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1、EcientandrobustcalibrationoftheHestonoptionpricingmodelforAmericanoptionsusinganimprovedCuckooSearchAlgorithmStefanHaringRonaldHochreiterAugust3,2015AbstractInthispaperanimprovedCuckooSearchAlgorithmisdevelopedtoallowforanecientandrobustcalibrationoftheHestonopt
2、ionpricingmodelforAmericanoptions.CalibrationofstochasticvolatilitymodelsliketheHestonissigni cantlyharderthanclassicaloptionpricingmodelsasmoreparametershavetobeestimated.ThediculttaskofcalibratingoneofthesemodelstoAmericanPutoptionsdataisthemainobjectiveofthisp
3、aper.Numericalresultsareshowntosubstantiatethesuitabilityofthechosenmethodtotacklethisproblem.Keywords.Optionpricing,Hestonmodel,Cuckoosearch,Finance1IntroductionTheclassicaltextbookexampleforpricingoptionsisthefamousBlack-Scholesmodel,see[1].Sinceitscreationin197
4、3,ithascausedadramaticincreaseinoptionstradingbecauseofitsrelativelysimpleusability.Itprovidesclosed-formsolutionsforEuropeanCallandPutoptionsaswellasAmericanCalloptions.ForAmericanPutoptions,noclosed-formsolutionexistsbecauseanoptimalstoppingtimeproblemhastobesol
5、ved.Overtheyears,criticismoftheBlack-Scholesmodelhasarisensinceitdoesnotaccuratelycapturethebehaviourofoptionpricesinthemarket.Forexample,thewell-knownvolatilitysmile,whichshowsthatdeepinthemoneyandoutthemoneyoptionshavehigherprices(andthereforehigherimpliedvolati
6、lity),isnottakenintoaccountintheBlack-Scholesmodelsinceoneofitsmainassumptionsisconstantvolatility.Toaccuratelyre
ectmarketbehaviour,optionpricingmodelsinwhichvolatilitychangesovertime,so-calledstochasticvolatilitymodels,havebeencreated.Inthesemodels,thevolatility
7、isitselffollowingaprocessthatchangeswithtimet.SomeexamplesforthesemodelsaretheHestonmodel[2],theCEVmodel[3][4]andtheChenmodel[5].Calibrationofthesestochasticvolatilitymodelsissigni cantlyharderthanfortheBlack-arXiv:1507.08937v1[cs.NE]31Jul2015Scholesmodel,sincemor
8、eparametershavetobeestimated.ThediculttaskofcalibratingoneofthesemodelstoAmericanPutoptionsdataisthemainobjectiveofthispaper.WewillfocusontheHestonmode
