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基于Poisson跳跃的信用价差期权定价 Introduction: Creditdefaultswaps(CDS)andcreditspreadoptionsaretwoimportanttoolsincreditriskmanagement.Theformerenablesmarketparticipantstotransfercreditrisktothirdparties,whilethelattergivesinvestorstherighttobuy(calloption)orsell(putoption)protectionagainstthedefaultofthereferencebond.Creditdefaultswapsarealreadywellestablishedandhavebeenwidelyusedinthemarket.Creditspreadoptions,ontheotherhand,areamorerecentinnovationandtheirpricingcontinuestoattractconsiderableinterestandattentionfromtheacademicandpractitionercommunities. OnepossibleapproachtopricingcreditspreadoptionsisbasedonPoissonjumpprocesses.Thisapproachcancapturetherandomandunpredictablenatureofcreditevents,aswellasthecorrelationbetweencreditspreadsandtheunderlyingmarketfactorsthatdrivethem. Inthispaper,weaimtodiscussthebasicprinciplesofPoissonjumpprocessesandhowtheycanbeappliedtopricecreditspreadoptions.Wewillprovideadetailedanalysisofkeyfeaturesofthisapproachandillustrateitsapplicationwithasimplebutpracticalexample. PoissonJumpProcesses: ThePoissonjumpprocessisatypeofstochasticprocessusedtomodeltheoccurrenceofdiscrete,randomeventsovertime.Theseeventsoccuratrandomintervalsandhavearandomimpactontheprocess.Theyareusuallyreferredtoasjumpsorarrivals. ThePoissonprocesshastwomaincomponents:therateofarrivalofjumpsandthesizeofeachjump.Therateofarrivalisdeterminedbyaparameterλ,whichmeasuresthemeannumberofjumpsperunitoftime.Thesizeofeachjumpisdescribedbyaprobabilitydistribution,whichcanbeassumedtobecontinuousordiscrete. CreditspreadoptionscanbemodeledusingPoissonjumpprocessesbyassumingthatthejumpeventsrepresentcreditevents,suchasdefaultsorratingdowngrades.Thesizeofeachjumpcanrepresentthechangeinthecreditspreadcausedbythecreditevent.Themodelcanalsoincludeotherfactorsthatinfluencethecreditspread,suchasinterestrates,marketvolatilityandmacroeconomicfactors. CreditSpreadOptionPricing: ThepriceofacreditspreadoptioncanbeobtainedusingtheBlack-Scholesmodel,whichassumesthatunderlyingassetpricesfollowacont