贵金属投资技术分析英文版26培训教材

Fi8000BasicsofOptions:Calls,PutsMilindShrikhandeDerivatives-OverviewDerivativesecuritiesarefinancialcontractsthatderivetheirvaluefromothersecurities.Theyarealsocalledcontingentclaimsbecausetheirpayoffsarecontingentofthepricesofothersecurities.Derivatives-OverviewExamplesofunderlyingassets:CommonstockandstockindexesForeignexchangerateandinterestrateFuturescontractsAgriculturalcommoditiesandpreciousmetalsExamplesofderivativesecurities:Options(Call,Put)ForwardandFuturescontractsFixedincomeandforeignexchangeinstrumentssuchasswapsLongPositioninaStockThepayoffincreasesasthevalue(price)ofthestockincreasesTheincreaseisone-for-one:foreachdollarincreaseinthepriceofthestock,thevalueofourpositionincreasesbyonedollarLongStock–aPayoffDiagramStockprice=STPayoff=+ST005510101515202025253030STPayoffShortPositioninaStockThepayoffdecreasesasthevalue(price)ofthestockincreasesThedecreaseisone-for-one:foreachdollarincreaseinthepriceofthestock,thevalueofourpositionincreasesbyonedollarNotethattheshortpositionisaliabilitywithavalueequaltothepriceofthestock(mirrorimageofthelongposition)ShortStock–aPayoffDiagramStockprice=STPayoff=-ST005-510-1015-1520-2025-2530-30Longvs.ShortPositioninaStock–PayoffDiagramsLongandShortPositionsintheRisk-freeAsset(Bond)ThepayoffisconstantregardlessofthechangesinthestockpriceThepayoffispositiveforalender(longbond)andnegativefortheborrower(shortbond)Lending–aPayoffDiagramStockprice=STPayoff=+X02052010201520202025203020Borrowing–aPayoffDiagramStockprice=STPayoff=-X0-205-2010-2015-2020-2025-2030-20Lendingvs.BorrowingPayoffDiagramsACallOptionAEuropean*calloptiongivesthebuyeroftheoptionarighttopurchasetheunderlyingasset,atthecontractedprice(theexerciseorstrikeprice)onacontractedfuturedate(theexpirationdate)*AnAmericancalloptiongivesthebuyeroftheoption(longcall)arighttobuytheunderlyingasset,attheexerciseprice,onorbeforetheexpirationdateCallOption-anExampleAMarch(European)calloptiononMicrosoftstockwithastrikeprice$20,entitlestheownerwitharighttopurchasetheMicrosoftstockfor$20ontheexpirationdate*.Whatistheowner’spayoffontheexpirationdate?Underwhatcircumstancesdoeshebenefitfromtheposition?*NotethatexchangetradedoptionsexpireonthethirdFridayoftheexpirationmonth.ThePayoffofaCallOptionOntheexpirationdateoftheoption:IfMicrosoftstockhadfallenbelow$20,thecallwouldhavebeenlefttoexpireworthless.IfMicrosoftwassellingabove$20,thecallholderwouldhavefounditoptimaltoexercise.Exerciseofthecallisoptimalatmaturityifthestockpriceexceedstheexerciseprice:Valueatexpiration(payoff)isthemaximumoftwo:Max{Stockprice–Exerciseprice,0}=Max{ST–X,0}Profitatexpiration=Payoffatexpiration-PremiumNotationS=thepriceoftheunderlyingasset(stock)(wewillrefertoS0=S,StorST)C=thepriceofacalloption(premium)(wewillrefertoC0=C,CtorCT)XorK=theexerciseorstrikepriceT=theexpirationdatet=atimeindexBuyingaCall–aPayoffDiagramStockprice=STPayoff=Max{ST-X,0}00501001502002553010BuyingaCall–aProfitDiagramStockprice=STProfit=Max{ST-X,0}-C0-710-720-725-23033584013BuyingaCallPayoffandProfitDiagramsWritingaCallOptionThesellerofacalloptionissaidtowriteacall,andhereceivestheoptionspricecalledapremium.Hehasanobligationtodelivertheunderlyingassetontheexpirationdate(European),fortheexercisepricewhichmaybelowerthanthemarketvalueoftheasset.Thepayoffofashortcallposition(