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I found this image on a presentation. enter image description here 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}
   \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)= ; %% I'd like to generate a  function brownian motion, starting at 100 with a \sig standard deviation over time
    }
    ]
        \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
    \def\KK{100}
    \def\TT{0.5}
    \def\RR{0}
    \def\SIG{0.15}

    \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)};
    \end{axis}
    \end{tikzpicture} 
    \end{document}

What I try to reach

JeT
  • 3,020
  • The projection of the red graph (yielding the cyan and blue graphs) is almost trivial: just set the y or z coordinate to zero. What's not trivial is to guess the red graph from your screen shot. So please add an MWE. An example, though in a slightly different context, can be found here. Yet this is unlikely the only example of this kind. –  Oct 24 '18 at 00:43

2 Answers2

5

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}

enter image description here

Similarly for the Brownian motion.

\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);}]
\pgfmathsetseed{42}
 \foreach \X in {0,...,50}
 {
 \ifnum\X=0
  \pgfmathsetmacro{\Y}{rand}
  \pgfmathsetmacro{\myf}{f(\X/10,\Y)}
  \xdef\LstBottom{(\X/10,{\Y},{0.31})}
  \xdef\LstOnSurf{(\X/10,{\Y},\myf)}
  \xdef\LstFront{(\X/10,{-2.5},\myf)}
 \else
  \pgfmathsetmacro{\Y}{\LastY+0.3*rand}
  \pgfmathsetmacro{\myf}{f(\X/10,\Y)}
  \xdef\LstBottom{\LstBottom (\X/10,{\Y},{0.31})}
  \xdef\LstOnSurf{\LstOnSurf (\X/10,{\Y},\myf)}
  \xdef\LstFront{\LstFront (\X/10,{-2.5},\myf)}
 \fi
 \xdef\LastY{\Y}}
 \begin{axis}[view={45}{40},axis on top,zmin=0.3,
 xlabel=$x$,ylabel=$y$,
 mesh/interior colormap name=hot,
 colormap/hot]
  \addplot3[domain=0:5,samples y=1,samples=51,blue] coordinates {\LstBottom};
  \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] coordinates {\LstOnSurf};
  \addplot3[domain=0:5,samples y=1,samples=51,red] coordinates {\LstFront};
 \end{axis}
\end{tikzpicture} 
\end{document}

enter image description here

  • I finally found a way to input the correct functions in MWE. I am no far from a solution. Instead of the g function of cosinus, i'd rather generate a brownian motion. It would be projected on the Call function, and projected again in the frame (time, option value). I feel the magic will happen ! – JeT Mar 03 '19 at 23:54
  • I accepted the answer. Unfortunately I am stuck on the projections :s – JeT Mar 04 '19 at 08:53
  • 1
    @Julien-ElieTaieb I think I misread your above comment, sorry! I read it as you could achieve what you wanted. Rereading it: you want a Brownian motion, right? In any case, I added one. –  Mar 05 '19 at 06:16
  • Merci @Marmot :) I'm going to apply your code to my functions and post an update once I have the solution. – JeT Mar 05 '19 at 12:59
  • I think I reached my ceiling in tikz :( I tried to adapt you code so that the brownian motion evolves with time on (x,y) , is then projected on the Call(x,y,\100,0.00, 0.15) (surf) function and is then projected on the (y, z) plane as in the graph I updated. But I got stuck 3h trying to adjust the domains and the definition of the brownian. No success. – JeT Mar 05 '19 at 23:20
  • 2
    @Julien-ElieTaieb You can always ask a new, separate question. One reason why you may not manage to achieve what you want may be that information does not come in small, well-defined pieces. This site lives from small well-defined questions getting clear answers. Your original question was well-defined. Then you wanted a Brownian motion instead, and fine, I added it. Now comes another request. What about those who may be wondering about your very first question? Don't you think they get overwhelmed by a lengthy answer? Please ask a new question. (Anyway, I will be offline for a bit.) –  Mar 06 '19 at 01:26
  • Understood marmot :) I thought that my comments and complements to the initial MWE actually helped the future reader to get the initial question and a solution to it in a shorter manner. – JeT Mar 06 '19 at 12:07
0

Thanks to Marmot answer I could achieve what I wanted. Many parameters to play with to see the deformations. enter image description here

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.15}
\usepackage{ifthen}


\tikzset{
    declare function={ 
        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); 
    }
}

\def\Type{Call} \def\KK{100}    \def\RR{0}  \def\SIG{0.1}   \def\LastS{120} 
\def\ViewX{260} \def\ViewY{30}  
\def\NbPoint{50}

\begin{document} 

\begin{tikzpicture}

    \pgfmathsetseed{4}

    \tikzset{
        TermPoint/.style={mark=ball, mark options={ball color=black,mark size=2}},
        LastPoint/.style={draw=none,mark=ball,mark size=5pt,mark options={ball color = red},mark repeat={\NbPoint}},
        LastPointPayOff/.style={draw=blue!60, mark=ball, mark size=2pt, mark options={ball color = blue}, mark repeat={\NbPoint}},
    }



    \foreach \T in {0,...,\NbPoint}
    {
        \ifnum\T=0
            \pgfmathsetmacro{\S}{\LastS}
            \pgfmathsetmacro{\myf}{\Type(\S,{\T/10+0.005},\KK,\RR,\SIG))}
            \xdef\LstBottom{(\T/10,{\S},{0.0})}
            \xdef\LstOnSurf{(\T/10,{\S},\myf)}
            \xdef\LstFront{(\T/10,{50},\myf)}
        \else
            \pgfmathsetmacro{\S}{\LastS+2*(rand+rand+rand+rand+rand)}
            \pgfmathsetmacro{\myf}{\Type(\S,{\T/10+0.005},\KK,\RR,\SIG))}
            \xdef\LstBottom{\LstBottom (\T/10,{\S},{00})}
            \xdef\LstOnSurf{\LstOnSurf (\T/10,{\S},\myf)}
            \xdef\LstFront{\LstFront (\T/10,{50},\myf)}
        \fi
        \xdef\LastS{\S}
    }


    \begin{axis}[
            view={\ViewX}{\ViewY},
            axis on top,
            xlabel=Time to maturity,
            ylabel=$S$,
            zlabel=\Type,
            mesh/interior colormap name=hot,
            colormap/hot,
        xtick = {0,1,2,3,4}]

        \addplot3[opacity=0.2,domain y=50:150,domain=0.1:5,surf,shader =faceted interp,]
        {\Type(y,x,\KK,\RR,\SIG))};
        \addplot3+[LastPointPayOff] coordinates {\LstBottom};
        \addplot3[LastPointPayOff,domain=0:5,samples y=1,samples=51,thick,smooth,black,mark options={ball color = black}] coordinates {\LstOnSurf};%        
        \addplot3[LastPointPayOff,domain=0:5,samples y=1,samples=51,red,thick,smooth,mark options={ball color = red}] coordinates {\LstFront};

    \end{axis}
\end{tikzpicture} 

\end{document}
JeT
  • 3,020