金融数学期末测试

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1、金融数学期末测试姓名：卞自成学号：2012626630103得分：＿＿＿一．计算题。1.giventhefollowingdatacomputethepriceoftheassociatedEuropeancalloption.(a)S0:80X:70R0.05T3moQ0.30解：V=查正态分布表得：代入公式可得：ThenthepriceoftheassociatedEuropeancalloptionis11.84.2.usingthedatainExercise1,computethepriceoftheassociatedEuropeanputoptionforh.(h)S0:25

2、X:25R0.05T3moQ0.28解：查正态分布表得：代入公式得：ThenthepriceoftheassociatedEuropeanputoptionis1.24.3.giventhefollowinginformation,findtheimpliedvolatilityfortheassociatedEuropeancalloption.(a)S040K40R0.05T3moV3.8解：使用Maple软件计算>with(finance)>solve(blackscholes(40,40,0.0.5.0.25,x)=3.8,x);解得：x=0.45Thentheimpliedvol

3、atilityfortheassociatedEuropeancalloptionis0.45.4.Assumethatastockmodelhastheparameteru=1.7d=0.8S0=120AEuropeancalloption,expiringatt=3,hasanexercisepricex=115andtheinterestrateis0.06overeachperiod.pricethisoptionatt=0usingthechainingmethod.解：一．英译汉。1.7.2.1HedgingwithputsOnecansimplypurchaseaputona

4、stockorpurchaseindexoptionputsonaportfolio.Thisraisesdelicatequestionsastowhatpercentoftheportfoliotohedgeandhowfaroutofthemoneytochoosetheput.Thecostofthehedgewilvarywidelydependingontheselection.Onecouldpurchaseputsoneachstockinaportfolio,butitismuchlessexpensivetopurchaseindexoptionputs.采用看跌期权对

5、冲人们可以通过直接购买股票看跌期权或者指数看跌期权来对资产组合进行对冲。由此产生的问题是资产组合对冲的比例的确定以及选择看跌期权的数量。　　对冲方案选择不一样，对冲的成本将差异很大。你可以选择购买资产组合中每一个股票的看跌期权，但如果选择指数看跌期权成本就低多了。2.7.2.2HedgingwithCollarsTohedgeastockwithacollar,onepurchaseanat-the-moneyputandsellsanout-of-the-moneycall.Properlychosen,thecashisrequiredfromtheinvestor.Ifthestoc

6、kdrops,theinvestorisprotected.Ifthestockincreasesinprice,thenitwillbecalledaway.采用双限对股票对冲采用双限对股票进行对冲，是指一方面买进平值看跌期权，同时又卖出虚值看跌期权。通过适当的选择，使卖出期权的收入正好等于购买期权所需金额，这样投资者就无需额外支出了。如果股票下跌，投资者处于保护状态。如果股票价格上升了，则在股票上得益。3.7.2.3HedgingwithPairedTradesSupposethatinthesaneindustrialgrouptherearetwocompanies:supergo

7、odandhaplessindustries.Itisagreedthatthenamesaccuratelyreflectthequalityofthecompanies.Supposewepurchase100sharesofsuperandshortanequaldollaramountofhapless.Iftheeconomysurgesstrongly,bothstocksshouldappreciate,b