1 Financial Marketsppt课件

FinancialMathematics 吴述金 sjwu Chapter1FinancialMarkets 1 Markets NearlyeveryonehasheardoftheHongKong Shanghai andShenzhenstockexchangesinourcountry Therearemanyotherfinancialmarkets suchastheShanghai Henan andDalianfutureexchanges Importantfinancialmarkets Stockmarkets Bondmarkets Currencymarkets Futuresandoptionsmarkets Everyitemthatistradedonsomefinancialmarketisofoneofthefollowingtypes Abasicequity Afinancialderivative theitem svaluemaybeindirectlyderivedfromthevalueofsomeothertradedequity termedtheunderlyingequity Astock abond oraunitofcurrency etc Forwards futures options etc Themainobjectiveofthiscourseistointroducethemethodsofcomputingderivativepricesintermsofunderlyingequityprices 2 StocksandTheirDerivatives Astockisacertificatethatshowsitsshareholderownsconcretenumberofsharesforsomecompany Thevalueofacompany sstockreflectstheviewsorpredictionsofinvestorsaboutthelikelydividendpayments futureearnings andresourcesthatthecompanywillcontrol Buyersandsellersofthestockexercisetheirviewsbytradingsharesinauctionmarkets Thatis mostofthetimeastock spriceisjudgedbywhatsomeoneelseiswillingtopayforitonagivenday Astockderivativeisaspecificcontractwhosevalueatsomefuturedatewilldependentirelyonthestock sfuturevalues Thepersonorfirmwhoformulatesthiscontractandoffersitforsaleistermedthewriter Thepersonorfirmwhopurchasesthecontractistermedtheholder Thestockthatthecontractisbasedonistermedtheunderlyingequity 2 1ForwardStockContracts Aforwardstockcontractisacontractthatassuresthat onsomespecificfuturedate onemustbuyashareofstockforaguarantedprice Herearethecontractconditions Onaspecificdate theexpirationdate theholdermustpayaprescribedamountofmoney theexerciseprice tothewriter Thewritermustdeliveroneshareofstocktotheholderontheexpirationdate ProfitorLossatExpiration Thecontracthasahighvalueiftoday spriceismuchhigherthantheexerciseprice X andexpirationisnottoofaraway Ontheotherhand iftoday sstockpriceisquitelow thenperhapsitisnearlyworthless ReplicatingInvestment Constructaportfolio Onecontract amountofcash Nowthenetworthoftheportfoliois Ontheexpirationdate theportfoliogainsashareofstockandpaystheexerciseprice butthecontrivedcashamounthasgrownintoexactlytheexerciseprice Infact thecashpartoftheinvestmentdisappearsandthereisnofee Ontheotherhand oneusuallycansellthiscontractinamarketevenifhedoesnotownit termedshortingtheequity Theinvestorcansellshortquitelargeamountsofthestocktoday Thisproduceinstantcash Hecouldusesomeofthecashtoformthecorrectnumberofportfoliounitstocovertheshortselling Thatis whenthestrikedatearrives theinvestorneutralizesalltheshortsalesofstockusingthereplicatingportfoliovalueasastockvalue Hecanpocketsomecashatthebeginning regardlessoffuturemarketbehavior Infact ifContractvalue Cashamount oneshareofstock Firstarbitrageopportunity Theinvestorcansellunitsoftheportfolioshort Similararithmeticshowsthattheinvestorcancovertheseshortsaleswithcheapstock purchasedimmediatelyaftersellingshort Again somecashisearnedatthebeginning regardlessoffuturemarketbehavior IfContractvalue Cashamount oneshareofstock Secondarbitrageopportunity Realfinancialmarketswouldnotalloweitherofthesemoney makingschemetowork Realfinancialmarketshavenoarbitrageopportunity i e Example1 SupposewehaveaforwardforEliLillystockthatwillexpire40daysfromnow Iftheexercisepriceis 65 andiftoday