New in Wolfram
Mathematica
8: Parametric Probability Distributions
◄
previous
|
next
►
Core Algorithms
Use Stable Distribution to Model Stock Prices
Assuming daily logarithmic return of the stock market follows a stable distribution, simulate and visualize stock prices over a period of five years.
In[1]:=
X
log\[ScriptCapitalD] = StableDistribution[1, 1.388, -0.16, -0.00048, 0.00559]; logReturns = BlockRandom[SeedRandom[2010]; RandomVariate[log\[ScriptCapitalD], 5*365]];
In[2]:=
X
ListLinePlot[1000 Exp[Accumulate[logReturns]], PlotRange -> {1000, 8000}, PlotLabel -> Framed[Style[Row[{"Model: ", log\[ScriptCapitalD]}], 14], BaseStyle -> {FontFamily -> "Verdana"}, Background -> Lighter[Blend[{Yellow, Orange}], 0.7], RoundingRadius -> 2], Frame -> {{True, False}, {True, False}}, FrameLabel -> {{Style["stock price", Bold, 12], ""}, {Style["days", Bold, 12], ""}}, Filling -> Axis, Epilog -> Inset[Framed[ Grid[{{"Value at Risk at the 95% Level", VaR = InverseSurvivalFunction[log\[ScriptCapitalD], 0.95]}, {"Expected Shortfall of Logarithmic Return ", NExpectation[x \[Conditioned] x < VaR, x \[Distributed] log\[ScriptCapitalD]]}}, ItemSize -> {{11, 6}, 2}, Background -> {None, {{Lighter[Blend[{Red, Blue}], .8], Lighter[Blend[{Green, Blue}], .8]}}}], RoundingRadius -> 10], {0, 8000}, {Left, Top}], ImageSize -> 500]
Out[2]=