1风险管理与金融衍生品

[e-mail]1RiskManagement&FinancialDerivativeRiskRisk-uncertaintyoftheoutcomebringunexpectedgainscauseunforeseenlossesRisksinFinancialMarketasset(stocks,…),interestrate,foreignexchange,credit,commodity,…………TwoattitudestowardrisksRiskaversionRiskseekingFinancialDerivativesManyformsoffinancialderivativesinstrumentsexistinthefinancialmarkets.Amongthem,the3mostfundamentalfinancialderivativesinstruments:ForwardcontractsFutureOptionsIftheunderlyingassetsarestocks,bondsetc.,thenthecorrespondingriskmanagementinstrumentsare:stockfutures,bondfutures,etc..RiskManagementriskmanagement-underlyingassetsMethod–hedging-usingfinancialderivativesi.e.holdstwopositionsofequalamountsbutoppositedirections,oneintheunderlyingmarkets,andtheotherinthederivativesmarkets,simultaneously.UnderlyingassetputorcallDerivativecallorput=ForwardContractsanagreementtobuyorsellataspecifiedfuturetimeacertainamountofanunderlyingassetataspecifiedprice.anagreementtoreplaceariskbyacertaintytradedOTClongposition-thebuyerinacontractshortposition-thesellerinacontractdeliveryprice-thespecifiedpricematurity-specifiedfuturetimeFutureTSTVTSTVKK00LongpositionShortpositionTTVSKTTVKSFuturessameasaforwardcontracthaveevolvedfromstandardizationofforwardcontractsdifferences–futuresaregenerallytradedonanexchangeafuturecontractcontainsstandardizedarticlesthedeliverypriceonafuturecontractisgenerallydeterminedonanexchange,anddependsonthemarketdemandsOptionsanagreementthattheholdercanbuyfrom(orsellto)theseller(thebuyer)oftheoptionataspecifiedfuturetimeacertainamountofanunderlyingassetataspecifiedprice.Buttheholderisundernoobligationtoexercisethecontract.aright,noobligationtheholderhastopaypremiumforthisrightisacontingentclaimHasamuchhigherlevelofleverageTwoOptionsAcalloption-acontracttobuyataspecifiedfuturetimeacertainamountofanunderlyingassetataspecifiedpriceAputoption-acontracttosellataspecifiedfuturetimeacertainamountofanunderlyingassetataspecifiedprice.exerciseprice-thespecifiedpriceexpirationdate-thespecifieddateexercise-theactiontoperformthebuyingorsellingoftheassetaccordingtotheoptioncontractOptionTypesEuropeanoptions-canbeexercisedonlyontheexpirationdate.Americanoptions-canbeexercisedonorpriortotheexpirationdate.Otheroptions–Asiaoptionetc.TotalGainofanOptionTSTPTSKK00Calloptionputoption()TTPSKp()TTPKSpTPp[Totalgain]=[Gainoftheoptionatexpiration]-[Premium]OptionPricingriskyasset’spriceisarandomvariablethepriceofanyoptionderivedfromriskyassetisalsorandomthepricealsodependsontimetthereexistsafunctionsuchthatknownHowtofindout(,)VSt(,)ttVVSt()()TTTSKcallVKSput0(,0)?pVSTypesofTradersHedger-toinvestonbothsidestoavoidlossSpeculator-totakeactioncharacterizedbywillingtoriskwithone'smoneybyfrequentlybuyingandsellingderivatives(futures,options)fortheprospectofgainingfromthefrequentpricechanges.Arbitrage-basedonobservationsofthesamekindofriskyassets,takingadvantageofthepricedifferencesbetweenmarkets,thearbitrageurtradessimultaneouslyatdifferentmarketstogainrisklessinstantprofitsHedgerExampleIn90days,ApaysB£1000,000Toavoidrisk,Ahas2plansPurchaseaforwardcontracttobuy£1000,000with$1,650,00090dayslaterPurchaseacalloptiontobuy£1000,000with$1,600,00090dayslater.Apaysapremiumof$64,000(4%)currentrate($/£)90-daylaterRate($/£)nohedging$forwardcont.hedging$calloptionhedging$1.60up1.70down1.551,700,0001,550,0001,650,0001,650,0001,664,0001,614,000SpeculatorExampleStockAis$66.6onApril30,maygrowAspeculatorhas2plansbuys10,000shareswith$666,000onApril30paysapremiumof$39,000USDtopurchaseacalloptiontobuy10,000sharesatthestrikeprice$68.0pershareonAugust22SpeculatorExamplecont.SituationI:Thestock$73.0on8/22.StrategyAReturn=(730-666)/666*100%=9.6%StrategyBReturn=(730-680-39)/39*100%=28.2%SituationII:Thestock$66.0on8/22.StrategyAReturn=(660-666)/666*100%=-0.9%StrategyBlossallinvestmentReturn=-100%Chapter2Arbitrage-FreePrincipleFinancialMarketTwoKindsofAssetsRiskfreeassetBondRiskyassetStocksOptions….Portfolio–aninvestmentstrategytoholddifferentassetsInvestmentAttime0,investSWhent=T,Payoff=Return=Forariskyasset,thereturnisuncertain,i.e.,Sisarandomvariable0TSS00()/TSSSAPortfolioarisk-freeassetBnriskyassetsaportfolioiscalledainvestmentstrategyontimet,wealth:,1,...iitSSin1,,niiiiBS1,,...nportionofthecor.Asset1()nttttititiVBSArbitrageOpportunitySelf-financing-during[0,T]noaddorwithdrawfundArbitrageOpportunity-Aself-financinginvestment,andProbabilityProb**0(0,],..()0,()0TTTstVV*()00.TVArbitrageFreeTheoremTheorem2.1themarketisarbitrage-freeintime[0,T],areany2portfoliossatisfying&1,212()(),TTVV12Prob{()()}0TTVV[0,),tT12()().ttVVProofofTheoremSupposefalse,i.e.,DenoteBisarisk-freebondsatisfyingConstructaportfolioat***12[0,),..()()tttTstVV**21()()0ttEVVc*tt*c12=+/BtEB**()ttBVB*****12()()(){/}()0ctttttVVVEBVBProofofTheoremcont.r–riskfreeinterestrate,att=TThenFromthesupposition*12()()(){/}()TcTTT