v2直播merton model教育frm二級培訓(xùn)知識點(diǎn)

假設(shè)某股東投資了一家公司，初始投資額為S0=100，同時(shí)公司向債權(quán)人了面值為K=100、期限為1年的零息債券，到期償還本金，因此會折價(jià)。企業(yè)的初始價(jià)值（可以看成是總資產(chǎn)）V0=B0+S0，現(xiàn)情況V1=300>B1=K=S1=200=V1–情況V1=200>B1=K=S1=100=V1–情況V1=100=B1=K=S1=0=V1–情況V1=80<B1=V1=S1=V1=B1+B1=Min(K,=K–Max(K–S1=Max(V1– InferCreditRiskfromEquityVT<D,defaultoccursifthevalueofthefirmisinsufficienttorepaythedebtpripal.BondholdershavepriorityovershareholdersandseizetheentirevalueofthefirmVT.VT≥D,bondholdersreceivewhattheyaredue:the ipalPayoff:Min(D,VT)=D–max(D–VT,D= debt–putoptiononThepayoffreceivedbycorporatebondholderscanbeseenasthepayoffofarisklessbondminusaputonthevalueofthefirm.VT<D,receivenothingifthefirmVT≥D,profitfromalltheupsidewhenthefirmissolvent,whieanstheentirevalueofthefiroftherepaymentofthedebt(VT–D)fallsinthehandsofshareholders.Payoff:Max(VT–D,E=calloptiononThepayofftoequityholdersissimilartothepayoffofacallonthevalueofthefirmstruckatD.UndertheMertonframework,theequity(shareholder)payoffprofileresemblesthepayoffofalongcalloptionanddebtresemblesthepayoffofashortputoption:Thevalueofequity=Calloptionon=valueoffirm’sasset(V)–valueofriskyThevalueofriskydebt=Risk-debt–putoptiononRecallBlack-ScholespricingformulasforEuropeancallasCallSNdKe-rNd

StockCallVN Ke-rNValueoftheStockCallVN Ke-rNValueofthecorporateBondBondKe-rPutVN(-d)Ke-rN(dIntheB-Smodel,N(d2)istheprobabilityofexercisingcalloption,orthatthebondwillnotdefault.Conversely,N(-d2)istherisk-neutralprobabilityofRisk-Neutralvs.Real-World:Risk-Ratevs.AssetThecapitalstructureofABCCorporationconsistsoftwoparts,one5yearbondwithfacevalueof$100millionandtherestisequity.Thecurrentmarketvalueofthefirmassetsis$130andtheexpectedrateofchangeofthefirm’svalueis25%.Thevolatilityis30%.Thefirm’sriskmanagementdivisionestimatesthedistancetodefaultusingMertonmodel.Giventhedistancetodefault,theestimatedphysicaldefaultprobabilityis?(N(1.92)=97.25%;N(2.58)=99.52%)WhichofthefollowingstatementsregardingtheMertonmodelisAfirmwithnumerousdebtissuesthatmatureatdifferenttimesiseasytovaluewiththeMertonmodel.TheMertonmodelassumesalognormaldistributionandconstantvarianceforchangesinfirmvalue.TheMertonmodelisabletopredictdefaultbecauseitallowsfordefaultsurprises(i.e.,jumps