Financial Engineering.ppt

,1.1,FinancialEngineering金融工程学,1.2,References,JohnC.Hull,FundamentalsofFuturesandOptionsMarkets,PrenticeHall,4thEd.,2002.(清华大学出版社)RobertW.Kolb,Futures,OptionsandSwaps,BlackwellPublishing,4thEd.,2002.LawrenceGalitz,FinancialEngineering:ToolsandTechniquestoManageFinancialRisks,PitmanPublishing,1995.(中译本：唐旭，经济科学出版社，1998）JohnF.Mrshall,VipulK.Bansal,FinancialEngineering,SimonStockPrice=62.75),1.24,LongCallonMicrosoft(Figure1.2,Page7),ProfitfrombuyingaEuropean(欧式)calloptiononMicrosoft:optionprice=$5,strikeprice=$60,1.25,ShortCallonMicrosoft(Figure1.4,page9),ProfitfromwritingaEuropeancalloptiononMicrosoft:optionprice=$5,strikeprice=$60,1.26,LongPutonIBM(Figure1.3,page8),ProfitfrombuyingaEuropeanputoptiononIBM:optionprice=$7,strikeprice=$90,1.27,ShortPutonIBM(Figure1.5,page9),ProfitfromwritingaEuropeanputoptiononIBM:optionprice=$7,strikeprice=$90,1.28,Payoffs(损益)fromOptionsWhatistheOptionPositioninEachCase?,K=Strikeprice,ST=Priceofassetatmaturity,1.29,Optionsvs.Futures/Forwards,Afutures/forwardcontractgivestheholdertheobligationtobuyorsellatacertainpriceAnoptiongivestheholdertherighttobuyorsellatacertainprice,1.30,TypesofTraders,Hedgers(套期保值者)Speculators(投机者)Arbitrageurs(套利者),Someofthelargetradinglossesinderivativesoccurredbecauseindividualswhohadamandate(授权)tohedgerisksswitchedtobeingspeculators,1.31,HedgingExamples,AUScompanywillpay10millionforimportsfromBritainin3monthsanddecidestohedgeusingalongpositioninaforwardcontract(The3-monthforwardexchangerateis1.6056).Whatarethealternativestrategies?Aninvestorowns1,000Microsoftsharescurrentlyworth$73pershare.Atwo-monthputwithastrikepriceof$65costs$2.50.Theinvestordecidestohedgebybuying10contracts,1.32,Differencesinthetwohedgealternatives,Forwardcontractsaredesignedtoneutralizeriskbyfixingthepricethatthehedgerwillpayorreceivefortheunderlyingasset.Thereisnoassurancethattheoutcomewithhedgingisbetterthantheoutcomewithouthedging.Thehedgeusingforwardcontractrequiresnoinitialpayment,1.33,Optioncontractsprovideassurance.Theyofferawayforinvestorstoprotectthemselvesagainstadversepricemovementsinthefuturewhilestillallowingthemtobenefitfromfavorablepricemovements.Optioninvolvethepaymentofanup-frontfee.,1.34,SpeculationExample1,AninvestorfeelsthatsterlingwillstrengthenrelativetotheU.S.dollaroverthenexttwomonths.Thecurrentrateis1.6470$/andthe2-monthfuturespriceis1.6410$/.Whatarethealternativestrategies?,1.35,Twostrategies:,Buy250,000for$411,750,depositthesterlinginaninterest-earningaccountfortwomonths.Takealongpositionin4two-monthfuturescontractsonsterling(eachfor62,500).,1.36,Possibleoutcomes,Exchangerateis1.7000intwomonths.Theinvestormakes$(1.7000-1.6470)x250,000=$13,250usingthefirststrategyand$(1.7000-1.6410)x250000=$14,750usingthesecondstrategy.Exchangerateis1.6000intwomonth.Theinvestorhasalossof$(1.6470-1.6000)x25000=$11,750usingthefirststrategyand$(1.6410-1.6000)x25000=$10,250usingthesecondstrategy.,1.37,SpeculationExample2,Aninvestorwith$4,000toinvestfeelsthatthepriceofAwillincreaseoverthenext2months.Thecurrentstockpriceis$40andthepriceofa2-monthcalloptionwithastrikeof45is$2Whatarethealternativestrategies?,1.38,Twostrategies:,Buy100sharesofA.Buy2,0002-monthcalloptions(i.e.20contracts)onAwitha$45strikeprice.Thecostofeachalternativeis$4,000.,1.39,Possibleoutcomes,Arisesto$70twomonthslater.TheInvestormakesaprofitof$100 x(70-40)=$3,000usingthefirststrategyand$2,000 x(70-45)-$2,000 x2=$46,000usingthesecond.Afallsto$30twomonthslater.Theinvestorlosses$100 