Die Dynamik von abgeleiteten Preisen Stochastische Differentialgleichungen.

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Die Dynamik von Die Dynamik von abgeleiteten Preisen abgeleiteten Preisen Stochastische Stochastische Differentialgleichungen Differentialgleichungen

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  • Die Dynamik von abgeleiteten PreisenStochastische Differentialgleichungen

  • bersichtEinfhrungGeometrische Beschreibung des Pfades von Stoschastischen DifferentialgleichungenLsungen von SDGsBedeutende Modelle von SDGsStochastische VolatilittZusammenfassung

  • Einfhrung (1)Stochastische Differentialgleichung (SDG):

  • Einfhrung (2)Verschiedene Marktteilnehmer knnen verschiedene Funktionen a(St,t) und (St,t)Abhngig von der Menge an InformationenZ.B.: Insider Informationen und Kenntnis aller zuflligen Ereignisse, die den Marktpreise beeinflussen (kein Diffusionsterm): dSt=a*(St,t)dtNormaler Marktteilnehmer: dSt=a(St,t)dt+(St,t)dWtWobei a*a

  • Einfhrung (3)Die Drift- und Diffusionsparameter hngen von St und t ab und sind daher selbst Zufallsvariablen.Sie sind aber Informationsadaptiert und werden daher beim Informationsstand It zum Zeitpunkt t fixiert.Sie mssen folgende Bedingungen einhalten:

  • Geometrische Beschreibung des Pfades von SDGs

  • Lsungen von SDGs (1)Die Lsung (St) ist selbst ein stochastischer Prozess

  • Lsungen von SDGs (2)Starke Lsung:Wt bekannt (Fehlerteil)hnlich wie bei normalen DifferentialgleichungenHngt ab von t und Wt (und von den Parametern)

  • Lsungen von SDGs (3)Schwache Lsung:=f(t,)Wobei und gleichzeitig bestimmt werdenGegeben sind nur die Drift- und Diffusionsparameter a(.) und (.) ist ein Wiener Prozessd und dW haben beide Erwartungswert 0 und eine Varianz von dtdt=a(t,t)dt+(t,t)dtSt ist It adaptiert, whrend t Ht adaptiert ist

  • Lsungen von SDGs (4)Verifikation

  • Lsungen von SDGs (5)VerifikationdSt=a*dt+*dWtSt=f(a, , S0, t, Wt)Wt und daher auch St sind stochastische ProzesseDaher ist St nicht ableitbarVerifikation aber mit Itos Lemma mglich

  • Lsungen von SDGs (6)Verifikation Black-Scholes

  • Lsungen von SDGs (7)Verifikation Black-ScholesStarke LsungEinsetzen in Itos Lemma zu Verifikation

  • Lsungen von SDGs (8)Verifikation Black-Scholes

  • Lsungen von SDGs (9)Wichtiges Beispiel

  • Lsungen von SDGs (10)Wichtiges BeispielLsung direkt mittels IntegralNtig ist die Dichtefunktion von WtEs existiert aber noch eine zweite Methode

  • Lsungen von SDGs (11)Wichtiges BeispielSubstituierenAnwenden von Itos LemmaIntegrieren fhrt zu einem einfachen IntegralDurch Rcksubstituieren erhalten wirDies fhrt zum folgenden Schluss: Der jetzige Wert einer Aktie entspricht dem abgezinsten Erwartungswert

  • Bedeutende Modelle von SDGs (1)Lineare SDG mit konstanten KoeffizientenFluktuiert rund um einen linearen TrendGeeignet fr bestimmte Aktien

