衍生工具与风险管理第8章课件

D.M.ChanceAnIntroductiontoDerivativesandRiskManagement,6thed.Ch.9:1Chapter8:PrinciplesofPricingForwards,Futures,andOptionsonFuturesToknowvalueistoknowthemeaningofthemarket.CharlesDowMoneyTalks(byRosalieMaggio),1998,p.23D.M.ChanceAnIntroductiontoDerivativesandRiskManagement,6thed.Ch.9:2ImportantConceptsinChapter9PriceandvalueofforwardandfuturescontractsRelationshipbetweenforwardandfuturespricesDeterminationofthespotpriceofanassetCostofcarrymodelfortheoreticalfairpriceContango,backwardation,andconvenienceyieldFuturespricesandriskpremiumsFuturesspreadpricingPricingoptionsonfuturesD.M.ChanceAnIntroductiontoDerivativesandRiskManagement,6thed.Ch.9:3SomePropertiesofForwardandFuturesPricesTheConceptofPriceVersusValueNormallyinanefficientmarket,price=value.Forfuturesorforward,priceisthecontractedrateoffuturepurchase.Valueissomethingdifferent.Atthebeginningofacontract,value=0forbothfuturesandforwards.NotationVt(0,T),F(0,T),vt(T),ft(T)arevaluesandpricesofforwardandfuturescontractscreatedattime0andexpiringattimeT.D.M.ChanceAnIntroductiontoDerivativesandRiskManagement,6thed.Ch.9:4SomePropertiesofForwardandFuturesPrices(continued)TheValueofaForwardContractForwardpriceatexpiration:F(T,T)=ST.Thatis,thepriceofanexpiringforwardcontractisthespotprice.Valueofforwardcontractatexpiration:VT(0,T)=ST-F(0,T).Anexpiringforwardcontractallowsyoutobuytheasset,worthST,attheforwardpriceF(0,T).Thevaluetotheshortpartyis-1timesthis.D.M.ChanceAnIntroductiontoDerivativesandRiskManagement,6thed.Ch.9:5SomePropertiesofForwardandFuturesPrices(continued)TheValueofaForwardContract(continued)TheValueofaForwardContractPriortoExpirationA:GolongforwardcontractatpriceF(0,T)attime0.B:AttgolongtheassetandtakeoutaloanpromisingtopayF(0,T)atT•AttimeT,AandBareworththesame,ST–F(0,T).Thus,theymustbothbeworththesamepriortot.•SoVt(0,T)=St–F(0,T)-(T-t)•SeeTable9.1,p.306.Example:Golong45daycontractatF(0,T)=$100.Risk-freerate=.10.20dayslater,thespotpriceis$102.Thevalueoftheforwardcontractis102-100(1.10)-25/365=2.65.D.M.ChanceAnIntroductiontoDerivativesandRiskManagement,6thed.Ch.9:6SomePropertiesofForwardandFuturesPrices(continued)TheValueofaFuturesContractFuturespriceatexpiration:fT(T)=ST.Valueduringthetradingdaybutbeforebeingmarkedtomarket:vt(T)=ft(T)-ft-1(T).Valueimmediatelyafterbeingmarkedtomarket:vt(T)=0.D.M.ChanceAnIntroductiontoDerivativesandRiskManagement,6thed.Ch.9:7SomePropertiesofForwardandFuturesPrices(continued)ForwardVersusFuturesPricesForwardandfuturespriceswillbeequalOnedaypriortoexpirationMorethanonedaypriortoexpirationif•Interestratesarecertain•FuturespricesandinterestratesareuncorrelatedFuturespriceswillexceedforwardpricesiffuturespricesarepositivelycorrelatedwithinterestrates.Defaultriskcanalsoaffectthedifferencebetweenfuturesandforwardprices.D.M.ChanceAnIntroductiontoDerivativesandRiskManagement,6thed.Ch.9:8AForwardandFuturesPricingModelSpotPrices,RiskPremiums,andtheCostofCarryforGenericAssetsFirstassumenouncertaintyoffutureprice.Letsbethecostofstoringanassetandibetheinterestratefortheperiodoftimetheassetisowned.ThenS0=ST-s-iS0Ifwenowallowuncertaintybutassumepeopleareriskneutral,wehaveS0=E(ST)-s-iS0Ifwenowallowpeopletoberiskaverse,theyrequireariskpremiumofE().NowS0=E(ST)-s-iS0-E()D.M.ChanceAnIntroductiontoDerivativesandRiskManagement,6thed.Ch.9:9AForwardandFuturesPricingModelSpotPrices,RiskPremiums,andtheCostofCarryforGenericAssets(continued)LetusdefineiS0asthenetinterest,whichistheinterestforegoneminusanycashreceived.Defines+iS0asthecostofcarry.Denotecostofcarryas.NotehowcostofcarryisameaningfulconceptonlyforstorableassetsD.M.ChanceAnIntroductiontoDerivativesandRiskManagement,6thed.Ch.9:10AForwardandFuturesPricingModelTheTheoreticalFairPriceDothefollowingBuyassetinspotmarket,payingS0;sellfuturescontractatpricef0(T);storeandincurcosts.Atexpiration,makedelivery.Profit:•P=f0(T)-S0-Thismustbezerotoavoidarbitrage;thus,•f0(T)=S0+SeeFigure9.1,p.313.Notehowarbitrageandquasi-arbitragemakethishold.D.M.ChanceAnIntroductiontoDerivativesandRiskManagement,6thed.Ch.9:11AForwardandFuturesPricingModel(continued)TheTheoreticalFairPrice(continued)SeeFigure9.2,p.314foranillustrationofthedeterminationoffuturesprices.Contangoisf0(T)S0.SeeTable9.2,p.315.Whenf0(T)S0,convenienceyieldisc,anadditionalreturnfromholdingassetwheninshortsupplyoranon-pecuniaryreturn.Marketissaidtobeatlessthanfullcarryandinbackwardationorinverted.SeeTable9.3,p.316.Marketcanbebothbackwardationandcontango.SeeTable9.4,p.317.D.M.ChanceAnIntroductiontoDerivativesandRiskManagement,6thed.Ch.9:12AForwardandFuturesPricingModel(continued)FuturesPricesandRiskPremiaThenorisk-premiumhypothesisMarketconsistsofonlyspeculators.f0(T)=E(ST).SeeFigure9.3,p.319.Therisk-premiumhypothesisE(fT(T))f0(T).Whenhedgersgoshortfutures,theytransferriskpremiumtospeculatorswhogolongfutures.E(ST)=f0(T)+E().SeeFigure9.4,p.321.Normalcontango:E(ST)f0(T)Normalbackwardation:f0(T)E(ST)D.M.ChanceAnIntroductiontoDerivativesandRiskManagement,6thed.Ch.9:13