Fix this economy model?

Questions
, , ,
1

Dear all. Im desperately looking for Help. My capacities in Wolfram aren’t the biggest and I’m trying to get my Model to run. Can someone Help me? ~ Greetings Philipp. P.S. The Model is attached

(*Clear variables*)

Clear[P, DC, DF, DB, DS, F, ?, ?, ?, ?];
(*Model Equations*)
DC[t_] := DC[t] = ?*(P[t] - F); 
DF[t_] := DF[t] = ?*(F - P[t]);
DB[t_] := DB[t] = ?;
DS[t_] := DS[t] = -?; 
P[t_] := P[t] = 
   P[t - 1] + ?[(?*DC[t - 1] - ?*DF[t - 1])*(P[t - 1] - 
         F) + ? (DB[t - 1] - DS[t - 1])];

(*Abhängikeiten darstellen*)


(*parameter setting*)
? = 0.010;
F = 0;
? = 1.011;
? = 1.000;
? = 0.165;

(*Startwerte setzten*)
P[0] = F; P[1] = F;

logprices = Table[P[i], {i, 1, 5000}];
logreturns = Differences@logprices;

ListLinePlot[Exp@logprices, PlotStyle -> Black, PlotRange -> All, 
 Frame -> True, FrameLabel -> {{"price", None}, {"time", None}}, 
 AspectRatio -> 0.4, GridLines -> {{}, {Exp[F]}}]

(*Entwicklung der log Renditen*)
ListLinePlot[logreturns, 
 PlotStyle -> Black, PlotRange -> All, Frame -> True, 
 FrameLabel -> {{"log returns", None}, {"time", None}}, 
 AspectRatio -> 0.4, Axes -> None]
2

Hi,

I think that the model equations for P are incorrect. Just behind the \mu you are using square brackets where you should use round brackets.

P[t_] := P[t] = 
   P[t - 1] + \[Mu] ((\[Chi]*DC[t - 1] - \[Phi]*DF[t - 1])*(P[t - 1] -
           F) + \[Kappa] (DB[t - 1] - DS[t - 1]));

should do. You will still have an overflow when you try to evaluate

Table[P[i], {i, 1, 5000}]

though. You see that this behaves badly if you use:

logprices = Table[P[i], {i, 1, 450}];
logreturns = Differences@logprices;

ListLinePlot[Exp@logprices, PlotStyle -> Black, PlotRange -> All, 
 Frame -> True, FrameLabel -> {{"price", None}, {"time", None}}, 
 AspectRatio -> 0.4, GridLines -> {{}, {Exp[F]}}]

ScreenShot2016-12-07at16.11.39.png
ScreenShot2016-12-07at16.11.39.png506×238 5.79 KB

If you iterate to the first 480 elements you get:

ScreenShot2016-12-07at16.14.50.png
ScreenShot2016-12-07at16.14.50.png504×220 7.61 KB

At 481 you get to values of about 10^{183}.

Cheers,

Marco

3

Welcome to Wolfram Community! Please make sure you know the rules: https://wolfr.am/READ-1ST

And please EDIT your post and make your title NOT generic, but about the actual model.

4

I think it’s the [ and ] near the mu in your P function. Also it diverges at around t=450. See if this fixes you up.

Eric

Ps. I see Marco found the same issue before me.

5

Thank you very much,… I’ll see if it works better now :slight_smile: