the valuation of russian options for double exponential jump diffusion processes

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1、Asia-PacificJournalofOperationalResearchVol.27,No.2(2010)227242(?)WorldScientificPublifihirigCo.ScOperationalResearchSocietyofSingaporeIX)1:IO.U42/S021759591000265XTHEVALUATIONOFRUSSIANOPTIONSFORDOUBLEEXPONENTIALJUMPDIFFUSIONPROCESSESATSUOSUZUKI-FacultyofUrbanScience,MeijoUniversityKani-shi,5

2、09-0261,Japanatsuo@urban.meijo-u.ac.jpKATSUSHIGESAWAKINamanBu.sincssSchoolNagoya-Shi,466-8673,JapansawakiÚnanzan-u.ac.jpInthispaper,wederiveclosedformsolutionforRussianoptionwithjumps.First,wediscussthepricingofRussianoptionswhenthestockpaysdividendscontinuously.Sec-ondly,wederivethevaluefunc

3、tionofRussianoptionsbysolvingtheordinarydifferentialequationwithsomeconditions(thevaluefunctioniscontinuousanddifferentiableattheoptimalboundaryforthebuyer).Andweinvestigatepropertiesofoptimalboundariesofthebuyer.Finally,somenumericalresultsarepresentedtodemonstrateanalyticalpropertiesoftheva

4、luefunction.Keywords:Russianoption;jumpdiffusionprocess.1.IntroductionFîussianoptionintroducedbySheppandShiryaev(1993.1994),whichisoneofperpetualAmericanoptions,isacontracttliatthebuyerhastherighttoexerciseitatanytime,itspayoffdependsonthemaximumofthestockpricepriortotheexercisetime.AndDuffie

5、andHarrison(1993)statesthevaluefimctionforRussianojítionsisfinitewhendividendrateispositive.Merton(1976)firstderivedtheclosedformsolutionforoptionswiththejumpdiffusionprocess.KouandWang(2004)introducedthemodelbyastandardBrow-iiianmotionandthejumpsizeshavingthedoubleexponentialdistribution,and

6、derivedperpetualAmericanputoptionsandsoon.Sepp(2005)derivedthepric-ingformulamultiplyingRussianoptionbythemaximumofthestockpriceinthedoubleexponentialmodel.ThispaperextendsSheppandShiryaev(1993,1994)tothemodelforjnm[)diffusionprocessesandderivestheclosedformsolution.'Correspondingauthor.22722

7、8A.Suzuki&K.SawakiThispaperisorganizedasfollows.Section2describesthepricingmodelforadoubleexponentialjumpdiffusionprocessandgivesthevaluefunctionofperpetualAmericancalloptionswithdividend.InSec.3,wediscussaboutRussianoptionsandderivetheclosed