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ID:61518274
大小:1.62 MB
页数:24页
时间:2021-02-11
《金融工程数值方法分析.ppt》由会员上传分享,免费在线阅读,更多相关内容在教育资源-天天文库。
1、CHAPTER15thebinomialmodelInthisChapterasimplemodelforanassetpricerandomwalkdeltahedgingnoarbitragethebasicsofthebinomialmethodforvaluingoptionsriskneutralityThebinomialmodelisasimpleandfast,accuratenumericalmethodforvaluingoptions.Itrequiresonlybasicarithmeticandnocomplicated
2、stochasticcalculus.Wearegoingtoexamineaverysimplemodelforthebehaviorofastock,andbasedonthismodelseehowtovalueoptions.Wewillhaveastock,andacalloptiononthatstockexpiringtomorrow.Thestockcaneitherriseorfallbyaknownamountbetweentodayandtomorrow.Interestratesarezero.THEOPTIONVALUE
3、Thecorrectansweris...0.5Why?Threequestionsfollowfromtheabovesimpleargument:Whyshouldthis‘theoreticalprice’bethe‘marketprice’?HowdidIknowtosell½ofthestockforhedging?Howdoesthischangeifinterestratesarenon-zero?WHYSHOULDTHIS‘THEORETICALPRICE’BETHE‘MARKETPRICE’?Thisoneissimple,be
4、causeifit’snot,thenthereisrisk-freemoneytobemade.Iftheoptioncostslessthan0.5simplybuyitandhedgetomakeaprofit.Ifitisworthmorethan0.5inthemarketthensellitandhedge,andmakeaguaranteedprofit.HOWDIDIKNOWTOSELL½OFTHESTOCKFORHEDGING?Weintroduceasymbol:TheGeneralFormulaforWecanthinkof
5、asthesensitivityoftheoptiontochangesinthestock.HOWDOESTHISCHANGEIFINTERESTRATESARENON-ZERO?-------multiplyingbyadiscountfactorCOMPLETEMARKETSThepracticalimplicationofcompletemarketsisthatoptionsarehedgeableandthereforecanbepricedwithoutanyneedtoknowprobabilities.Wecanhedgeano
6、ptionwithstocktoreplicate’arisk-freeinvestmentandwecanreplicateanoptionusingstockandarisk-freeinvestment.Wecouldalso,ofcourse,replicatestockwithanoptionandrisk-free.THEREALANDRISK-NEUTRALWORLDSRisk-neutralpricingisaverypowerfultechnique.ANDNOWUSINGSYMBOLSuSV+dSV-SV例1:现有A股票的欧式
7、看涨期权,执行价格为9元,还有一年到期,A股票现在的价格为10元,明年可能涨至12元,也可能跌8元,无风险利率为5%(连续复利),请用二叉树模型计算该期权现在的价值。例2:现有A股票的欧式看跌期权,执行价格为10元,还有0.5年到期,A股票现在的价格为10元,明年可能涨至12元,也可能跌8元,无风险利率为6%(连续复利),请用二叉树模型计算该期权现在的价值。
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