writingacall)isthenegativeoflongcall(buyingacall):-Max{Stockprice–Exerciseprice,0}=-Max{ST–X,0}WritingaCall–aPayoffDiagramStockprice=STPayoff=-Max{ST-X,0}0010015020025-530-1040-20BuyingaCallvs.WritingaCallPayoffDiagramsMoneynessWesaythatanoptionisin-the-moneywhenthepayofffromexercisingispositiveAcalloptionsisin-to-moneywhen(St–X)>0(i.e.whenstockprice>strikeprice)Wesaythatanoptionisout-of-the-moneywhenthepayofffromexercisingiszeroAcalloptionsisout-of-the-moneywhen(St–X)<0(i.e.whenthestockprice>0(i.e.whenthestockprice>>thestrikeprice)APutOptionAEuropean*putoptiongivesthebuyeroftheoptionarighttoselltheunderlyingasset,atthecontractedprice(theexerciseorstrikeprice)onacontractedfuturedate(theexpirationdate)*AnAmericanputoptiongivesthebuyeroftheoption(longput)arighttoselltheunderlyingasset,attheexerciseprice,onorbeforetheexpirationdatePutOption-anExampleAMarch(European)putoptiononMicrosoftstockwithastrikeprice$20,entitlestheownerwitharighttoselltheMicrosoftstockfor$20ontheexpirationdate.Whatistheowner’spayoffontheexpirationdate?Underwhatcircumstancesdoeshebenefitfromtheposition?ThePayoffofaPutOptionOntheexpirationdateoftheoption:IfMicrosoftstockwassellingabove$20,theputwouldhavebeenlefttoexpireworthless.IfMicrosofthadfallenbelow$20,theputholderwouldhavefounditoptimaltoexercise.Exerciseoftheputisoptimalatmaturityifthestockpriceisbelowtheexerciseprice:Value(payoff)atexpirationisthemaximumoftwo:Max{Exerciseprice-Stockprice,0}=Max{X-ST,0}Profitatexpiration=Payoffatexpiration-PremiumBuyingaPut–aPayoffDiagramStockprice=STPayoff=Max{X-ST,0}0205151010155200250300WritingaPutOptionThesellerofaputoptionissaidtowriteaput,andhereceivestheoptionspricecalledapremium.Heisobligatedtobuytheunderlyingassetontheexpirationdate(European),fortheexercisepricewhichmaybehigherthanthemarketvalueoftheasset.Thepayoffofashortputposition(writingaput)isthenegativeoflongput(buyingaput):-Max{Exerciseprice-Stockprice,0}=-Max{X-ST,0}WritingaPut–aPayoffDiagramStockprice=STPayoff=-Max{X-ST,0}0-205-1510-1015-5200250300BuyingaPutvs.WritingaPutPayoffDiagramsBuyingaCallvs.BuyingaPutPayoffDiagrams–Symmetry?WritingaCallvs.WritingaPutPayoffDiagrams–Symmetry?InvestmentStrategiesAPortfolioofInvestmentVehiclesWecanusemorethanoneinvestmentvehicletofromaportfoliowiththedesiredpayoff.Wemayuseanyoftheinstrument(stock,bond,putorcall)atanyquantityorposition(longorshort)asourinvestmentstrategy.Thepayoffoftheportfoliowillbethesumofthepayoffsoftheit’sinstrumentsInvestmentStrategiesProtectivePutLongonestock.ThepayoffattimeTis:STBuyone(European)putoptiononthesamestock,withastrikepriceofX=$20andexpirationatT.ThepayoffattimeTis:Max{X-ST,0}=Max{$20-ST,0}ThepayoffoftheportfolioattimeTwillbethesumofthepayoffsofthetwoinstrumentsIntuition:possiblelosesofthelongstockpositionareboundedbythelongputpositionProtectivePut–IndividualPayoffsStockpriceLongStockBuyPut0020551510101015155202002525030300ProtectivePut–PortfolioPayoffStockpriceLongStockBuyPutAll(Portfolio)002020551520101010201515520202002025250253030030InvestmentStrategiesCoveredCallLongonestock.ThepayoffattimeTis:STWriteone(European)calloptiononthesamestock,withastrikepriceofX=$20andexpirationatT.ThepayoffattimeTis:-Max{ST-X,0}=-Max{ST-$20,0}ThepayoffoftheportfolioattimeTwillbethesumofthepayoffsofthetwoinstrumentsIntuition:thecallis“covered