倒向随机微分方程和Monte-Carlo方法在期权和期货上的应用

《倒向随机微分方程和Monte-Carlo方法在期权和期货上的应用》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、AbstractInrecentyears，moreandmorepeopleareconcernedaboutthederivativesmarket，fortheimprovementofthefinancialmarketsandthesharpfluctuationsinthespotmarket．Therealetwokindsofbasicresearchinderivativesmarket,theyareispncmgandhedging．Inordertosatisfythedifferentrequirementsforthecustomersandtoavoidth

2、emarkerrisk，therearemanynon-standardizedderiva—tivesinOver‘the-Countermarketinadditiontostandardoptionsinexchangemar-ket．Manyfinancialissuesconcerntothepricingoftheseexoticderivatives，butthecalculationisdifficultbecausemanyofthoseproductsarepath-dependent,there-forethepricingmethodismorecomplexth

3、anthe乜aditionalEuropeanoptions．Thispaperstudiestwodifferentpricingmethodsforstandardoptionsandex—oticoptions。OneapproachisBackwardStochasticDifferentialEquationsmeth-ods，theotheroneistheMonte-Carlomethod．ItcalculatesStandardEuropeanoptionsandtwokindsofexoticOPtionswithbothofthemethods，andthencoin

4、-parestheresultsforthesetwomethods．ThereasonitcalculatesthetraditionalEu—ropeanoptionsisthatmostofexoticoptionsaretheinnovationfromthetraditionones，thereforetheexoticoptionsandthestandardoneshaveagreatrelationship．研1emaincontentisasfollows：Chapter1istheintroductionofthisarticle．Itreviewstheconcep

5、tionoftheoptionbrieflyandseveralmethodsofoptionpricingatpresent．Furthermore，issummarizessomehistorydocumentswhichisrelatedtooptionpricing．Intheend，themaincontentsandtheideaofthisarticleisgiven．Chapter2istheintroductionforbasicmathematicalmodels．Itdescribesindetailtheno-arbitragepricingtheorywhich

6、isthemostcommonlyusedinmodels．Bothofthetwomethoddiscussedarebaseonno-arbitragetheory．Itintroducessomeexoticoptionsasexamplesusedinthearticlelater．Chapter3providesahigheraccuracynumericalmethodofbackwardstochas—ticdifferentialequations，thenumericalmethodisbasedonthefinenatttreforrelationshipforthe

7、backwardstochasticdifferentialequationsandpartialdiffer-entialequations．ThealgorithmalsotakesthecharacterofMarkovforthesolutionⅢⅣ第0章Abstractofbackwardstochasticdifferentialequations．Itgivesafewexamplestoconfirmthehigh-