La lecture à portée de main
Description
Informations
Publié par | karlsruher_institut_fur_technologie |
Publié le | 01 janvier 2011 |
Nombre de lectures | 22 |
Langue | English |
Poids de l'ouvrage | 2 Mo |
Extrait
MinimallyCross-Entropic
ConditionalDensity:
AGeneralizationoftheGARCHModel
ZurErlangungdesakademischenGrades
einesDoktorsderWirtschaftswissenschaften
(Dr.rer.pol.)
vonderFakulta¨tfu¨r
Wirtschaftswissenschaften
desKarlsruherInstitutsfu¨rTechnologie(KIT)
angenommene
Dissertation
nov
Dipl.Wi.-Ing.MatthiasScherer
Tagdermu¨ndlichenPru¨fung:
Referent:
Korreferent:
11.Mai2011
Prof.Dr.S.T.Rachev
Prof.Dr.M.Uhrig-Homburg
2011,Karlsruhe
oT
alE
Acknowledgements
v
IwouldliketoexpressmydeeplyfeltgratitudetomysupervisorProf.Dr.
Svetlozar.T.RachevandhisassistantDr.YoungShinKimfortheirvery
enthusiasticandinspiringsupportduringmywork.Iamverygratefulfor
thepossibilitiestheygavemeandthetrusttheyhadinme.Iamalso
indebtedtomyco-supervisorProf.Dr.MarlieseUhrig-Homburgandto
Prof.Dr.FrankJ.Fabozzifortheirsupportinwritingandnishingthis
dissertation.
Specialthanksgotomyfamilyandmyfriendswithoutwhomthiseort
wouldhavebeenimpossible.Inparticular,Iwouldliketodedicateathank
youtoMs.Elz_bietaZ_ukandMr.SimonNotheisfortheirgreatsuggestions
andvaluableadvices.
iv
Contents
Introduction1
1Probabilitytheory5
1.1Distributionsandrandomvariables...............5
1.2Skewnessandheavy-tails....................10
1.3Likelihoodandentropy......................15
2Econometricmodels19
2.1Stochasticprocesses.......................19
2.2TheARMAmodel........................22
2.3TheGARCHmodel.......................24
2.4TheARMA-GARCHmodel...................27
2.5Modelinference..........................28
3TheMCECDmodel33
3.1Conditionaldensity........................33
3.2Minimumcross-entropy.....................34
3.3TheMCECDdenition.....................36
3.4Stationarity............................39
4Conditionalvolatility41
4.1TheVola-MCECDmodel....................41
4.1.1Vola-MCECDandGARCH...............41
4.1.2Non-Gaussianmodels..................42
4.2TheMean-Vola-MCECDmodel.................48
4.3Simulationandempiricalresults................49
4.3.1Time-varyingmeanandvolatility............50
4.3.2Thetime-varyingproperty................52
4.3.3Qualityofone-dayforecasting..............53
iiv
iiiv
CONTENTS
5Conditionalskewness57
5.1Skewnessmodels.........................58
5.1.1TheARCDmodel....................60
5.1.2Skewnessestimation...................62
5.2TheSkew-MCECDmodel....................66
5.2.1Thedenition.......................66
5.2.2ExplicitSkew-MCECDdynamics............67
5.3TheVola-Skew-MCECDmodel.................68
5.4Simulationandempiricalresults................71
5.4.1Thetime-varyingproperty................71
5.4.2Empiricalskewness....................73
Conclusion
Bibliography
81
83
AProofs91
A.1Theiterativeformula.......................91
A.2Predictability...........................92
A.3Convergenceofweightedgeometricseries...........93
A.4Stationarity............................94
A.5EquivalenceofVola-MCECDandGARCH...........97
A.6ExplicitMean-Vola-MCECDdynamics.............100
A.7ExplicitSkew-MCECDdynamics................103
BTables
107
ListofFigures
4.1Log-elasticityofPDFofastableParetiandistribution....
4.2Conditionalmeantrajectoriesofsimulateddata........
4.3Conditionalvolatilitytrajectoriesofsimulateddata......
4.4ConditionalmeanofS&P500index..............
4.5ConditionalvolatilityofS&P500index............
5.1Eectsofmeantransformation.................
5.2Eectsofvariancetransformation................
5.3Eectsofskewnesstransformation...............
5.4ComparisonofMMandMLskewnessestimators.......
5.5ComparisonofMLskewnessestimators............
5.6Eectsofskewnessparameteronvolatilityestimator.....
5.7Estimatedtrajectoriesfortime-varyingskewness.......
5.8Estimatedtrajectoriesforconstantskewness..........
5.9Time-varyingskewnessofARCDforU.S.stockindices....
5.10Time-varyingskewnessofMCECDforU.S.stockindices...
5.11TripletofMCECDmodelforDowJones............
xi
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8595955666073747778797
x
LITSOFIFUGERS
ListofTables
4.1Goodness-of-tresultsforsimulateddata...........51
4.2One-dayVaRbacktestingresultsforstockindices.......55
5.1Estimatesforsimulated,time-varyingskewness........72
5.2Goodness-of-tforsimulated,time-varyingskewness.....72
5.3Estimatesforsimulated,constantskewness..........73
5.4Goodness-of-tforsimulated,constantskewness.......74
B.1ParameterestimatesforS&P500................108
B.2ParameterestimatesforDowJones...............109
B.3ParameterestimatesforNasdaq100..............110
B.4Goodness-of-tforS&P500...................111
B.5Goodness-of-tforDowJones..................112
B.6Goodness-of-tforNasdaq....................113
B.7One-dayCDFforecastingresults................114
B.8Goodness-of-