  • Bedeutende Modelle von SDGs (2)Lineare SDG mit konstanten Koeffizienten

    Diagramm1

    100

    99.9999752783

    99.9994103465

    99.9993188974

    99.9997910408

    99.9993675996

    100.0001571003

    99.9995312475

    100.000166056

    99.9996466305

    99.9999615069

    100.0001556527

    99.9997447744

    100.0000568088

    100.0001464082

    99.9994283081

    100.0005791228

    99.9998190259

    99.9999348781

    99.9994864525

    99.9996610592

    100.0000394356

    100.0000320146

    100.0000263606

    99.9996346016

    99.9998906893

    99.9996908918

    100.0000278133

    100.0001142125

    99.9999127823

    100.0003262299

    99.9998172272

    100.000334597

    100.0003877576

    99.999930519

    100.0002386741

    100.0004352946

    100.0003251754

    100.0003248229

    99.9996086089

    99.9998093613

    100.000299051

    99.9998190817

    100.0005488538

    100.0003694765

    100.0000014887

    100.0003813528

    100.0005416599

    99.9998539237

    100.0003627496

    100.0005426227

    100.0004530245

    100.0000977135

    100.0002268057

    100.0006317054

    100.0004642659

    100.000350623

    100.0006329062

    100.0008940516

    100.0003980876

    100.0009433091

    100.0004041959

    100.0001458655

    100.0008004215

    100.0004160283

    100.0006441334

    100.0002430573

    100.0005387002

    99.9999758168

    100.0004595437

    100.0001409162

    100.0001685531

    100.0008185075

    100.0005848682

    100.0001772594

    100.001056229

    100.0004467901

    100.0006324568

    100.0009427885

    100.0002128018

    100.0010022138

    100.0007444431

    100.0008132658

    100.0007219043

    100.0002522201

    100.0007522654

    100.0006463989

    100.0012473115

    100.0011075218

    100.0004231772

    100.0015938975

    100.000817853

    100.000542668

    100.0012968669

    100.0004367819

    100.0008362038

    100.0004834767

    100.0009708789

    100.0008606906

    100.0009125677

    100.0007076467

    100.0011868893

    100.0010196436

    100.0012533568

    100.0010288156

    100.0006605522

    100.0007283013

    100.000712335

    100.0003004888

    100.0012607843

    100.0007819055

    100.0009836586

    100.0011490546

    100.0013390131

    100.0008519706

    100.00120804

    100.0007084205

    100.0007997171

    100.0012598992

    100.0010415899

    100.0010776967

    100.0008164861

    100.0003353549

    100.0012594932

    100.0013294339

    100.0012979091

    100.0014314201

    100.0015634065

    100.0007812655

    100.0009791939

    100.0020470265

    100.0002747152

    100.0010477542

    100.0010449791

    100.0013713984

    100.0017104863

    100.0010634973

    100.0008765131

    100.0012319129

    100.0012399985

    100.0015187781

    100.0007718161

    100.0012407365

    100.001665856

    100.0015566417

    100.0020587579

    100.0017851265

    100.0014509763

    100.0011731233

    100.0007659398

    100.0017695828

    100.0012615357

    100.0013378447

    100.0009747695

    100.0017585478

    100.0012855956

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    100.0015437414

    100.0011776598

    100.0015231866

    100.0014487533

    100.0013039013

    100.0012926709

    100.0013796964

    100.0011609931

    100.0022019508

    100.0010861483

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    100.0021417338

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    100.0018032601

    100.0016255459

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    100.0014940171

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    100.0016789834

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    100.0015578313

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    100.0016774933

    100.0016625249

    100.0020349883

    100.0017680352

    100.0014077912

    100.0014620322

    100.0019263692

    100.0016222251

    St

    Time

    St

    Linear Constant Coefficient SDEs

    Tabelle1

    WtTimeSt

    0.00598118960100

    0.00482380070.00199.9999752783

    -0.01434059410.00299.9994103465

    -0.01772223190.00399.9993188974

    -0.00231744930.00499.9997910408

    -0.01676548890.00599.9993675996

    0.00921786520.006100.0001571003

    -0.01197722670.00799.9995312475

    0.00884972450.008100.000166056

    -0.00879779240.00999.9996466305

    0.00136475360.0199.9999615069

    0.00750294480.011100.0001556527

    -0.00652632930.01299.9997447744

    0.00354148140.013100.0000568088

    0.00619479580.014100.0001464082

    -0.01807520680.01599.9994283081

    0.01995194910.016100.0005791228

    -0.00571794770.01799.9998190259

    -0.00218954030.01899.9999348781

    -0.01747039280.01999.9994864525

    -0.01198350220.0299.9996610592

    0.00029571080.021100.0000394356

    -0.00028499020.022100.0000320146

    -0.000806790.023100.0000263606

    -0.01419875840.02499.9996346016

    -0.00599583250.02599.9998906893

    -0.0129890850.02699.9996908918

    -0.00209170140.027100.0000278133

    0.00045494060.028100.0001142125

    -0.00659273380.02999.9999127823

    0.0068555210.03100.0003262299

    -0.01044456890.03199.9998172272

    0.00646775790.032100.000334597

    0.00790644210.033100.0003877576

    -0.00766817720.03499.999930519

    0.00227032610.035100.0002386741

    0.00849100840.036100.0004352946

    0.00448703760.037100.0003251754

    0.00414195260.038100.0003248229

    -0.02006518120.03999.9996086089

    -0.01370676730.0499.9998093613

    0.00228288850.041100.000299051

    -0.01404941940.04299.9998190817

    0.00994298260.043100.0005488538

    0.00363040730.044100.0003694765

    -0.00896918660.045100.0000014887

    0.00335961660.046100.0003813528

    0.00836985240.047100.0005416599

    -0.0148880190.04899.9998539237

    0.00173951090.049100.0003627496

    0.00740194540.05100.0005426227

    0.00408200550.051100.0004530245

    -0.00809502580.052100.0000977135

    -0.00412528610.053100.0002268057

    0.00903803540.054100.0006317054

    0.00312338670.055100.0004642659

    -0.00099804540.056100.000350623

    0.00807806370.057100.0006329062

    0.01644957590.058100.0008940516

    -0.00041588920.059100.0003980876

    0.01742482710.06100.0009433091

    -0.0008789470.061100.0004041959

    -0.00982329310.062100.0001458655

    0.01166190490.063100.0008004215

    -0.00148453410.064100.0004160283

    0.00578563690.065100.0006441334

    -0.00791690130.066100.0002430573

    0.00160453060.067100.0005387002

    -0.0174915840.06899.9999758168

    -0.00170068690.069100.0004595437

    -0.01265493670.07100.0001409162

    -0.01206703930.071100.0001685531

    0.00926477240.072100.0008185075

    0.00114346220.073100.0005848682

    -0.01277683170.074100.0001772594

    0.01618882380.075100.001056229

    -0.00445913880.076100.0004467901

    0.00139641540.077100.0006324568

    0.01140747370.078100.0009427885

    -0.01325875020.079100.0002128018

    0.01272164810.08100.0010022138

    0.0037959580.081100.0007444431

    0.00575671490.082100.0008132658

    0.0023779990.083100.0007219043

    -0.0136114750.084100.0002522201

    0.00272336820.085100.0007522654

    -0.00113884650.086100.0006463989

    0.01855823940.087100.0012473115

    0.01356524990.088100.0011075218

    -0.00957957130.089100.0004231772

    0.02911110640.09100.0015938975

    0.00290962130.091100.000817853

    -0.00659654230.092100.000542668

    0.01821008480.093100.0012968669

    -0.01079274630.094100.0004367819

    0.00218798280.095100.0008362038

    -0.00990291940.096100.0004834767

    0.00601048670.097100.0009708789

    0.0020042080.098100.0008606906

    0.00340011180.099100.0009125677

    -0.00376392110.1100.0007076467

    0.01187750060.101100.0011868893

    0.00596930930.102100.0010196436

    0.01342641550.103100.0012533568

    0.00560837630.104100.0010288156

    -0.00700040350.105100.0006605522

    -0.00507543520.106100.0007283013

    -0.00594097860.107100.000712335

    -0.0200025170.108100.0003004888

    0.01167400110.109100.0012607843

    -0.00462196110.11100.0007819055

    0.00176980850.111100.0009836586

    0.00694967640.112100.0011490546

    0.01294829420.113100.0013390131

    -0.00361978890.114100.0008519706

    0.00791585530.115100.00120804

    -0.00907145930.116100.0007084205

    -0.00636157440.117100.0007997171

    0.0086444970.118100.0012598992

    0.00103418640.119100.0010415899

    0.00190441370.12100.0010776967

    -0.00713594090.121100.0008164861

    -0.0235069820.122100.0003353549

    0.00696429650.123100.0012594932

    0.008962320.124100.0013294339

    0.007578160.125100.0012979091

    0.01169519240.126100.0014314201

    0.01576140680.127100.0015634065

    -0.01064329350.128100.0007812655

    -0.00437901240.129100.0009791939

    0.03088207450.13100.0020470265

    -0.02852830220.131100.0002747152

    -0.0030936690.132100.0010477542

    -0.00351950580.133100.0010449791

    0.0070278020.134100.0013713984

    0.01799739950.135100.0017104863

    -0.00390223250.136100.0010634973

    -0.0104683750.137100.0008765131

    0.00104495260.138100.0012319129

    0.00098114010.139100.0012399985

    0.00994045880.14100.0015187781

    -0.01529160730.141100.0007718161

    0.00000574120.142100.0012407365

    0.01384305510.143100.001665856

    0.00986924530.144100.0015566417

    0.02627311910.145100.0020587579

    0.01681873980.146100.0017851265

    0.00534706710.147100.0014509763

    -0.00424803370.148100.0011731233

    -0.01815415090.149100.0007659398

    0.01496728150.15100.0017695828

    -0.00230095340.151100.0012615357

    -0.00009065390.152100.0013378447

    -0.01252649330.153100.0009747695

    0.01326611710.154100.0017585478

    -0.00283229160.155100.0012855956

    -0.00109265560.156100.0013477846

    0.00510590330.157100.0015437414

    -0.00743015110.158100.0011776598

    0.00375407580.159100.0015231866

    0.00093963310.16100.0014487533

    -0.00422210180.161100.0013039013

    -0.00492977960.162100.0012926709

    -0.00236226470.163100.0013796964

    -0.00998570610.164100.0011609931

    0.02437955120.165100.0022019508

    -0.01314720070.166100.0010861483

    0.01072316990.167100.0018122594

    -0.00738485820.168100.0012790186

    -0.02265223880.169100.0008309971

    0.00877978440.17100.0017839578

    0.02037231750.171100.0021417338

    -0.00527044220.172100.001382451

    0.00842319420.173100.0018032601

    0.00216605260.174100.0016255459

    0.01029397940.175100.0018793837

    -0.00689329910.176100.0013737653

    0.01138550940.177100.0019321296

    0.01397588680.178100.0020198409

    -0.00388490660.179100.0014940171

    0.00816849020.18100.001865619

    -0.00162235660.181100.0015818936

    0.00128063680.182100.0016789834

    0.00441692690.183100.0017830721

    0.00327797810.184100.0017589037

    -0.00989543880.185100.0013737012

    0.00749989790.186100.0019055613

    0.00045799880.187100.0017043043

    -0.00247332540.188100.0016263646

    -0.00509110120.189100.0015578313

    0.00512770840.19100.0018743956

    -0.00176903540.191100.0016774933

    -0.0026013140.192100.0016625249

    0.00948080010.193100.0020349883

    0.0002490310.194100.0017680352

    -0.01209243690.195100.0014077912

    -0.01061773670.196100.0014620322

    0.0045268280.197100.0019263692

    -0.00594463930.198100.0016222251

    Tabelle1

    0

    0

    0

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    0

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    0

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    St

    Time

    St

    Linear Constant Coefficient SDEs

    Tabelle2

    Tabelle3

  • Bedeutende Modelle von SDGs (3)Geometrische SDGFluktuiert rund um einen exponentiellen TrendBesser geeignet fr Aktien als lineare SDGs

