,SIG) = x*normcdf(d1(x,y,KK,RR,SIG),0,1)-KK*exp(-RR*y)*normcdf(d2(x,y,KK,RR,SIG),0,1); 

       Brownian(x)=100*sin(x*100)+0.2*cos(567*x); %% I'd like to generate a  function brownian motion, starting at 100 with a sig standard deviation

    }

    ]

        begin{axis}[view={20}{20},axis on top,xlabel=$S$,ylabel=Time,zlabel=Option 

   price,mesh/interior colormap name=hot,colormap/hot,3d box=complete,grid,grid 

   style={thin,gray!40},axis line style={gray!40}]



    % I fix the following parameters of the Call function

    defKK{100}

    defTT{0.5}

    defRR{0}

    defSIG{0.15}



    %addplot3[domain=50:150,samples y=1,samples=51,blue] (x,{g(x)},Call(0,1,KK,RR,SIG)});  %am doing something wrong here

    addplot3[line width=0.5pt,surf, opacity=0.25, shader=flat,y 

    domain=0.1:1,domain=50:150] {Call(x,y,KK,RR,SIG)};

    addplot3[domain=50:150,samples y=1,samples=51] (x,{g(x)}, 

   {Call(x,g(x),KK,RR,SIG)});

     addplot3[domain=50:150,samples y=1,samples=51,red] (x,{1}, 

   {Call(x,g(x),KK,RR,SIG)}); %am doing something wrong here too

    end{axis}

    end{tikzpicture} 

    end{document}

If you have a function, you can do the projections by, well, projecting the result.

documentclass[tikz,border=3.14mm]{standalone}

usepackage{pgfplots}

pgfplotsset{compat=1.16}

begin{document}

begin{tikzpicture}[scale=1.8,declare function={f(x,y)=exp(0.1*y);

g(x)=sin(x*100)+0.2*cos(567*x);}]

begin{axis}[view={45}{40},axis on top,

xlabel=$x$,ylabel=$y$,

mesh/interior colormap name=hot,

colormap/hot]

 addplot3[domain=0:5,samples y=1,samples=51,blue] (x,{g(x)},{f(0,-2.5)});

 addplot3[domain=0:5,domain y=-2.5:2.5,surf,shader =faceted interp,opacity=0.5]

 {f(x,y)};

 addplot3[domain=0:5,samples y=1,samples=51] (x,{g(x)},{f(x,g(x))});

 addplot3[domain=0:5,samples y=1,samples=51,red] (x,{-2.5},{f(x,g(x))});

end{axis}

end{tikzpicture} 

end{document}