资源描述:
《Why We Have Never Used the Black-Scholes-Merton Option Pricing Formula.pdf》由会员上传分享,免费在线阅读,更多相关内容在学术论文-天天文库。
1、WhyWeHaveNeverUsedtheBlack-Scholes-MertonOptionPricingFormulaEspenGaarderHaug&NassimNicholasTalebJanuary2008-FourthVersionAbstract:Optionstradersuseapricingformulawhichtheyadaptbyfudgingandchangingthetailsandskewnessbyvaryingoneparameter,thestandardd
2、eviationofaGaussian.Suchformulaispopularlycalled“Black-Scholes-Merton”owingtoanattributedeponymousdiscovery(thoughchangingthestandarddeviationparameterisincontradictionwithit).Howeverwehavehistoricalevidencethat1)Black,ScholesandMertondidnotinventany
3、formula,justfoundanargumenttomakeawellknown(andused)formulacompatiblewiththeeconomicsestablishment,byremovingthe“risk”parameterthrough“dynamichedging”,2)Optiontradersuse(andevidentlyhaveusedsince1902)heuristicsandtricksmorecompatiblewiththepreviousve
4、rsionsoftheformulaofLouisBachelierandEdwardO.Thorp(thatallowabroadchoiceofprobabilitydistributions)andremovedtheriskparameterbyusingput-callparity.3)Optiontradersdidnotuseformulasafter1973butcontinuedtheirbottom-upheuristics.TheBachelier-Thorpapproac
5、hismorerobust(amongotherthings)tothehighthimpactrareevent.Thepaperdrawsonhistoricaltradingmethodsand19andthearly20centuryreferencesignoredbythefinanceliterature.Itistimetostopcallingtheformulabythewrongname.however,didnotrecognizethesecontributions,B
6、REAKINGTHECHAINOFTRANSMISSIONsubstitutingtherediscoveriesorsubsequentreformulationsdoneby(some)economists.ThereisevidenceofanattributionproblemwithBlack-Scholes-Forus,practitioners,theoriesshouldarisefrom1Mertonoption“formula”,whichwasdeveloped,used,
7、practice.Thisexplainsourconcernwiththe“scientific”andadaptedinarobustwaybyalongtraditionofnotionthatpracticeshouldfittheory.Optionhedging,researchersandusedheuristicallybyoptionbookpricing,andtradingisneitherphilosophynorrunners.Furthermore,inacaseof
8、scientificpuzzle,themathematics.Itisarichcraftwithtraderslearningexactformulacalled“Black-Sholes-Merton”waswrittenfromtraders(ortraderscopyingothertraders)anddown(andused)byEdwardThorpwhich,tricksdevelopingunderevolutionpressures,inaparadoxically,whi