  • Bedeutende Modelle von SDGs (4)Geometrische SDG

    Diagramm2

    100

    99.6699156549

    100.3670049981

    100.3753336137

    99.8899789783

    100.4716052145

    100.4437642052

    100.0169692098

    100.5495609196

    100.678431194

    100.3662724573

    100.2556490676

    100.4466171217

    100.8282706498

    100.7714437446

    100.8712031418

    100.9550177155

    100.7546112007

    100.7034380436

    100.7033118102

    100.5841274949

    100.352014053

    100.5693910783

    100.2026948311

    99.9813136258

    100.9890124687

    101.4265549534

    100.4777536279

    100.5505527825

    100.3258399224

    101.0724179419

    101.246095358

    101.494899987

    101.0793611598

    101.4020437705

    100.7714011328

    100.800694803

    100.9250412062

    100.7977942032

    100.6380982425

    100.9764485539

    101.2238098124

    101.212611258

    100.7131642223

    101.3953981716

    101.4064251383

    101.0418149521

    100.7733610147

    101.1276204733

    100.9815931353

    101.3747095847

    101.4759042849

    101.4195478443

    101.155359795

    101.0604929635

    101.0452128837

    100.6800894083

    101.0946701335

    101.2216606827

    100.6354348214

    101.5139119415

    100.993000288

    101.2005102798

    101.2994097676

    101.2978251552

    100.8996275

    101.0326251772

    101.1957726941

    101.6559795789

    100.7768770016

    102.0107539219

    101.4880143407

    101.5562883529

    101.3690528417

    101.0338389087

    100.8733789056

    101.7716091608

    101.7268955431

    101.2811319134

    101.353313116

    101.1242945446

    101.5385032987

    101.628163919

    101.8928548148

    102.2204585863

    101.6417373972

    101.426053438

    101.9149109369

    101.6601292964

    101.9659020019

    101.7491371898

    101.8592126514

    101.4993721996

    101.2473768707

    101.2336928955

    102.3744686994

    101.6891216396

    101.4075249881

    101.8794760363

    101.3475799198

    101.6243656209

    101.6351481797

    101.8189209093

    101.5000763389

    101.7562361663

    102.3627415041

    102.0473986313

    101.894313304

    101.3181093027

    101.9411757271

    101.7302575851

    102.0112322198

    102.0355366834

    102.0636565256

    102.1538494426

    102.1482855538

    102.0912532939

    101.7117656173

    102.2092934012

    102.2698062633

    102.6253723185

    101.8665050805

    102.0530912984

    101.7200851639

    102.2866695748

    102.2330252721

    102.5906364011

    102.2974711752

    102.2429807164

    102.371012007

    102.0564487889

    101.9123413391

    102.1713716395

    102.5010769341

    101.8968025816

    102.3274199156

    101.8843609953

    101.8034772274

    102.3604969319

    102.1741757294

    102.6248623901

    101.9908142166

    102.5710375324

    102.4671782715

    102.4304244889

    102.5948824349

    102.1572871599

    102.2771752261

    102.1929748153

    102.0990413874

    102.2278688409

    102.644598665

    102.78753027

    102.112851017

    102.5867772626

    102.6338769239

    102.859869103

    102.9841150964

    102.3581463535

    102.5300117762

    102.9772076621

    102.3089700827

    102.6032324358

    103.0367581657

    102.6486227551

    103.0737346124

    102.9618116644

    102.3317821017

    102.7100488131

    102.3511767845

    103.0899693904

    102.9922977633

    102.6367344784

    102.868447921

    103.0829609126

    102.6057897523

    102.7966700105

    102.7798708791

    102.9351665597

    102.8019106248

    103.2113571413

    102.8611897258

    102.7030305544

    102.8995574733

    103.243083755

    102.9917622055

    103.4077027771

    103.0092972378

    103.9288596128

    103.5450019561

    103.5998394255

    102.7351709775

    103.064488542

    102.8936902979

    103.2880863679

    103.0344271312

    103.0079067525

    102.4293156552

    103.1318526184

    St

    Time

    St

    Geometric SDEs

    Lineare

    WtTimeSt

    0.00598118960100

    0.00482380070.00199.9999752783

    -0.01434059410.00299.9994103465

    -0.01772223190.00399.9993188974

    -0.00231744930.00499.9997910408

    -0.01676548890.00599.9993675996

    0.00921786520.006100.0001571003

    -0.01197722670.00799.9995312475

    0.00884972450.008100.000166056

    -0.00879779240.00999.9996466305

    0.00136475360.0199.9999615069

    0.00750294480.011100.0001556527

    -0.00652632930.01299.9997447744

    0.00354148140.013100.0000568088

    0.00619479580.014100.0001464082

    -0.01807520680.01599.9994283081

    0.01995194910.016100.0005791228

    -0.00571794770.01799.9998190259

    -0.00218954030.01899.9999348781

    -0.01747039280.01999.9994864525

    -0.01198350220.0299.9996610592

    0.00029571080.021100.0000394356

    -0.00028499020.022100.0000320146

    -0.000806790.023100.0000263606

    -0.01419875840.02499.9996346016

    -0.00599583250.02599.9998906893

    -0.0129890850.02699.9996908918

    -0.00209170140.027100.0000278133

    0.00045494060.028100.0001142125

    -0.00659273380.02999.9999127823

    0.0068555210.03100.0003262299

    -0.01044456890.03199.9998172272

    0.00646775790.032100.000334597

    0.00790644210.033100.0003877576

    -0.00766817720.03499.999930519

    0.00227032610.035100.0002386741

    0.00849100840.036100.0004352946

    0.00448703760.037100.0003251754

    0.00414195260.038100.0003248229

    -0.02006518120.03999.9996086089

    -0.01370676730.0499.9998093613

    0.00228288850.041100.000299051

    -0.01404941940.04299.9998190817

    0.00994298260.043100.0005488538

    0.00363040730.044100.0003694765

    -0.00896918660.045100.0000014887

    0.00335961660.046100.0003813528

    0.00836985240.047100.0005416599

    -0.0148880190.04899.9998539237

    0.00173951090.049100.0003627496

    0.00740194540.05100.0005426227

    0.00408200550.051100.0004530245

    -0.00809502580.052100.0000977135

    -0.00412528610.053100.0002268057

    0.00903803540.054100.0006317054

    0.00312338670.055100.0004642659

    -0.00099804540.056100.000350623

    0.00807806370.057100.0006329062

    0.01644957590.058100.0008940516

    -0.00041588920.059100.0003980876

    0.01742482710.06100.0009433091

    -0.0008789470.061100.0004041959

    -0.00982329310.062100.0001458655

    0.01166190490.063100.0008004215

    -0.00148453410.064100.0004160283

    0.00578563690.065100.0006441334

    -0.00791690130.066100.0002430573

    0.00160453060.067100.0005387002

    -0.0174915840.06899.9999758168

    -0.00170068690.069100.0004595437

    -0.01265493670.07100.0001409162

    -0.01206703930.071100.0001685531

    0.00926477240.072100.0008185075

    0.00114346220.073100.0005848682

    -0.01277683170.074100.0001772594

    0.01618882380.075100.001056229

    -0.00445913880.076100.0004467901

    0.00139641540.077100.0006324568

    0.01140747370.078100.0009427885

    -0.01325875020.079100.0002128018

    0.01272164810.08100.0010022138

    0.0037959580.081100.0007444431

    0.00575671490.082100.0008132658

    0.0023779990.083100.0007219043

    -0.0136114750.084100.0002522201

    0.00272336820.085100.0007522654

    -0.00113884650.086100.0006463989

    0.01855823940.087100.0012473115

    0.01356524990.088100.0011075218

    -0.00957957130.089100.0004231772

    0.02911110640.09100.0015938975

    0.00290962130.091100.000817853

    -0.00659654230.092100.000542668

    0.01821008480.093100.0012968669

    -0.01079274630.094100.0004367819

    0.00218798280.095100.0008362038

    -0.00990291940.096100.0004834767

    0.00601048670.097100.0009708789

    0.0020042080.098100.0008606906

    0.00340011180.099100.0009125677

    -0.00376392110.1100.0007076467

    0.01187750060.101100.0011868893

    0.00596930930.102100.0010196436

    0.01342641550.103100.0012533568

    0.00560837630.104100.0010288156

    -0.00700040350.105100.0006605522

    -0.00507543520.106100.0007283013

    -0.00594097860.107100.000712335

    -0.0200025170.108100.0003004888

    0.01167400110.109100.0012607843

    -0.00462196110.11100.0007819055

    0.00176980850.111100.0009836586

    0.00694967640.112100.0011490546

    0.01294829420.113100.0013390131

    -0.00361978890.114100.0008519706

    0.00791585530.115100.00120804

    -0.00907145930.116100.0007084205

    -0.00636157440.117100.0007997171

    0.0086444970.118100.0012598992

    0.00103418640.119100.0010415899

    0.00190441370.12100.0010776967

    -0.00713594090.121100.0008164861

    -0.0235069820.122100.0003353549

    0.00696429650.123100.0012594932

    0.008962320.124100.0013294339

    0.007578160.125100.0012979091

    0.01169519240.126100.0014314201

    0.01576140680.127100.0015634065

    -0.01064329350.128100.0007812655

    -0.00437901240.129100.0009791939

    0.03088207450.13100.0020470265

    -0.02852830220.131100.0002747152

    -0.0030936690.132100.0010477542

    -0.00351950580.133100.0010449791

    0.0070278020.134100.0013713984

    0.01799739950.135100.0017104863

    -0.00390223250.136100.0010634973

    -0.0104683750.137100.0008765131

    0.00104495260.138100.0012319129

    0.00098114010.139100.0012399985

    0.00994045880.14100.0015187781

    -0.01529160730.141100.0007718161

    0.00000574120.142100.0012407365

    0.01384305510.143100.001665856

    0.00986924530.144100.0015566417

    0.02627311910.145100.0020587579

    0.01681873980.146100.0017851265

    0.00534706710.147100.0014509763

    -0.00424803370.148100.0011731233

    -0.01815415090.149100.0007659398

    0.01496728150.15100.0017695828

    -0.00230095340.151100.0012615357

    -0.00009065390.152100.0013378447

    -0.01252649330.153100.0009747695

    0.01326611710.154100.0017585478

    -0.00283229160.155100.0012855956

    -0.00109265560.156100.0013477846

    0.00510590330.157100.0015437414

    -0.00743015110.158100.0011776598

    0.00375407580.159100.0015231866

    0.00093963310.16100.0014487533

    -0.00422210180.161100.0013039013

    -0.00492977960.162100.0012926709

    -0.00236226470.163100.0013796964

    -0.00998570610.164100.0011609931

    0.02437955120.165100.0022019508

    -0.01314720070.166100.0010861483

    0.01072316990.167100.0018122594

    -0.00738485820.168100.0012790186

    -0.02265223880.169100.0008309971

    0.00877978440.17100.0017839578

    0.02037231750.171100.0021417338

    -0.00527044220.172100.001382451

    0.00842319420.173100.0018032601

    0.00216605260.174100.0016255459

    0.01029397940.175100.0018793837

    -0.00689329910.176100.0013737653

    0.01138550940.177100.0019321296

    0.01397588680.178100.0020198409

    -0.00388490660.179100.0014940171

    0.00816849020.18100.001865619

    -0.00162235660.181100.0015818936

    0.00128063680.182100.0016789834

    0.00441692690.183100.0017830721

    0.00327797810.184100.0017589037

    -0.00989543880.185100.0013737012

    0.00749989790.186100.0019055613

    0.00045799880.187100.0017043043

    -0.00247332540.188100.0016263646

    -0.00509110120.189100.0015578313

    0.00512770840.19100.0018743956

    -0.00176903540.191100.0016774933

    -0.0026013140.192100.0016625249

    0.00948080010.193100.0020349883

    0.0002490310.194100.0017680352

    -0.01209243690.195100.0014077912

    -0.01061773670.196100.0014620322

    0.0045268280.197100.0019263692

    -0.00594463930.198100.0016222251

    Lineare

    100

    99.9999752783

    99.9994103465

    99.9993188974