sstockpriceis whatisthecontractpricetoday peryear Solution Wehavethat So Exercise1 SupposeTomhas100forwardsforGEstockthatwillexpire73daysfromnow Iftheexercisepriceis 100 andiftoday sGEstockpriceis 101 whatisthevalueofthe100forwardcontractstoday peryear Solution Sothevalueofthe100forwardcontractsis 2 2FuturesContracts Afuturecontractisanagreementbetweentwoparties thebuyerandtheseller toconsummateatransactiononaspecifieddateinthefuture Nogoodsormoneyisexchangedtoday Example2 ItisFeb 23 2011 ThebuyerandthesellerenterintoanagreementwherebyonMay23 2011 thesellerwillturnoverabarrelofoiltothebuyer and thebuyerwillpaythesellerthepreviouslyagreed onpriceof 90forthebarrelonthatday Itisafuturecontract Thedifferencesbetweenfuturesandforwards Futurescontractisusuallytradedinsomefuturesexchange Futurescontracthasstandardizedarticles Theexpirationdateoffuturescontractissomefuturemonthbutanexactlyday Therearefuturescontractsforstockindexes currencies interestrates andcommodities Dow S P500 Russell2000 Wheat Cotton Coffee Copper U S Treasurybond Eurodollars LIBOR StockFutures SupposeabuyeragreestotakedeliveryofashareofstockatadatedenotedbyT andthebuyerandsellerwishtodetermineapriceof Xthatthebuyershouldpaythesellerwhenthebuyertakesthedelivery Whatamount X wouldthebuyerandselleragreeon Example3 ThefollowingareclosingpricesonJune8 1998 TheWallStreetJournal June9 1998 S P5001115 72SeptS P500Indexfuture1129 213 weekTreasurybillrate4 995 TimePeriod102days Jun8 Sept15 Ineffect ourprojectedvaluefortheS P500Indexfutureis CommoditiesFutures Commoditiesfuturesareverycomplicated soweskipthem 2 3CallOptions Acalloptionisacontractthatassuresthattheholderhasarighttobuyashareofstockinthefutureforaguarantedprice Herearethecalloptionconditions Thebuyeroftheoptionpaysthesellerafeefortheoption termedthepremium Ontheexpirationdate theholderoftheoptionmaypaythewriteroftheoptiontheexerciseprice Ifthewriterreceivestheexercisepricefromtheholder thewritermustdeliveroneshareofstocktotheholderontheexpirationdate ProfitorLossatExpiration Callpayoff d AEuropeancalloptionhasthelimitationthattheholdermayuseitonlywhenitexpires AnAmericancalloptionislessrestricted Theholderisallowedtoconvertitanytimebeforeexpiration Example4 European SupposeweholdacallforashareofGeneralElectric GE andthecallwillexpireonOct 10 2011 Supposethestrikepriceis 88 SupposethemarketpriceforGEis 84onOct 10 2011 thenwedon texercisethecalloption SupposethemarketpriceforGEis 95onOct 10 2011 thenweexercisethecalloptiontomakeaprofitof 2 4PutOptions Aputoptionisacontractthatassuresthattheholderhasarighttosellashareofstockinthefutureforaguarantedprice Herearethecalloptionconditions Thebuyeroftheoptionpaysthesellerafeefortheoption calledthepremium Ontheexpirationdate theholdermaygivethewriterashareofstockor equivalently themarketpriceofashareofstock Ifthewriterreceivestheshareoritspricefromtheholder thewritermustpaytheexercisefeetotheholderontheexpirationdate ProfitorLossatExpiration Callpayoff d AEuropeanputoptionhasthelimitationthattheholdermayuseitonlywhenitexpires AnAmericanputoptionislessrestricted Theholderisallowedtoconvertitanytimebeforeexpiration Example5 ProtectivePut Dr BrownownsasubstantialamountofstocksofFord Fordstockistradingat 30pershare andshebelievesthatthestockpriceislikelytovarywidelyinthemonthsahead Shebeginsaprogramofbuyingputsofapproximately