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RafałM.Łochowski
SzkołaGłównaHandlowawWarszawie
THEGEOMETRICBROWNIANMOTIONMODEL
VS.THEJUMP-DIFFUSIONMODELAPPLIED
TOSELECTEDWIG20COMPANIES
INTHEYEAR2011
Introduction
Intheyear2011,especiallyinitssecondhalf,financialmarketsused
toreactstronglytothesignsofthedeepeningEurozonecrisis.Inthisturbulent
timestockpricesbehavedinveryvolatileway,reactingtotheinflowofthe
informationsonthedebtproblemsofthedifferentEurozonemembers
andemergencysolutionsapplied.Tocapturesucharapid,sometimeseven
discontinuousmovementsofstockprices,thejump-diffusionmodelofthe
evolutionofstockprices,proposedbyRobertMertonin[3],seemstobe
adequate.Thismodel,inoppositetotheclassicalgeometricBrownianmotion
model,doesnotinferthenormalityoflogarithmicreturnsanditusuallybetter
fitsthedistributionofthelogarithmicreturnsinshorterperiods(e.g.dailylo-
garithmicreturns)thantheclassicalgeometricBrownianmotionmodel.
Inthispaperwecomparedtwomodelsmentioned.Wecalibratedand
testedthesemodelsusingrealdataonstockpricesin2011ofninemajorcom-
paniesquotedattheWarsawStockExchange.Toobtainbettercomparison
wechosecompaniesfromdifferentbranchesofeconomy:ASSECO(IT),GTC
(construction),KERNEL(agriculture),KGHM(mining),ORLEN(oilrefining
andretail),PKOBP(banking),TAURON(energy),TPS.A.(telecommuni-
cation)andTVN(television).Allchosencompaniesweremajor,WIG20com-
panies;thusonemayassumethattheactionsoftheindividualinvestorshad
limitedimpactontheirprices.Onfig.1wepresentthegraphsofstockprices
ofthesecompaniesintheyear2011.