    99.9997910408

    99.9993675996

    100.0001571003

    99.9995312475

    100.000166056

    99.9996466305

    99.9999615069

    100.0001556527

    99.9997447744

    100.0000568088

    100.0001464082

    99.9994283081

    100.0005791228

    99.9998190259

    99.9999348781

    99.9994864525

    99.9996610592

    100.0000394356

    100.0000320146

    100.0000263606

    99.9996346016

    99.9998906893

    99.9996908918

    100.0000278133

    100.0001142125

    99.9999127823

    100.0003262299

    99.9998172272

    100.000334597

    100.0003877576

    99.999930519

    100.0002386741

    100.0004352946

    100.0003251754

    100.0003248229

    99.9996086089

    99.9998093613

    100.000299051

    99.9998190817

    100.0005488538

    100.0003694765

    100.0000014887

    100.0003813528

    100.0005416599

    99.9998539237

    100.0003627496

    100.0005426227

    100.0004530245

    100.0000977135

    100.0002268057

    100.0006317054

    100.0004642659

    100.000350623

    100.0006329062

    100.0008940516

    100.0003980876

    100.0009433091

    100.0004041959

    100.0001458655

    100.0008004215

    100.0004160283

    100.0006441334

    100.0002430573

    100.0005387002

    99.9999758168

    100.0004595437

    100.0001409162

    100.0001685531

    100.0008185075

    100.0005848682

    100.0001772594

    100.001056229

    100.0004467901

    100.0006324568

    100.0009427885

    100.0002128018

    100.0010022138

    100.0007444431

    100.0008132658

    100.0007219043

    100.0002522201

    100.0007522654

    100.0006463989

    100.0012473115

    100.0011075218

    100.0004231772

    100.0015938975

    100.000817853

    100.000542668

    100.0012968669

    100.0004367819

    100.0008362038

    100.0004834767

    100.0009708789

    100.0008606906

    100.0009125677

    100.0007076467

    100.0011868893

    100.0010196436

    100.0012533568

    100.0010288156

    100.0006605522

    100.0007283013

    100.000712335

    100.0003004888

    100.0012607843

    100.0007819055

    100.0009836586

    100.0011490546

    100.0013390131

    100.0008519706

    100.00120804

    100.0007084205

    100.0007997171

    100.0012598992

    100.0010415899

    100.0010776967

    100.0008164861

    100.0003353549

    100.0012594932

    100.0013294339

    100.0012979091

    100.0014314201

    100.0015634065

    100.0007812655

    100.0009791939

    100.0020470265

    100.0002747152

    100.0010477542

    100.0010449791

    100.0013713984

    100.0017104863

    100.0010634973

    100.0008765131

    100.0012319129

    100.0012399985

    100.0015187781

    100.0007718161

    100.0012407365

    100.001665856

    100.0015566417

    100.0020587579

    100.0017851265

    100.0014509763

    100.0011731233

    100.0007659398

    100.0017695828

    100.0012615357

    100.0013378447

    100.0009747695

    100.0017585478

    100.0012855956

    100.0013477846

    100.0015437414

    100.0011776598

    100.0015231866

    100.0014487533

    100.0013039013

    100.0012926709

    100.0013796964

    100.0011609931

    100.0022019508

    100.0010861483

    100.0018122594

    100.0012790186

    100.0008309971

    100.0017839578

    100.0021417338

    100.001382451

    100.0018032601

    100.0016255459

    100.0018793837

    100.0013737653

    100.0019321296

    100.0020198409

    100.0014940171

    100.001865619

    100.0015818936

    100.0016789834

    100.0017830721

    100.0017589037

    100.0013737012

    100.0019055613

    100.0017043043

    100.0016263646

    100.0015578313

    100.0018743956

    100.0016774933

    100.0016625249

    100.0020349883

    100.0017680352

    100.0014077912

    100.0014620322

    100.0019263692

    100.0016222251

    St

    Time

    St

    Linear Constant Coefficient SDEs

    Geometrische

    WthtSt

    -0.01129094470100

    -0.02279375620.00199.6699156549

    0.00001950870.002100.3670049981

    -0.0002038860.003100.3753336137

    -0.01682187760.00499.8899789783

    0.00208701750.005100.4716052145

    0.000663340.006100.4437642052

    -0.01400030670.007100.0169692098

    0.00324973830.008100.5495609196

    0.00702193570.009100.678431194

    -0.00381323840.01100.3662724573

    -0.00798722790.011100.2556490676

    -0.00213785820.012100.4466171217

    0.0100273610.013100.8282706498

    0.00764869130.014100.7714437446

    0.0104485480.015100.8712031418

    0.01271823750.016100.9550177155

    0.00560121410.017100.7546112007

    0.00340821770.018100.7034380436

    0.00290403930.019100.7033118102

    -0.00154102510.02100.5841274949

    -0.00973320770.021100.352014053

    -0.00301272390.022100.5693910783

    -0.01566672840.023100.2026948311

    -0.02353117450.02499.9813136258

    0.00956506480.025100.9890124687

    0.0235069820.026101.4265549534

    -0.00817490220.027100.4777536279

    -0.00625980190.028100.5505527825

    -0.01420921760.029100.3258399224

    0.01009589140.03101.0724179419

    0.01532371240.031101.246095358

    0.02301512720.032101.494899987

    0.00886784620.033101.0793611598

    0.01900907590.034101.4020437705

    -0.00222169090.035100.7714011328

    -0.001752710.036100.800694803

    0.00185924590.037100.9250412062

    -0.00284344420.038100.7977942032

    -0.00862451090.039100.6380982425

    0.00208232220.04100.9764485539

    0.00974796420.041101.2238098124

    0.00887919210.042101.212611258

    -0.00806958270.043100.7131642223

    0.01401051580.044101.3953981716

    0.01387302290.045101.4064251383

    0.00138791170.046101.0418149521

    -0.00796828770.047100.7733610147

    0.00324973830.048101.1276204733

    -0.00206356390.049100.9815931353

    0.01041294130.05101.3747095847

    0.01324035570.051101.4759042849

    0.010889130.052101.4195478443

    0.00170612110.053101.155359795

    -0.00191998880.054101.0604929635

    -0.002923980.055101.0452128837

    -0.01546886780.056100.6800894083

    -0.00224285940.057101.0946701335

    0.00144432310.058101.2216606827

    -0.01836069710.059100.6354348214

    0.01023697680.06101.5139119415

    -0.00736779380.061100.993000288

    -0.00101880460.062101.2005102798

    0.00173873790.063101.2994097676

    0.0011865950.064101.2978251552

    -0.01241660360.065100.8996275

    -0.00852287490.066101.0326251772

    -0.00364020710.067101.1957726941

    0.01101875570.068101.6559795789

    -0.01830730980.069100.7768770016

    0.02200486050.07102.0107539219

    0.00442366850.071101.4880143407

    0.00616610120.072101.5562883529

    -0.00047944010.073101.3690528417

    -0.01200232870.074101.0338389087

    -0.01779626470.075100.8733789056

    0.01138550940.076101.7716091608

    0.00942100090.077101.7268955431

    -0.0056855470.078101.2811319134

    -0.00380994150.079101.353313116

    -0.01184196210.08101.1242945446

    0.00131149140.081101.5385032987

    0.00375489440.082101.628163919

    0.01193657230.083101.8928548148

    0.02215383570.084102.2204585863

    0.0027821670.085101.6417373972

    -0.00479117260.086101.426053438

    0.01077496560.087101.9149109369

    0.00194181670.088101.6601292964

    0.0114677960.089101.9659020019

    0.00388160970.09101.7491371898

    0.0069877160.091101.8592126514

    -0.00528802960.092101.4993721996

    -0.01406378940.093101.2473768707

    -0.01501430230.094101.2336928955

    0.02204815250.095102.3744686994

    -0.00076688590.096101.6891216396

    -0.01049752430.097101.4075249881

    0.00451582310.098101.8794760363

    -0.01338696620.099101.3475799198

    -0.00478345330.1101.6243656209

    -0.00492977960.101101.6351481797

    0.00059742430.102101.8189209093

    -0.01034086380.103101.5000763389

    -0.00242839630.104101.7562361663

    0.01693952070.105102.3627415041

    0.00617071690.106102.0473986313

    0.00067025210.107101.894313304

    -0.0186794750.108101.3181093027

    0.00131921070.109101.9411757271

    -0.00607751640.11101.7302575851

    0.00262900810.111102.0112322198

    0.00292318420.112102.0355366834

    0.00334181320.113102.0636565256

    0.00578745580.114102.1538494426

    0.00510590330.115102.1482855538

    0.00274480950.116102.0912532939

    -0.01014566350.117101.7117656173

    0.00565948990.118102.2092934012

    0.0071329850.119102.2698062633

    0.01822213560.12102.6253723185

    -0.00692632510.121101.8665050805

    -0.00132074550.122102.0530912984

    -0.01269763740.123101.7200851639

    0.00536914510.124102.2866695748

    0.00312097650.125102.2330252721

    0.01428097680.126102.5906364011

    0.00425557120.127102.2974711752

    0.00198001540.128102.2429807164

    0.00565410120.129102.371012007

    -0.00508848640.13102.0564487889

    -0.01029527540.131101.9123413391

    -0.00232295180.132102.1713716395

    0.00793365870.133102.5010769341

    -0.01221733330.134101.8968025816

    0.00136938070.135102.3274199156

    -0.013563340.136101.8843609953

    -0.01670960050.137101.8034772274

    0.00102879770.138102.3604969319

    -0.00553868630.139102.1741757294

    0.00866452870.14102.6248623901

    -0.01242983670.141101.9908142166

    0.00603341730.142102.5710375324

    0.00215821960.143102.4671782715

    0.00046259170.144102.4304244889

    0.00531445040.145102.5948824349

    -0.00940312930.146102.1572871599

    -0.00599125090.147102.2771752261

    -0.00923544120.148102.1929748153

    -0.01279936440.149102.0990413874

    -0.00909340090.15102.2278688409

    0.00399486450.151102.644598665

    0.00813649880.152102.78753027

    -0.01424291440.153102.112851017

    0.00072775490.154102.5867772626

    0.00175815560.155102.6338769239

    0.00859790820.156102.859869103

    0.0121242920.157102.9841150964

    -0.00863672080.158102.3581463535

    -0.00353985570.159102.5300117762

    0.0104988430.16102.9772076621

    -0.01163175510.161102.3089700827

    -0.00254437960.162102.6032324358

    0.01103983320.163103.0367581657

    -0.00201670220.164102.6486227551

    0.01128805710.165103.0737346124

    0.00716854630.166102.9618116644

    -0.01372832230.167102.3317821017

    -0.00190674430.168102.7100488131

    -0.01405351210.169102.3511767845

    0.00950719820.17103.0899693904

    0.00584906270.171102.9922977633

    -0.00615870020.172102.6367344784

    0.00086665750.173102.868447921

    0.00731770340.174103.0829609126

    -0.00861230090.175102.6057897523

    -0.0029112130.176102.7966700105

    -0.00395594950.177102.7798708791

    0.00058056460.178102.9351665597

    -0.00423464140.179102.8019106248

    0.00854158770.18103.2113571413

    -0.00326748480.181102.8611897258

    -0.00889281180.182102.7030305544

    -0.00301432690.183102.8995574733

    0.00761388040.184103.243083755

    -0.00100035320.185102.9917622055

    0.01196158340.186103.4077027771

    -0.00138096540.187103.0092972378

    0.02787564880.188103.9288596128

    0.01506409720.189103.5450019561

    0.01632943170.19103.5998394255

    -0.01199134660.191102.7351709775

    -0.00180634740.192103.064488542

    -0.00783034010.193102.8936902979

    0.00444647410.194103.2880863679

    -0.00423966640.195103.0344271312

    -0.00559764430.196103.0079067525

    -0.0248208380.197102.4293156552

    -0.00245834140.198103.1318526184

    Geometrische

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

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    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

