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edit approved Aug 13, 2013 at 11:29

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Milan, the easiest way to do it is by using Dynamic[].

Manipulate[SeedRandom[seed];
meanvector := Mean[assets];
assets = Table[RandomFunction[GeometricBrownianMotionProcess[\[Mu]Table[RandomFunction[GeometricBrownianMotionProcess[μ, \[Sigma]σ, S0], {0, time, 0.1}]["Path"], {P}];
processes = Transpose[assets[[#]]][[2]] & /@ Range@Length[assets];
processesposition=Flatten[Position[Min[processes[[#]]]&/@Range@Length[assets], _?(# > watermark &)]];
watermarkedassets = assets[[#]] & /@ processesposition;
watermarkedmeanvector = Mean[watermarkedassets];
G1 := ListLogPlot[assets, GridLines -> {{}, {watermark}},GridLinesStyle -> Directive[Green, Thick], Joined -> True, AxesLabel -> {"Time", "St"}, PlotLabel -> Style["Forecasted Stock Price\n (Brownian Motion)", Bold], PlotRange -> All, PlotStyle -> Directive[{Thin, Lighter@Gray}]];
G2 := ListLogPlot[{meanvector, watermarkedmeanvector},Joined -> True, PlotStyle -> {Directive[{Thick, Darker@Red}], Directive[{Thick, Darker@Blue}]}];
Show[G1, G2], 
{{S0, 100, "Initial Stock Value"}, 1, 500, 0.5, Appearance -> "Labeled"}, 
{{\[Mu]μ, 0.08, "Drift \[Mu]"μ"}, 0.01, 0.2, 0.01, Appearance -> "Labeled"}, 
{{\[Sigma]σ, 0.2, "Standard Deviation \[Sigma]"σ"}, 0.01, 1, 0.05, Appearance -> "Labeled"}, 
{{P, 6, "Paths"}, 1, 20, 1, Appearance -> "Labeled"}, 
{{time, 10, "Time t"}, 1, 20, 1, Appearance -> "Labeled"}, 
{{watermark, 75, "Watermark"}, 1, 500, Appearance -> "Labeled"}, 
{{seed, 1, "New Random Case"}, 1, 100, 1}, 
Button["Set Initial Values", {S0 = 100, \[Mu]μ = 0.08, \[Sigma]σ = 0.20, P = 6, time = 10, watermark = 75}, ImageSize -> 150], 
Dynamic["Mean watermarked processes = "<>ToString[watermarkedmeanvector[[-1]][[2]]]],
Dynamic["Mean of all processes = "<>ToString[meanvector[[-1]][[2]]]],    
ControlPlacement -> Left]

enter image description here

Milan, the easiest way to do it is by using Dynamic[].

Manipulate[SeedRandom[seed];
meanvector := Mean[assets];
assets = Table[RandomFunction[GeometricBrownianMotionProcess[\[Mu], \[Sigma], S0], {0, time, 0.1}]["Path"], {P}];
processes = Transpose[assets[[#]]][[2]] & /@ Range@Length[assets];
processesposition=Flatten[Position[Min[processes[[#]]]&/@Range@Length[assets], _?(# > watermark &)]];
watermarkedassets = assets[[#]] & /@ processesposition;
watermarkedmeanvector = Mean[watermarkedassets];
G1 := ListLogPlot[assets, GridLines -> {{}, {watermark}},GridLinesStyle -> Directive[Green, Thick], Joined -> True, AxesLabel -> {"Time", "St"}, PlotLabel -> Style["Forecasted Stock Price\n (Brownian Motion)", Bold], PlotRange -> All, PlotStyle -> Directive[{Thin, Lighter@Gray}]];
G2 := ListLogPlot[{meanvector, watermarkedmeanvector},Joined -> True, PlotStyle -> {Directive[{Thick, Darker@Red}], Directive[{Thick, Darker@Blue}]}];
Show[G1, G2], 
{{S0, 100, "Initial Stock Value"}, 1, 500, 0.5, Appearance -> "Labeled"}, 
{{\[Mu], 0.08, "Drift \[Mu]"}, 0.01, 0.2, 0.01, Appearance -> "Labeled"}, 
{{\[Sigma], 0.2, "Standard Deviation \[Sigma]"}, 0.01, 1, 0.05, Appearance -> "Labeled"}, 
{{P, 6, "Paths"}, 1, 20, 1, Appearance -> "Labeled"}, 
{{time, 10, "Time t"}, 1, 20, 1, Appearance -> "Labeled"}, 
{{watermark, 75, "Watermark"}, 1, 500, Appearance -> "Labeled"}, 
{{seed, 1, "New Random Case"}, 1, 100, 1}, 
Button["Set Initial Values", {S0 = 100, \[Mu] = 0.08, \[Sigma] = 0.20, P = 6, time = 10, watermark = 75}, ImageSize -> 150], 
Dynamic["Mean watermarked processes = "<>ToString[watermarkedmeanvector[[-1]][[2]]]],
Dynamic["Mean of all processes = "<>ToString[meanvector[[-1]][[2]]]],    
ControlPlacement -> Left]

enter image description here

Milan, the easiest way to do it is by using Dynamic[].