x(40-30)=$1,000withthefirststrategyand$4,000withthesecondstrategy.,1.40,AComparison,Bothfuturesandoptionscontractsprovideawayinwhichatypeofleveragecanbeobtained(comparedwiththespotmarket).Goodoutcomesbecomesverygood,whilebadoutcomesbecomeverybad.Inexample1:thefirstalternativerequiresanup-frontinvestmentof$411,750whilethesecondalternativeonlyrequiresasmallamountsay,$25,000(depositedinamarginaccount).Inexample2:theprofit(loss)fromthesecondstrategyisover15(4)timesasmuchasthefirst.,Leverage:witharelativelusmallinitialmoney,theinvestorisabletotakealargespeculativeposition.,1.41,Inthefuturessetting,thespeculatorspotentiallossaswellasthepotentialgainisverylargeIntheoptionssetting,nomatterhowbadthingsget,thespeculatorslossislimitedtothecostoftheoptions(premium),1.42,ArbitrageExample(pages14),Astockpriceisquotedas100inLondonand$172inNewYorkThecurrentexchangerateis1.7500Whatisthearbitrageopportunity?,1.43,NoArbitrageAssumption,Theforcesofsupplyanddemand=Arbitrageopportunitiescannotlastlong=Assumption:therearenoarbitrageopportunities,1.44,Summary(page15),Manual,seepages471-474ofthebook:JohnC.Hull,FundamentalsofFuturesandOptionsMarkets,PrenticeHall,4thEd.,2002.(清华大学出版社),Software:DerivaGem,1.45,Assignments(page16-18,4thedition),1.5,1.9,1.17,1.20,1.21,2.46,FuturesMarketsandtheUseofFuturesforHedgingChapter2,2.47,FuturesContracts,AvailableonawiderangeofunderlyingsExchangetradedSpecifications(规定)needtobedefined:Whatcanbedelivered,Whereitcanbedelivered,NoDividends(Equation7.3,page174),Considerthefollowing2portfolios:PortfolioA:Europeancallonastock+PVofthestrikepriceincashPortfolioC:Europeanputonthestock+thestockBothareworthMAX(ST,X)atthematurityoftheoptionsTheymustthereforebeworththesametodayThismeansthatc+Xe-rT=p+S0,TangYincai,ShanghaiNormalUniversity,7.216,Put-CallParityCashFlows(NODividends),Considerthefollowing2portfoliosPortfolioA:Europeancallonastock+thepresentvalueofthestrikepriceincashPortfolioC:Europeanputonthestock+thestockSTXBuyCall0ST-XLendXe-rTatrXXPortfolioA=MAX(ST,X)NetFlowsXSTBuyPutX-ST0BuyStockSTSTPortfolioC=MAX(ST,X)NetFlowsXST,TangYincai,ShanghaiNormalUniversity,7.217,Put-CallParityGraphically(NODividends),Considerthefollowing2portfoliosPortfolioX:BuyaEuropeancallonastock+SellaEuropeanputPortfolioY:Buythestock+borrowthepresentvalueofthestrikeprice,TangYincai,ShanghaiNormalUniversity,7.218,Put-CallParityGraphs(NODividends),PortfolioXPortfolioY,X,ST,Payoff,X,ST,Payoff,ShortPut,LongCall,X,ST,Payoff,X,ST,Payoff,X,ST,Payoff,BorrowXe-rT,LongStock,X,ST,Payoff,NetPosition,-X,NetPosition,TangYincai,ShanghaiNormalUniversity,7.219,Put-CallParityGraphs(NODividends)(continued),Becausethesetwoportfolioshaveidenticalpayoffs,arbitragetheorystatesthattheymustcostthesametoestablish.Therefore,TangYincai,ShanghaiNormalUniversity,7.220,Puts:AnArbitragePossibility?,Supposethatc=3S0=48T=1r=5%X=50D=0Whatarethearbitragepossibilitieswhen?p=3?p=2?,TangYincai,ShanghaiNormalUniversity,7.221,Puts:AnArbitragePossibility?(continued),Ifp=3Therefore,because00.44,needtobuytheright-handsideandselltheleftbuylow,sellhigh,?,?,?,?,TangYincai,ShanghaiNormalUniversity,7.224,Puts:AnArbitragePossibility?(continued),Setupthetablesp=2Algebraically,t=0STXBuyStock-S0STSTBorrowXe-rTatrXe-rT-X-XSellCallc0-(ST-X)BuyPut-pX-ST0NetFlowsc-p-S+Xe-rT00Numerically,t=0STXBuyStock-48.00STSTBorrowXe-rTatr47.56-50-50SellCall3.000-(ST-50)BuyPut-2.0050-ST0NetFlows0.5600,TangYincai,ShanghaiNormalUniversity,7.225,LowerBoundforEuropeanOptions(withDividends),Ifthestockpaysdividends,whosenetpresentvaluetodayisdenotedasD,thenallthatweneedtodoistoreplaceS0withS0-Dandpretendliketherearenodividendsc(S0-D)-Xe-rT=S0-D-Xe-rTpXe-rT-(S0-D)=Xe-rT+D-S0,TangYincai,ShanghaiNormalUniversity,7.226,ExtensionsofPut-CallParity,Americanoptions;D=0(Equation7.4)S0-X0Equation7.7)c+D+Xe-rT=p+S0Americanoptions;D0(Equation7.8)S0-D-X4.367t=0ST=18ST=22Buycall-0.60001SellShares5.000-18*0.25=-4.50-22*0.25=-5.50Lend4.367atr-4.3674.504.50NetFlows0.03300,TangYincai,ShanghaiNormalUniversity,9.264,Generalization(continued):ProofwithanExample,Iff0.633,e.g.f=0.65=S0-f=0.25*20-0.65=4.35weakautocorrelation,15.495,ForecastingFutureVolatility(Equation15.13,page379),Afe