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    0

    0

    0

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    0

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    0

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    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

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    0

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    0

    0

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    0

    0

    0

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    0

    0

    0

    0

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    0

    0

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    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

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    0

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    0

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    0

    0

    0

    0

    St

    Time

    St

    Geometric SDEs

    Tabelle3

  • Bedeutende Modelle von SDGs (5)Quadratwurzel-ProzesseVarianz des Fehlerteils ist jetzt proportional zu Sk (anstatt zu Sk^2)Fr langweiligere Aktien (Blue Chips, ...)

  • Bedeutende Modelle von SDGs (6)Quadratwurzel-Prozesse

    Diagramm3

    100

    100.0203634494

    100.051793787

    100.0655872709

    100.0837970326

    100.087771741

    100.1110821824

    100.1515937605

    100.105194759

    100.1765806664

    100.1700602788

    100.2077357519

    100.2055337382

    100.1946050885

    100.1884733219

    100.2530704984

    100.2101139307

    100.2918947708

    100.2715562286

    100.2880142153

    100.2869125602

    100.294620618

    100.2935850021

    100.366778536

    100.3624109924

    100.3863795958

    100.3799197267

    100.4394871596

    100.4403451017

    100.435902894

    100.4839806094

    100.4846450848

    100.4986684651

    100.5199990529

    100.4808881674

    100.5246958955

    100.5629750918

    100.5447616424

    100.6178791705

    100.6351767678

    100.6024143208

    100.6593595538

    100.6282404744

    100.6526847176

    100.6605944135

    100.6836214541

    100.6855667731

    100.6709981316

    100.7345367742

    100.7872385714

    100.7741522492

    100.7713255325

    100.8212381735

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    101.054987002

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    101.5297206531

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    101.5708708303

    101.5998989262

    101.6326860964

    101.6765143566

    101.6983614311

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    101.6716298372

    101.670537041

    101.7041959724

    101.7718894459

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    101.7785663942

    101.8526364062

    101.8460419811

    101.8470835669

    101.7943060711

    101.8127828424

    101.8844423172

    101.8896377111

    101.8843291204

    101.8732895302

    101.8855894034

    101.9809842545

    101.9646593181

    101.9762152008

    101.9804720944

    101.9867020345

    102.0578571614

    102.0335698654

    102.0747918366

    102.0280901439

    102.0986744719

    102.0976920518

    102.1375514807

    102.1675896027

    102.0903700686

    102.1490187206

    102.1412383073

    102.1523775442

    102.1833639502

    102.2284604216

    102.1977689261

    102.2697569837

    102.2339433106

    102.2828740076

    102.3106997179

    102.3193723698

    102.3291598843

    102.352932391

    102.3458540674

    102.3701501857

    102.4122878502

    102.3603682166

    102.3745939185

    102.4621827136

    102.4695910198

    102.5312376414

    102.4615667235

    102.5081548692

    102.5127158079

    102.5197438028

    102.5059087205

    102.5921842971

    102.5520733173

    102.6077950418

    102.5942714867

    102.6470850726

    102.6586528044

    102.637686252

    102.6860292284

    102.6826738035

    102.6254209427

    102.6838645801

    102.6707501576

    102.6872758565

    102.8043960985

    102.7433885754

    102.7673928428

    102.8169463041

    102.7972564967

    102.8025193819

    102.8657440688

    102.8445291573

    102.8705692886

    102.8648318569

    102.9114540403

    102.9224879344

    103.0071213341

    102.9886391223

    102.9522477122

    102.9558447637

    103.0248504333

    103.0417924249

    St

    Time

    St

    Square Root Process

    Lineare

    WtTimeSt

    0.00598118960100

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    0.01821008480.093100.0012968669

    -0.01079274630.094100.0004367819

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    -0.00990291940.096100.0004834767

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    0.0020042080.098100.0008606906

    0.00340011180.099100.0009125677

    -0.00376392110.1100.0007076467

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    0.01342641550.103100.0012533568

    0.00560837630.104100.0010288156

    -0.00700040350.105100.0006605522

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    -0.0200025170.108100.0003004888

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    0.00093963310.16100.0014487533

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    0.00327797810.184100.0017589037

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    0.00045799880.187100.0017043043

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    -0.0026013140.192100.0016625249

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    -0.01061773670.196100.0014620322