Manipulate[SeedRandom[seed];
meanvector := Mean[assets];
assets = Table[RandomFunction[GeometricBrownianMotionProcess[μ, σ, S0], {0, time, 0.1}]["Path"], {P}];
processes = Transpose[assets[[#]]][[2]] & /@ Range@Length[assets];
processesposition=Flatten[Position[Min[processes[[#]]]&/@Range@Length[assets], _?(# > watermark &)]];
watermarkedassets = assets[[#]] & /@ processesposition;
watermarkedmeanvector = Mean[watermarkedassets];
G1 := ListLogPlot[assets, GridLines -> {{}, {watermark}},GridLinesStyle -> Directive[Green, Thick], Joined -> True, AxesLabel -> {"Time", "St"}, PlotLabel -> Style["Forecasted Stock Price\n (Brownian Motion)", Bold], PlotRange -> All, PlotStyle -> Directive[{Thin, Lighter@Gray}]];
G2 := ListLogPlot[{meanvector, watermarkedmeanvector},Joined -> True, PlotStyle -> {Directive[{Thick, Darker@Red}], Directive[{Thick, Darker@Blue}]}];
Show[G1, G2], 
{{S0, 100, "Initial Stock Value"}, 1, 500, 0.5, Appearance -> "Labeled"}, 
{{μ, 0.08, "Drift μ"}, 0.01, 0.2, 0.01, Appearance -> "Labeled"}, 
{{σ, 0.2, "Standard Deviation σ"}, 0.01, 1, 0.05, Appearance -> "Labeled"}, 
{{P, 6, "Paths"}, 1, 20, 1, Appearance -> "Labeled"}, 
{{time, 10, "Time t"}, 1, 20, 1, Appearance -> "Labeled"}, 
{{watermark, 75, "Watermark"}, 1, 500, Appearance -> "Labeled"}, 
{{seed, 1, "New Random Case"}, 1, 100, 1}, 
Button["Set Initial Values", {S0 = 100, μ = 0.08, σ = 0.20, P = 6, time = 10, watermark = 75}, ImageSize -> 150], 
Dynamic["Mean watermarked processes = "<>ToString[watermarkedmeanvector[[-1]][[2]]]],
Dynamic["Mean of all processes = "<>ToString[meanvector[[-1]][[2]]]],    
ControlPlacement -> Left]

enter image description here

Source Link

created Jun 7, 2013 at 13:30

Rod

3.3k
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Milan, the easiest way to do it is by using Dynamic[].

Manipulate[SeedRandom[seed];
meanvector := Mean[assets];
assets = Table[RandomFunction[GeometricBrownianMotionProcess[\[Mu], \[Sigma], S0], {0, time, 0.1}]["Path"], {P}];
processes = Transpose[assets[[#]]][[2]] & /@ Range@Length[assets];
processesposition=Flatten[Position[Min[processes[[#]]]&/@Range@Length[assets], _?(# > watermark &)]];
watermarkedassets = assets[[#]] & /@ processesposition;
watermarkedmeanvector = Mean[watermarkedassets];
G1 := ListLogPlot[assets, GridLines -> {{}, {watermark}},GridLinesStyle -> Directive[Green, Thick], Joined -> True, AxesLabel -> {"Time", "St"}, PlotLabel -> Style["Forecasted Stock Price\n (Brownian Motion)", Bold], PlotRange -> All, PlotStyle -> Directive[{Thin, Lighter@Gray}]];
G2 := ListLogPlot[{meanvector, watermarkedmeanvector},Joined -> True, PlotStyle -> {Directive[{Thick, Darker@Red}], Directive[{Thick, Darker@Blue}]}];
Show[G1, G2], 
{{S0, 100, "Initial Stock Value"}, 1, 500, 0.5, Appearance -> "Labeled"}, 
{{\[Mu], 0.08, "Drift \[Mu]"}, 0.01, 0.2, 0.01, Appearance -> "Labeled"}, 
{{\[Sigma], 0.2, "Standard Deviation \[Sigma]"}, 0.01, 1, 0.05, Appearance -> "Labeled"}, 
{{P, 6, "Paths"}, 1, 20, 1, Appearance -> "Labeled"}, 
{{time, 10, "Time t"}, 1, 20, 1, Appearance -> "Labeled"}, 
{{watermark, 75, "Watermark"}, 1, 500, Appearance -> "Labeled"}, 
{{seed, 1, "New Random Case"}, 1, 100, 1}, 
Button["Set Initial Values", {S0 = 100, \[Mu] = 0.08, \[Sigma] = 0.20, P = 6, time = 10, watermark = 75}, ImageSize -> 150], 
Dynamic["Mean watermarked processes = "<>ToString[watermarkedmeanvector[[-1]][[2]]]],
Dynamic["Mean of all processes = "<>ToString[meanvector[[-1]][[2]]]],    
ControlPlacement -> Left]

enter image description here