The Research Of Some Problems On Default Risk

With the development of global economy,financial markets have becomeincreasinglyprosperous.Moreand Morefinancialderivativesemergeasthetimesrequire,such as options,futures,mortgage‐backed security,collateralized debtobligation,credit default swap and so on . These financial instruments bringconvenience,butitalsocontainsalotofdefaultriskatthesametime.Peoplehaveanewlookatdefaultriskbecauseofthefinancialcrisisin2007,whichmademanyfinancialinstitutionscloseddown.Inliterature[1]'sopinion, weshouldmeasurethe default risk correctly though their capital leverage is very high . China hasintroducedcall(put)warrants, personalforeignexchangeoptions, stocklendingandborrowingandotherfinancialinstrumentsinrecentyears.Itisobservedthatthegovernment'sattitudetowardstheintroductionofthesefinancialinstrumentsispositive. It's important to understand the default risk correctly for the stability offinancial system and the health development of the financial markets.Default riskalmostinvolvesinallfinancialderivatives.Thisdissertationwasintendedtoanalyzethedefaultriskbycreatingthemathematicalmodelsaboutcorporatebonds, theprobabilityofdefaultandtheexchangefinancialproducts.Firstly,thispaperhasanoverviewofdefaultrisk,characteristics,historyofthedevelopmentandresearchsituationathomeandabroad;Chapter2introducedthebasicconceptsandrelatedknowledgeofdefaultrisk.Basedonliterature[2]andliterature[3], supposingthattheprimaryvalueobeystandardgeometricBrownmotionandundertheassumptionthat the interest rate obeys Vasicek model and so on,the explicit expression ofcorporatebondpricewithdefaultcorrelationinadouble‐timeperiodwasgivenbyPDE method in Chapter 3 . In the numerical results part,we compared therelationshipbetweenthecorporatebondpriceandinterestrate,thecorrelationofinterest rate and the primary value and the recovery rate . The interpretations offinancial significance were also give .In Chapter 4,We studied the probability ofdefaultinhousingcreditfromthefactorofthepersonalcurrentassets.TheperiodtimewasdividedintoNgroupsaccordingtothedifferentrepaymenttime.Supposing that both of the house price and the personal current assets obey standardgeometric Brown process,We got the PDE equation which was suitable for theprobabilityofdefaultinhousingcreditbyKolmogrovtheoremineachtimeperiod,andweobtainedtherecurrenceformulabyputtingthenextprobabilityofdefaultasknown condition. Then,the applications of the model about the probability ofdefaultwerepointedoutinthecalculationofexpectedvalueofloan,thecontrolofthelineofcreditandthecalculationofcapitaladequacyratio.Basedonliterature[6],undertheassumptionthattheAmericaninterestrateisconstantandtheNationA'sinterest rate obeys Vasicek model, we used PDE method so as to calculate thecontractvalueofexchangefinancialproduct(LiangDeLi)issuedbyICBCconsideringwhetherthecustomerdefaultornotinChapter5.Inthenumericalresultspart,wecompared the relationship between the contract value and the parameters at thetimeofinitial.Theinterpretationsoffinancialsignificancewerealsogiven.Atlast,asummary of this dissertation was made and further research directions were putforward.