    0.0045268280.197100.0019263692

    -0.00594463930.198100.0016222251

    Lineare

    100

    99.9999752783

    99.9994103465

    99.9993188974

    99.9997910408

    99.9993675996

    100.0001571003

    99.9995312475

    100.000166056

    99.9996466305

    99.9999615069

    100.0001556527

    99.9997447744

    100.0000568088

    100.0001464082

    99.9994283081

    100.0005791228

    99.9998190259

    99.9999348781

    99.9994864525

    99.9996610592

    100.0000394356

    100.0000320146

    100.0000263606

    99.9996346016

    99.9998906893

    99.9996908918

    100.0000278133

    100.0001142125

    99.9999127823

    100.0003262299

    99.9998172272

    100.000334597

    100.0003877576

    99.999930519

    100.0002386741

    100.0004352946

    100.0003251754

    100.0003248229

    99.9996086089

    99.9998093613

    100.000299051

    99.9998190817

    100.0005488538

    100.0003694765

    100.0000014887

    100.0003813528

    100.0005416599

    99.9998539237

    100.0003627496

    100.0005426227

    100.0004530245

    100.0000977135

    100.0002268057

    100.0006317054

    100.0004642659

    100.000350623

    100.0006329062

    100.0008940516

    100.0003980876

    100.0009433091

    100.0004041959

    100.0001458655

    100.0008004215

    100.0004160283

    100.0006441334

    100.0002430573

    100.0005387002

    99.9999758168

    100.0004595437

    100.0001409162

    100.0001685531

    100.0008185075

    100.0005848682

    100.0001772594

    100.001056229

    100.0004467901

    100.0006324568

    100.0009427885

    100.0002128018

    100.0010022138

    100.0007444431

    100.0008132658

    100.0007219043

    100.0002522201

    100.0007522654

    100.0006463989

    100.0012473115

    100.0011075218

    100.0004231772

    100.0015938975

    100.000817853

    100.000542668

    100.0012968669

    100.0004367819

    100.0008362038

    100.0004834767

    100.0009708789

    100.0008606906

    100.0009125677

    100.0007076467

    100.0011868893

    100.0010196436

    100.0012533568

    100.0010288156

    100.0006605522

    100.0007283013

    100.000712335

    100.0003004888

    100.0012607843

    100.0007819055

    100.0009836586

    100.0011490546

    100.0013390131

    100.0008519706

    100.00120804

    100.0007084205

    100.0007997171

    100.0012598992

    100.0010415899

    100.0010776967

    100.0008164861

    100.0003353549

    100.0012594932

    100.0013294339

    100.0012979091

    100.0014314201

    100.0015634065

    100.0007812655

    100.0009791939

    100.0020470265

    100.0002747152

    100.0010477542

    100.0010449791

    100.0013713984

    100.0017104863

    100.0010634973

    100.0008765131

    100.0012319129

    100.0012399985

    100.0015187781

    100.0007718161

    100.0012407365

    100.001665856

    100.0015566417

    100.0020587579

    100.0017851265

    100.0014509763

    100.0011731233

    100.0007659398

    100.0017695828

    100.0012615357

    100.0013378447

    100.0009747695

    100.0017585478

    100.0012855956

    100.0013477846

    100.0015437414

    100.0011776598

    100.0015231866

    100.0014487533

    100.0013039013

    100.0012926709

    100.0013796964

    100.0011609931

    100.0022019508

    100.0010861483

    100.0018122594

    100.0012790186

    100.0008309971

    100.0017839578

    100.0021417338

    100.001382451

    100.0018032601

    100.0016255459

    100.0018793837

    100.0013737653

    100.0019321296

    100.0020198409

    100.0014940171

    100.001865619

    100.0015818936

    100.0016789834

    100.0017830721

    100.0017589037

    100.0013737012

    100.0019055613

    100.0017043043

    100.0016263646

    100.0015578313

    100.0018743956

    100.0016774933

    100.0016625249

    100.0020349883

    100.0017680352

    100.0014077912

    100.0014620322

    100.0019263692

    100.0016222251

    St

    Time

    St

    Linear Constant Coefficient SDEs

    Geometrische

    WthtSt

    -0.0010549570100

    -0.00392618630.00199.928863121

    -0.00551640370.00299.896179866

    -0.0014829880.003100.0320411401

    -0.0124364760.00499.7183360155

    -0.01379930840.00599.692523954

    0.00684101450.006100.3247835974

    0.01154492110.007100.4814078383

    0.00925185760.008100.4273569744

    -0.00208310670.009100.1009189274

    0.00484874360.01100.3240994406

    -0.0106581410.01199.8724337837

    -0.00796198950.01299.9681960145

    -0.00023601390.013100.2148967966

    -0.00621149640.014100.0502793223

    -0.00256018210.015100.174881368

    -0.00683520510.016100.0614326236

    0.00221227760.017100.3480330646

    0.00169836770.018100.3476143128

    -0.01005776080.019100.0087566199

    0.00527659270.02100.4838288222

    0.01431071720.021100.7712364242

    0.00877416820.022100.6189746433

    0.00356674260.023100.4768777421

    0.00637094220.024100.5764764381

    -0.01879452610.02599.8322466711

    0.01003240870.026100.7105788076

    -0.0004296680.027100.409592854

    -0.00242918080.028100.3644232151

    -0.0028163640.029100.3678200511

    0.01044193140.03100.7820870873

    0.0058073510.031100.6570795958

    -0.00461004670.032100.3576027063

    -0.00051161350.033100.496049027

    0.01071093720.034100.8494700363

    -0.00189972980.035100.4830637317

    -0.00345285120.036100.4513174733

    0.01204016370.037100.9332732976

    -0.02364249670.03899.8679429749

    0.01653302210.039101.0865970905

    0.0021229880.04100.6647616881

    0.00322716010.041100.713206767

    -0.0077567620.042100.3964459446

    -0.01067842280.043100.3235081039

    -0.00894976890.044100.3905840155

    -0.00350648860.045100.56957883

    -0.0094712050.046100.4047035631

    -0.00128757160.047100.6662668521

    0.00926829670.048101.0001527504

    0.00350974010.049100.8408182428

    -0.00747661490.05100.5235824591

    -0.00443042150.051100.6305252768

    0.02843953550.052101.6379361692

    0.00850748170.053101.0454260138

    -0.00649229150.054100.6058852871

    0.01122175490.055101.1556173661

    0.00997940790.056101.1330895946

    0.00834708090.057101.0987348767

    0.0163818640.058101.3575916104

    -0.0248208380.059100.1199332548

    -0.01530393090.06100.4208008755

    -0.00187480960.061100.8404329298

    0.00234967960.062100.9833587908

    -0.00606280540.063100.7436499994

    -0.00382640340.064100.8263525369

    -0.00567115420.065100.7856766402

    0.01322016490.066101.3719868047

    -0.00106880410.067100.9526422515

    0.02464166760.068101.7464471608

    -0.0196425390.069100.4099809242

    0.01351932040.07101.423976922

    -0.01220928430.071100.6563412967

    -0.02205688360.072100.3740727513

    -0.01558119040.073100.5841263731

    -0.00268369150.074100.9883990895

    -0.006069240.075100.9009770109

    0.00251357050.076101.1759163485

    -0.00199640910.077101.0542023406

    0.0233521860.078101.8378350868

    -0.00399237480.079101.0176975016

    -0.01302651070.08100.7590678731

    0.01202122350.081101.5313176384

    -0.00204872780.082101.1179851292

    0.00062425440.083101.214238799

    -0.00348371710.084101.1046853704

    -0.01690750650.085100.712688673

    0.01265493670.086101.6209895166

    0.00459049260.087101.3903776299

    0.00701508040.088101.4793351489

    -0.00062271970.089101.2620333869

    -0.00617906150.09101.108428749

    -0.01429796160.091100.8773282454

    0.00096422350.092101.3543423819

    0.00378363440.093101.4552733927

    0.01145158420.094101.7038778677

    0.01391922520.095101.7944240478

    0.01774433260.096101.926505591

    0.00705820180.097101.6150345776

    0.0052853920.098101.5762335937

    0.02831075110.099102.2931188033

    0.01110479390.1101.7804474642

    -0.01149146560.101101.1057573122

    0.00988045490.102101.7691704353

    -0.00062884740.103101.46357892

    -0.02493907230.104100.7388177287

    -0.00575762440.105101.3336234664

    0.00721709060.106101.743255975

    -0.01166492890.107101.1821820203

    0.01485332180.108102.0023116885

    -0.00040057560.109101.5508321978

    0.00034546020.11101.5887929885

    0.01792450350.111102.1397814443

    0.00491941140.112101.7566012317

    0.0057657530.113101.7977009772

    -0.00725883640.114101.415208655

    0.00580464530.115101.8278716522

    -0.01138112110.116101.3181488281

    0.01387904830.117102.1011406319

    -0.00906798050.118101.4135804583

    0.01614080250.119102.1957463775

    -0.0134831680.12101.3028426074

    0.00044727810.121101.7413961713

    0.00468334060.122101.8859522553

    -0.00526868010.123101.5970438158

    -0.00642537540.124101.5770283236

    -0.02180277080.125101.1236678407

    -0.01519383660.126101.3393322909

    0.00836985240.127102.0709117423

    0.02051447150.128102.4581060847

    0.00467053950.129101.9864730199

    -0.00987422480.13101.5567602265

    0.00087356970.131101.8994470965

    0.00728375650.132102.1106903629

    -0.01324588080.133101.4971183331

    -0.00460834140.134101.7753485083

    0.00501808020.135102.084534535

    0.01093490030.136102.281051963

    0.00363286290.137102.0723361015

    0.0010018880.138102.0070820255

    -0.00483412350.139101.8437887368

    0.00162467590.14102.0564018844

    0.00393940810.141102.1425803175

    0.00495743960.142102.1890970146

    0.00559138020.143102.2238599227

    0.00324650960.144102.1672829843

    -0.00518275560.145101.9242495426

    -0.00199329410.146102.0370632208

    0.01384505590.147102.5371983967

    0.00059359310.148102.1449486135

    0.01805565260.149102.6953687079

    0.00598026870.15102.3387472129

    -0.01317084750.151101.7661276516

    0.00977877330.152102.4820407848

    -0.00980101050.153101.8954402292

    0.00590086980.154102.3907095478

    -0.00488232670.155102.0748384102

    0.00163088320.156102.2896000898

    0.00734773950.157102.4803760139

    0.00495138010.158102.4220741273

    0.00220521770.159102.3530571435

    0.00345934270.16102.4069191598

    0.00261001110.161102.3961869671

    0.01099210750.162102.6690348094

    0.00226639260.163102.4156769464

    -0.00301432690.164102.268790759

    -0.01206544770.165102.0064369257

    -0.01611551850.166101.897797902

    0.01584403440.167102.8900649895

    -0.00551374340.168102.2462475565

    -0.00624957010.169102.2390138383

    0.00214881770.17102.5119425552

    0.00009065390.171102.4640234366

    0.00800828270.172102.722774673

    -0.0049461960.173102.3389670892

    0.00312257950.174102.6020429798

    0.00073235920.175102.5438608408

    -0.00395511960.176102.4150407663

    0.00218641390.177102.6190986437

    -0.00293675840.178102.4767709118

    -0.01018029250.179102.2694542312

    0.00504412580.18102.751892536

    -0.02192809920.181101.9358711708

    -0.00543464010.182102.4555440864

    -0.01514549690.183102.172433082

    -0.00226797280.184102.5824773382

    -0.00173563420.185102.614247294

    0.00223736830.186102.7519454309

    0.00793575050.187102.9430141801

    0.00508151740.188102.8703086242

    -0.00170068690.189102.6764329354

    -0.00171155530.19102.6914996198

    -0.00029800730.191102.750451155

    0.00164405950.192102.8257281939

    0.01119451550.193103.1357618331

    -0.0173485660.194102.2680884607

    0.00565679560.195102.9892429783

    -0.00510677860.196102.6721316569

    0.00403465490.197102.9691036178

    0.01163325580.198103.2192753191

    Geometrische

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

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    0

    0

    0

    0

    0

    0

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    0

    0

    0

    0

    0

    0

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    0

    0

    0

    0

    0

    0

    0

    0

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    0

    0

    0

    0

    0

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    0

    0

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    0

    0

    0

    0

    0

    0

    0

    0

    0

    St

    Time

    St

    Geometric SDEs

    Square

    WthtSt

    -0.00233237640100

    -0.000544560.001100.0203634494

    0.00493064360.002100.051793787

    0.00452598670.003100.0655872709

    0.00559227830.004100.0837970326

    0.00191453180.005100.087771741

    0.00467907740.006100.1110821824

    0.01317266650.007100.1515937605

    -0.00728574610.008100.105194759

    0.01149442140.009100.1765806664

    0.00431846270.01100.1700602788

    0.01186203920.011100.2077357519

    0.00612360510.012100.2055337382

    -0.00252067590.013100.1946050885

    -0.0095674750.014100.1884733219

    0.00693994480.015100.2530704984

    -0.01236714980.016100.2101139307

    0.00985928640.017100.2918947708

    -0.00191764680.018100.2715562286

    -0.00144586920.019100.2880142153

    -0.00681975510.02100.2869125602

    -0.00926124810.021100.294620618

    -0.01461330610.022100.2935850021

    0.00474146870.023100.366778536

    -0.00172087770.024100.3624109924

    0.00124516650.025100.3863795958

    -0.00591362550.026100.3799197267

    0.00889508560.027100.4394871596

    0.00416946480.028100.4403451017

    -0.00231901820.029100.435902894

    0.00866118630.03100.4839806094

    0.00387005910.031100.4846450848

    0.00352113150.032100.4986684651

    0.00560121410.033100.5199990529

    -0.01241496650.034100.4808881674

    -0.00285938310.035100.5246958955

    0.0048539050.036100.5629750918

    -0.00621428170.037100.5447616424

    0.01307851110.038100.6178791705

    0.01381122270.039100.6351767678

    -0.00209092830.04100.6024143208

    0.01181886090.041100.6593595538

    -0.00353659290.042100.6282404744

    -0.0004296680.043100.6526847176

    -0.00281795560.044100.6605944135

    -0.00018399080.045100.6836214541

    -0.00455481770.046100.6855667731

    -0.01441158020.047100.6709981316

    0.00168051880.048100.7345367742

    0.0141652890.049100.7872385714

    0.00480060860.05100.7741522492

    -0.00115732060.051100.7713255325

    0.01039718430.052100.8212381735

    -0.00230802470.053100.7980895423

    -0.00265595190.054100.8121613173

    -0.00716358950.055100.8137054256

    -0.00099804540.056100.8473992155

    0.00227267950.057100.8723799864

    -0.00960624220.058100.8517189719

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    -0.01483490450.061100.8813387026

