风险管理与金融机构课件Ch06.ppt
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风险管理与金融机构课件Ch06.ppt
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HowTradersManageTheirExposures,Chapter6,RiskManagementandFinancialInstitutions,2e,Chapter6,CopyrightJohnC.Hull2009,1,ATradersGoldPortfolio.HowShouldRisksBeHedged?
(Table6.1,page114),RiskManagementandFinancialInstitutions,2e,Chapter6,CopyrightJohnC.Hull2009,2,Delta,Deltaofaportfolioisthepartialderivativeofaportfoliowithrespecttothepriceoftheunderlyingasset(goldinthiscase)Supposethata$0.1increaseinthepriceofgoldleadstothegoldportfolioincreasinginvalueby$100Thedeltaoftheportfoliois1000Theportfoliocouldbehedgedagainstshort-termchangesinthepriceofgoldbyselling1000ouncesofgold.Thisisknownasmakingtheportfoliodeltaneutral,RiskManagementandFinancialInstitutions,2e,Chapter6,CopyrightJohnC.Hull2009,3,LinearvsNonlinearProducts,WhenthepriceofaproductislinearlydependentonthepriceofanunderlyingassetahedgeandforgetstrategycanbeusedNon-linearproductsrequirethehedgetoberebalancedtopreservedeltaneutrality,RiskManagementandFinancialInstitutions,2e,Chapter6,CopyrightJohnC.Hull2009,4,ExampleofHedgingaNonlinearProduct(page116),Abankhassoldfor$300,000aEuropeancalloptionon100,000sharesofanondividendpayingstockS0=49,K=50,r=5%,s=20%,T=20weeks,m=13%TheBlack-Scholesvalueoftheoptionis$240,000Howdoesthebankhedgeitsrisktolockina$60,000profit?
RiskManagementandFinancialInstitutions,2e,Chapter6,CopyrightJohnC.Hull2009,5,DeltaoftheOption,RiskManagementandFinancialInstitutions,2e,Chapter6,CopyrightJohnC.Hull2009,6,DeltaHedging,Initiallythedeltaoftheoptionis0.522Thedeltaofthepositionis-52,200Thismeansthat52,200sharesmustpurchasedtocreateadeltaneutralpositionBut,ifaweeklaterdeltafallsto0.458,6,400sharesmustbesoldtomaintaindeltaneutralityTables6.2and6.3(pages118and119)provideexamplesofhowdeltahedgingmightworkfortheoption.,RiskManagementandFinancialInstitutions,2e,Chapter6,CopyrightJohnC.Hull2009,7,Table6.2:
Optionclosesinthemoney,RiskManagementandFinancialInstitutions,2e,Chapter6,CopyrightJohnC.Hull2009,8,Table6.3:
Optionclosesoutofthemoney,RiskManagementandFinancialInstitutions,2e,Chapter6,CopyrightJohnC.Hull2009,9,WheretheCostsComeFrom,DeltahedgingashortoptionpositiontendstoinvolvesellingafterapricedeclineandbuyingafterapriceincreaseThisisa“selllow,buyhigh”strategy.Thetotalcostsincurredareclosetothetheoreticalpriceoftheoption,RiskManagementandFinancialInstitutions,2e,Chapter6,CopyrightJohnC.Hull2009,10,Gamma,Gamma(G)istherateofchangeofdelta(D)withrespecttothepriceoftheunderlyingassetGammaisgreatestforoptionsthatareclosetothemoney,RiskManagementandFinancialInstitutions,2e,Chapter6,CopyrightJohnC.Hull2009,11,GammaMeasurestheDeltaHedgingErrorsCausedByCurvature(Figure6.4,page120),RiskManagementandFinancialInstitutions,2e,Chapter6,CopyrightJohnC.Hull2009,12,S,C,Stockprice,S,Callprice,C,C,Vega,Vega(n)istherateofchangeofthevalueofaderivativesportfoliowithrespecttovolatilityLikegamma,vegatendstobegreatestforoptionsthatareclosetothemoney,RiskManagementandFinancialInstitutions,2e,Chapter6,CopyrightJohnC.Hull2009,13,GammaandVegaLimits,Inpractice,atradersmustkeepgammaandvegawithinlimitssetbyriskmanagement,RiskManagementandFinancialInstitutions,2e,Chapter6,CopyrightJohnC.Hull2009,14,Theta,Theta(Q)ofaderivative(orportfolioofderivatives)istherateofchangeofthevaluewithrespecttothepassageoftimeThethetaofacallorputisusuallynegative.Thismeansthat,iftimepasseswiththepriceoftheunderlyingassetanditsvolatilityremainingthesame,thevalueoftheoptiondeclines,RiskManagementandFinancialInstitutions,2e,Chapter6,CopyrightJohnC.Hull2009,15,Rho,Rhoisthepartialderivativewithrespecttoaparallelshiftinallinterestratesinaparticularcountry,RiskManagementandFinancialInstitutions,2e,Chapter6,CopyrightJohnC.Hull2009,16,TaylorSeriesExpansion(Equation6.1,page126),RiskManagementandFinancialInstitutions,2e,Chapter6,CopyrightJohnC.Hull2009,17,InterpretationofGamma(Equation6.2,page126),Foradeltaneutralportfolio,DPQDt+GDS2,RiskManagementandFinancialInstitutions,2e,Chapter6,CopyrightJohnC.Hull2009,18,NegativeGamma,PositiveGamma,TaylorSeriesExpansionwhenVolatilityisUncertain,RiskManagementandFinancialInstitutions,2e,Chapter6,CopyrightJohnC.Hull2009,19,ManagingDelta,Gamma,&Vega,DcanbechangedbytakingapositionintheunderlyingToadjustG&nitisnecessarytotakeapositioninanoptionorotherderivative,RiskManagementandFinancialInstitutions,2e,Chapter6,CopyrightJohnC.Hull2009,20,HedginginPractice,Tradersusuallyensurethattheirportfoliosaredelta-neutralatleastonceadayWhenevertheopportunityarises,theyimprovegammaandvegaAsportfoliobecomeslargerhedgingbecomeslessexpensive,RiskManagementandFinancialInstitutions,2e,Chapter6,CopyrightJohnC.Hull2009,21,StaticOptionsReplication(page129),ThisinvolvesapproximatelyreplicatinganexoticoptionwithaportfolioofvanillaoptionsUnderlyingprinciple:
ifwematchthevalueofanexoticoptiononsomeboundary,wehavematcheditatallinteriorpointsoftheboundaryStaticoptionsreplicationcanbecontrastedwithdynamicoptionsreplicationwherewehavetotradecontinuouslytomatchtheoption,RiskManagementandFinancialInstitutions,2e,Chapter6,CopyrightJohnC.Hull2009,22,ScenarioAnalysis,Ascenarioanalysisinvolvestestingtheeffectonthevalueofaportfolioofdifferentassumptionsconcerningassetpricesandtheirvolatilities,RiskManagementandFinancialInstitutions,2e,Chapter6,CopyrightJohnC.Hull2009,23,
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