Plot two functions within manipulate

Question

I just want to plot all stochastic processes and their average process. The original code without the average is:

Manipulate[SeedRandom[seed]; 

 test2[μ_, σ_, S_, P_] := 
  Table[RandomFunction[
     GeometricBrownianMotionProcess[μ, σ, S], {0, 250, 0.05}]["Path"], {P}];

 ListLogPlot[test2[μ, σ, S, P], Joined -> True, 
  AxesLabel -> {"Time", "St"}, 
  PlotLabel -> Style["Forecasted Stock Price\n (Brownian Motion)", Bold], 
  PlotRange -> {{0, 250}, {0, 3000}}, ImageSize -> 500, 
  PlotStyle -> Directive[{Thin, Lighter@Gray}]], 

{{S, 100, "Initial Stock Value"}, 100, 500, 0.05, Appearance -> "Labeled"}, 
{{μ, 0.01, "Drift μ"}, 0.01, 1, 0.05, Appearance -> "Labeled"}, 
{{σ, 0.01, "Standard Deviation σ"}, 0.01, 1, 0.05, Appearance -> "Labeled"}, 
{{P, 1, "Paths"}, 1, 100, 1, Appearance -> "Labeled"},

{{seed, 77777, "New Random Case"}, 10000, 999999, 1}, 

 Button["Set Initial Values", {S = 100, μ = 0.01, σ = 0.01}, 
ImageSize -> 150], 
ControlPlacement -> Left]

So far I have done the following (changed the original gode a Little bit) but it’s not working properly since I only get the mean of all processes and not both, the processes (in grey colour) and their average process (in red colour).

Manipulate[SeedRandom[seed]; 

 test2[μ_, σ_, S_, P_] := 
  Table[RandomFunction[
     GeometricBrownianMotionProcess[μ, σ, S], {0, 250, 0.05}]["Path"], {P}];

meanPaths=Mean[test2[μ,σ,S,P][[All]]];

 ListLogPlot[{test2[μ, σ, S, P],meanPaths}, Joined -> True, 
  AxesLabel -> {"Time", "St"}, 
  PlotLabel -> Style["Forecasted Stock Price\n (Brownian Motion)", Bold], 
  PlotRange -> {{0, 250}, {0, 3000}}, ImageSize -> 500, 
PlotStyle -> Directive[{{Thin,Lighter@Gray},{Thickness[Medium],Red}}]],



{{S, 100, "Initial Stock Value"}, 100, 500, 0.05, Appearance -> "Labeled"}, 
{{μ, 0.01, "Drift μ"}, 0.01, 1, 0.05, Appearance -> "Labeled"}, 
{{σ, 0.01, "Standard Deviation σ"}, 0.01, 1, 0.05, Appearance -> "Labeled"}, 
{{P, 1, "Paths"}, 1, 100, 1, Appearance -> "Labeled"},

{{seed, 77777, "New Random Case"}, 10000, 999999, 1}, 

 Button["Set Initial Values", {S = 100, μ = 0.01, σ = 0.01}, 
ImageSize -> 150], 
ControlPlacement -> Left]

Any ideas what I could be missing?

Thank you for your help

Answer 1

A bit puzzling, but I think you have problems with the levels in ListLogPlot (where you added another set of values), and with the PlotStyle directives (where you added options to a Directive). I changed a few things quasi-randomly and got something which I think is closer to what you want.

Manipulate[
 SeedRandom[seed];
 Column[{
   test2[μ_, σ_, S_, P_] := 
    Table[RandomFunction[
       GeometricBrownianMotionProcess[μ, σ, S], {0, 250, 
        0.05}]["Path"], {P}]; 
   meanPaths = Mean[test2[μ, σ, S, P][[All]]];
   ListLogPlot[{meanPaths, Flatten[test2[μ, σ, S, P], 1]},
    Joined -> True,
    AxesLabel -> {"Time", "St"},
    PlotLabel -> 
     Style["Forecasted Stock Price\n (Brownian Motion)", Bold],
    PlotRange -> Full,
    PlotStyle -> {Directive[{Thick, Red}], Directive[{Thin, Gray}]},
    ImageSize -> 500]
   }],
 {{S, 100, "Initial Stock Value"}, 100, 500, 0.05, Appearance -> "Labeled"}, 
 {{μ, 0.01, "Drift μ"}, 0.01, 1, 0.05, Appearance -> "Labeled"}, 
 {{σ, 0.01, "Standard Deviation σ"}, 0.01, 1, 0.05, Appearance -> "Labeled"},
 {{P, 1, "Paths"}, 1, 100, 1, Appearance -> "Labeled"},
 {{seed, 77777, "New Random Case"}, 10000, 999999, 1}, 
 Button["Set Initial Values", {S = 100, μ = 0.01, σ = 
    0.01}, ImageSize -> 150],
 ControlPlacement -> Left]