    -0.00299751260.062100.932139227

    -0.00439586070.063100.9430644971

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    -0.00701900260.065100.965440327

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    -0.00907375580.067100.9895377967

    0.00761082220.068101.054987002

    0.00065567750.069101.0491700409

    0.00461516270.07101.0762680219

    0.00061122590.071101.0793531853

    -0.01435773810.072101.0493664947

    0.00418866650.073101.1204542812

    -0.01073813110.074101.0905917835

    0.00263851230.075101.146103536

    -0.00992542940.076101.1233682481

    -0.00750294480.077101.1458449133

    0.00301832870.078101.1927609316

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    -0.00155650920.08101.209312946

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    -0.01272510420.082101.2059584434

    -0.00432014530.083101.2465057986

    0.00984935010.084101.3044653756

    0.00075000340.085101.2921855355

    0.01451389830.086101.3489369743

    0.00091197310.087101.3230592389

    -0.01050150330.088101.3037915024

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    -0.01664811860.09101.3155798098

    0.02132564990.091101.4454453665

    0.00621705570.092101.4150099963

    -0.0037598170.093101.400080613

    0.00757510180.094101.449532601

    -0.00031943730.095101.4408953804

    -0.00177991520.096101.4516986278

    0.00987547540.097101.5021354417

    -0.02473825590.098101.4127425576

    0.00032173380.099101.5036636251

    0.01127214090.1101.5519864605

    0.01571124810.101101.5806395238

    -0.0004396270.102101.547042565

    0.000806790.103101.5660426853

    -0.01624584910.104101.5297206531

    0.01520356820.105101.6400172566

    -0.01269936550.106101.5708708303

    -0.00813756740.107101.5998989262

    -0.00233474110.108101.6326860964

    0.00711620490.109101.6765143566

    0.00929653650.11101.6983614311

    0.00893264770.111101.7125152876

    -0.00962324980.112101.6716298372

    -0.01502612580.113101.670537041

    -0.00894062850.114101.7041959724

    0.00839158930.115101.7718894459

    -0.00528802960.116101.7457543876

    0.00051161350.117101.7785663942

    0.01994067130.118101.8526364062

    0.01271650940.119101.8460419811

    0.00801460370.12101.8470835669

    -0.01446360330.121101.7943060711

    -0.01340386010.122101.8127828424

    0.00522391020.123101.8844423172

    0.00189272670.124101.8896377111

    -0.00490733780.125101.8843291204

    -0.01359990160.126101.8732895302

    -0.01458442970.127101.8855894034

    0.0118713160.128101.9809842545

    0.00143350010.129101.9646593181

    0.0001992930.13101.9762152008

    -0.00344472260.131101.9804720944

    -0.00643760810.132101.9867020345

    0.0119991910.133102.0578571614

    -0.00106572320.134102.0335698654

    0.0074867330.135102.0747918366

    -0.01297307790.136102.0280901439

    0.00526956680.137102.0986744719

    -0.00010671780.138102.0976920518

    0.00799038840.139102.1375514807

    0.01284461180.14102.1675896027

    -0.01767461980.141102.0903700686

    -0.00337823850.142102.1490187206

    -0.01099772360.143102.1412383073

    -0.01237701780.144102.1523775442

    -0.00721113340.145102.1833639502

    0.00260527030.146102.2284604216

    -0.01256851190.147102.1977689261

    0.00611344150.148102.2697569837

    -0.01074765810.149102.2339433106

    0.00032785010.15102.2828740076

    0.0044422450.151102.3106997179

    0.00224285940.152102.3193723698

    0.00041052320.153102.3291598843

    0.00318609640.154102.352932391

    -0.00420454850.155102.3458540674

    -0.00125750150.156102.3701501857

    0.00756592730.157102.4122878502

    -0.01459552550.158102.3603682166

    -0.01496728150.159102.3745939185

    0.00882937460.16102.4621827136

    0.00620777880.161102.4695910198

    0.02144615790.162102.5312376414

    -0.00655190890.163102.4615667235

    0.00372863270.164102.5081548692

    0.00016791550.165102.5127158079

    -0.00258073670.166102.5197438028

    -0.01219800650.167102.5059087205

    0.01114456150.168102.5921842971

    -0.00712016120.169102.5520733173

    0.00615777940.17102.6077950418

    -0.00335719510.171102.5942714867

    0.00895888660.172102.6470850726

    0.00769900910.173102.6586528044

    -0.00426477980.174102.637686252

    0.0065756240.175102.6860292284

    0.00040516850.176102.6826738035

    -0.02349479470.177102.6254209427

    -0.00932959670.178102.6838645801

    -0.0187102160.179102.6707501576

    -0.01834009710.18102.6872758565

    0.01511903060.181102.8043960985

    -0.01000714750.182102.7433885754

    -0.00718139290.183102.7673928428

    0.00404379530.184102.8169463041

    -0.00749887480.185102.7972564967

    -0.01083806180.186102.8025193819

    0.00487800660.187102.8657440688

    -0.00716556770.188102.8445291573

    -0.00367701890.189102.8705692886

    -0.01063388030.19102.8648318569

    -0.00038220380.191102.9114540403

    -0.00182890290.192102.9224879344

    0.02090628190.193103.0071213341

    0.00976151570.194102.9886391223

    -0.00726581670.195102.9522477122

    -0.01115738540.196102.9558447637

    0.00643855170.197103.0248504333

    0.00692730280.198103.0417924249

    Square

    0

    0

    0

    0

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    0

    0

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    St

    Time

    St

    Square Root Process

  • Bedeutende Modelle von SDGs (7)Mean Reverting ProcessFluktuiert um einen LangzeittrendGeeignet zum Modellieren von Zinsen