”since,incaseofdelivery,theinvestoralreadyownsthestock.CoveredCall–IndividualPayoffsStockpriceLongStockWriteCall0005501010015150202002525-53030-10CoveredCall–PortfolioPayoffStockpriceLongStockWriteCallAll(Portfolio)000055051010010151501520200202525-5203030-1020OtherInvestmentStrategiesLongstraddleBuyacalloption(strike=X,expiration=T)Buyaputoption(strike=X,expiration=T)Writeastraddle(shortstraddle)Writeacalloption(strike=X,expiration=T)Writeaputoption(strike=X,expiration=T)BullishspreadBuyacalloption(strike=X1,expiration=T)WriteaCalloption(strike=X2>X1,expiration=T)ThePutCallParityComparethepayoffsofthefollowingstrategies:StrategyI:Buyonecalloption(strike=X,expiration=T)Buyonerisk-freebond(facevalue=X,maturity=T,return=rf)StrategyIIBuyoneshareofstockBuyoneputoption(strike=X,expiration=T)StrategyI–PortfolioPayoffStockpriceBuyCallBuyBondAll(Portfolio)002020502020100202015020202002020255202530102030StrategyII–PortfolioPayoffStockpriceBuyStockBuyPutAll(Portfolio)002020551520101010201515520202002025250253030030ThePutCallParityIftwoportfolioshavethesamepayoffsineverypossiblestateandtimeinthefuture,theirpricesmustbeequal:Arbitrage–theLawofOnePriceIftwoassetshavethesamepayoffsineverypossiblestateinthefutureandtheirpricesarenotequal,thereisanopportunitytomakeanarbitrageprofit.Wesaythatthereexistsanarbitrageopportunityifweidentifythat:ThereisnoinitialinvestmentThereisnoriskoflossThereisapositiveprobabilityofprofitArbitrage–aTechnicalDefinitionLetCFtjbethecashflowofaninvestmentstrategyattimetandstatej.Ifthefollowingconditionsaremetthisstrategygeneratesanarbitrageprofit.allthepossiblecashflowsineverypossiblestateandtimearepositiveorzero-CFtj≥0foreverytandj.atleastonecashflowisstrictlypositive-thereexistsapair(t,j)forwhichCFtj>0.Arbitrage–anExampleIsthereanarbitrageopportunityifthefollowingarethemarketpricesoftheassets:Thepriceofoneshareofstockis$39;Thepriceofacalloptiononthatstock,whichexpiresinoneyearandhasanexercisepriceof$40,is$7.25;Thepriceofaputoptiononthatstock,whichexpiresinoneyearandhasanexercisepriceof$40,is$6.50;Theannualriskfreerateis6%.Arbitrage–anExampleInthiscasewemustcheckwhethertheputcallparityholds.Sincewecanseethatthisparityrelationisviolated,wewillshowthatthereisanarbitrageopportunity.TheConstructionofanArbitrageTransactionConstructingthearbitragestrategy:Moveallthetermstoonesideoftheequationsotheirsumwillbepositive;Foreachasset,usethesignasanindicatoroftheappropriateinvestmentintheasset.Ifthesignisnegativethenthecashflowattimet=0isnegative(whichmeansthatyoubuythestock,bondoroption).Ifthesignispositivereversetheposition.Arbitrage–anExampleInthiscasewemovealltermstotheLHS:Arbitrage–anExampleInthiscaseweshould:Sell(short)oneshareofstockWriteoneputoptionBuyonecalloptionBuyazerocouponrisk-freebond(lend)Arbitrage–anExampleTime:→t=0t=TStrategy:↓State:→STX=40ShortstockWriteputBuycallBuybondTotalCFCF0CFT1CFT2Arbitrage–anExampleTime:→t=0t=TStrategy:↓State:→STX=40Shortstock+S=$39Writeput+P=$6.5Buycall-C=(-$7.25)Buybond-X/(1+rf)=(-$37.736)TotalCFS+P-C-X/(1+rf)=0.514Arbitrage–anExampleTime:→t=0t=TStrategy:↓State:→STX=40Shortstock+S=$39-ST-STWriteput+P=$6.5-(X-ST)0Buycall-C=(-$7.25)0(ST-X)Buybond-X/(1+rf)=(-$37.736)XXTotalCFS+P-C-X/(1+rf)=0.514>0-ST-(X-ST)+X=0-ST-(X-ST)+X=0PracticeProblemsBKMCh.20:1-12,14-23PracticeSet:1-16