  • Bedeutende Modelle von SDGs (8)Mean Reverting Process

    Diagramm4

    100

    97.7490388119

    98.184919326

    98.4370454396

    99.893462202

    99.3666922806

    98.7977554202

    98.7132341234

    99.5427169475

    98.6095679833

    98.4724928746

    99.0212594356

    98.1075351275

    99.3378891712

    99.3356308735

    100.2121012844

    98.7511798273

    99.5327745563

    98.9356748086

    97.819026708

    99.6238097987

    98.7718178602

    99.8802797997

    99.5663782457

    97.7560310841

    98.0232280346

    97.8271378792

    99.7822195359

    100.1467678983

    99.740287835

    100.2603081031

    99.8020602084

    99.3192956849

    98.310829139

    99.1014817869

    100.2419078063

    100.662224045

    99.6189975447

    99.3390491593

    98.9360664569

    99.2181389668

    99.5014849452

    99.1955344037

    98.8967283576

    99.0574847028

    99.2493479523

    98.0471715

    99.9532676868

    99.0276381302

    99.448620307

    98.9879422708

    98.9908646783

    98.987528495

    98.8553307256

    99.0893987702

    100.0192532351

    98.5829895986

    98.8629140971

    98.5395528934

    98.4136815194

    99.8392999626

    100.160649703

    98.7105372607

    99.8729554715

    98.3977943199

    98.3917063076

    99.1851052099

    100.0501594782

    99.8072248257

    99.2019402894

    98.6212918656

    99.6379132963

    98.3256281466

    99.1833442222

    97.677974971

    98.5540806338

    98.8950907871

    98.9699797231

    98.7652109329

    98.4039867829

    98.0851242287

    98.6347245298

    97.8568873486

    98.6349263635

    97.0081614886

    98.4819248672

    99.1787677476

    99.8790762927

    98.4997563477

    100.4865926264

    99.7741459129

    98.6483900642

    99.8122881079

    99.9186911392

    97.2781436281

    98.475072591

    98.2709266723

    98.9237071176

    98.6896604527

    97.3072388642

    98.3006324524

    98.397489413

    98.6436634006

    98.6946685942

    98.0659189367

    98.4417239373

    99.0953675933

    99.3202552497

    98.4587718041

    98.8797496247

    98.5449180424

    98.2087734108

    97.6038018828

    98.2732829058

    98.951667914

    98.293681319

    98.2892787945

    98.740994243

    99.3316566878

    97.4089738119

    98.6092100606

    98.7115019122

    99.3502673012

    98.3280614766

    98.3338070898

    99.9126713764

    98.6619542942

    97.5964268426

    99.5654695598

    96.9693148803

    97.1503560527

    99.0379905349

    97.3384283238

    99.3532613332

    98.0139265426

    99.6396800146

    98.8249077396

    98.7707264629

    98.5889940311

    96.9515103063

    98.4589405548

    99.1786391137

    96.6668304684

    97.4048276368

    98.8056321993

    98.2200948705

    98.370949555

    98.5623171964

    99.1776487294

    98.3635489643

    99.2137433321

    98.971438479

    98.6852797765

    98.823728872

    96.2807838094

    98.4767633899

    98.6551798679

    96.8532945006

    97.4156667221

    99.0101449238

    98.7615277383

    98.5142136989

    99.3760271209

    97.6986165558

    99.1333635478

    96.8551186587

    97.8880652009

    98.3398145994

    97.8957643688

    98.4813891408

    98.0452414362

    100.4662957702

    97.7613375201

    97.5301509845

    97.9829222262

    97.4173735677

    96.2003713953

    97.2231532786

    98.6175194424

    97.461116073

    98.8639670248

    98.1850181267

    96.9216713671

    98.4599867686

    97.6976690532

    97.7355210995

    96.9805492988

    97.8869727987

    97.5468957069

    97.1779057623

    97.4065012369

    98.2422293298

    96.7240206374

    96.6930675073

    98.360015657

    97.6488920044

    98.1662539477

    98.4472224766

    98.08300394

    St

    Time

    St

    Mean Reverting Process

    Lineare

    WtTimeSt

    0.00598118960100

    0.00482380070.00199.9999752783

    -0.01434059410.00299.9994103465

    -0.01772223190.00399.9993188974

    -0.00231744930.00499.9997910408

    -0.01676548890.00599.9993675996

    0.00921786520.006100.0001571003

    -0.01197722670.00799.9995312475

    0.00884972450.008100.000166056

    -0.00879779240.00999.9996466305

    0.00136475360.0199.9999615069

    0.00750294480.011100.0001556527

    -0.00652632930.01299.9997447744

    0.00354148140.013100.0000568088

    0.00619479580.014100.0001464082

    -0.01807520680.01599.9994283081

    0.01995194910.016100.0005791228

    -0.00571794770.01799.9998190259

    -0.00218954030.01899.9999348781

    -0.01747039280.01999.9994864525

    -0.01198350220.0299.9996610592

    0.00029571080.021100.0000394356

    -0.00028499020.022100.0000320146

    -0.000806790.023100.0000263606

    -0.01419875840.02499.9996346016

    -0.00599583250.02599.9998906893

    -0.0129890850.02699.9996908918

    -0.00209170140.027100.0000278133

    0.00045494060.028100.0001142125

    -0.00659273380.02999.9999127823

    0.0068555210.03100.0003262299

    -0.01044456890.03199.9998172272

    0.00646775790.032100.000334597

    0.00790644210.033100.0003877576

    -0.00766817720.03499.999930519

    0.00227032610.035100.0002386741

    0.00849100840.036100.0004352946

    0.00448703760.037100.0003251754

    0.00414195260.038100.0003248229

    -0.02006518120.03999.9996086089

    -0.01370676730.0499.9998093613

    0.00228288850.041100.000299051

    -0.01404941940.04299.9998190817

    0.00994298260.043100.0005488538

    0.00363040730.044100.0003694765

    -0.00896918660.045100.0000014887

    0.00335961660.046100.0003813528

    0.00836985240.047100.0005416599

    -0.0148880190.04899.9998539237

    0.00173951090.049100.0003627496

    0.00740194540.05100.0005426227

    0.00408200550.051100.0004530245

    -0.00809502580.052100.0000977135

    -0.00412528610.053100.0002268057

    0.00903803540.054100.0006317054

    0.00312338670.055100.0004642659

    -0.00099804540.056100.000350623

    0.00807806370.057100.0006329062

    0.01644957590.058100.0008940516

    -0.00041588920.059100.0003980876

    0.01742482710.06100.0009433091

    -0.0008789470.061100.0004041959

    -0.00982329310.062100.0001458655

    0.01166190490.063100.0008004215

    -0.00148453410.064100.0004160283

    0.00578563690.065100.0006441334

    -0.00791690130.066100.0002430573

    0.00160453060.067100.0005387002

    -0.0174915840.06899.9999758168

    -0.00170068690.069100.0004595437

    -0.01265493670.07100.0001409162

    -0.01206703930.071100.0001685531

    0.00926477240.072100.0008185075

    0.00114346220.073100.0005848682

    -0.01277683170.074100.0001772594

    0.01618882380.075100.001056229

    -0.00445913880.076100.0004467901

    0.00139641540.077100.0006324568

    0.01140747370.078100.0009427885

    -0.01325875020.079100.0002128018

    0.01272164810.08100.0010022138

    0.0037959580.081100.0007444431

    0.00575671490.082100.0008132658

    0.0023779990.083100.0007219043

    -0.0136114750.084100.0002522201

    0.00272336820.085100.0007522654

    -0.00113884650.086100.0006463989

    0.01855823940.087100.0012473115

    0.01356524990.088100.0011075218

    -0.00957957130.089100.0004231772

    0.02911110640.09100.0015938975

    0.00290962130.091100.000817853

    -0.00659654230.092100.000542668

    0.01821008480.093100.0012968669

    -0.01079274630.094100.0004367819

    0.00218798280.095100.0008362038

    -0.00990291940.096100.0004834767

    0.00601048670.097100.0009708789

    0.0020042080.098100.0008606906

    0.00340011180.099100.0009125677

    -0.00376392110.1100.0007076467

    0.01187750060.101100.0011868893

    0.00596930930.102100.0010196436

    0.01342641550.103100.0012533568

    0.00560837630.104100.0010288156

    -0.00700040350.105100.0006605522

    -0.00507543520.106100.0007283013

    -0.00594097860.107100.000712335

    -0.0200025170.108100.0003004888

    0.01167400110.109100.0012607843

    -0.00462196110.11100.0007819055

    0.00176980850.111100.0009836586

    0.00694967640.112100.0011490546

    0.01294829420.113100.0013390131

    -0.00361978890.114100.0008519706

    0.00791585530.115100.00120804

    -0.00907145930.116100.0007084205

    -0.00636157440.117100.0007997171

    0.0086444970.118100.0012598992

    0.00103418640.119100.0010415899

    0.00190441370.12100.0010776967

    -0.00713594090.121100.0008164861

    -0.0235069820.122100.0003353549

    0.00696429650.123100.0012594932

    0.008962320.124100.0013294339

    0.007578160.125100.0012979091

    0.01169519240.126100.0014314201

    0.01576140680.127100.0015634065

    -0.01064329350.128100.0007812655

    -0.00437901240.129100.0009791939

    0.03088207450.13100.0020470265

    -0.02852830220.131100.0002747152

    -0.0030936690.132100.0010477542

    -0.00351950580.133100.0010449791

    0.0070278020.134100.0013713984

    0.01799739950.135100.0017104863

    -0.00390223250.136100.0010634973

    -0.0104683750.137100.0008765131

    0.00104495260.138100.0012319129

    0.00098114010.139100.0012399985

    0.00994045880.14100.0015187781

    -0.01529160730.141100.0007718161

    0.00000574120.142100.0012407365

    0.01384305510.143100.001665856

    0.00986924530.144100.0015566417

    0.02627311910.145100.0020587579

    0.01681873980.146100.0017851265

    0.00534706710.147100.0014509763

    -0.00424803370.148100.0011731233

    -0.01815415090.149100.0007659398

    0.01496728150.15100.0017695828

    -0.00230095340.151100.0012615357

    -0.00009065390.152100.0013378447

    -0.01252649330.153100.0009747695

    0.01326611710.154100.0017585478

    -0.00283229160.155100.0012855956

    -0.00109265560.156100.0013477846

    0.00510590330.157100.0015437414

    -0.00743015110.158100.0011776598

    0.00375407580.159100.0015231866

    0.00093963310.16100.0014487533

    -0.00422210180.161100.0013039013

    -0.00492977960.162100.0012926709

    -0.00236226470.163100.0013796964

    -0.00998570610.164100.0011609931

    0.02437955120.165100.0022019508

    -0.01314720070.166100.0010861483

    0.01072316990.167100.0018122594

    -0.00738485820.168100.0012790186

    -0.02265223880.169100.0008309971

    0.00877978440.17100.0017839578

    0.02037231750.171100.0021417338

    -0.00527044220.172100.001382451

    0.00842319420.173100.0018032601

    0.00216605260.174100.0016255459

    0.01029397940.175100.0018793837

    -0.00689329910.176100.0013737653

    0.01138550940.177100.0019321296

    0.01397588680.178100.0020198409

    -0.00388490660.179100.0014940171

    0.00816849020.18100.001865619

    -0.00162235660.181100.0015818936

    0.00128063680.182100.0016789834

    0.00441692690.183100.0017830721

    0.00327797810.184100.0017589037

    -0.00989543880.185100.0013737012

    0.00749989790.186100.0019055613

    0.00045799880.187100.0017043043

    -0.00247332540.188100.0016263646

    -0.00509110120.189100.0015578313

    0.00512770840.19100.0018743956

    -0.00176903540.191100.0016774933

    -0.0026013140.192100.0016625249

    0.00948080010.193100.0020349883

    0.0002490310.194100.0017680352

    -0.01209243690.195100.0014077912

    -0.01061773670.196100.0014620322

    0.0045268280.197100.0019263692

    -0.00594463930.198100.0016222251

    Lineare

    100

    99.9999752783

    99.9994103465

    99.9993188974

    99.9997910408

    99.9993675996

    100.0001571003

    99.9995312475

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