Preface1xiii
Preface2 xv
PartIOutline1
1 Introduction 3
1.1Theproblem3
1.2Narrowingthesubjectdown,settingtheobjectiveandsubdividingit3
1.3Theinsuranceconcept5
1.4Typesofprobleminthecontextofloanbusiness7
1.5Loaninterestratemodel8
1.6Modelforcalculatingrisksurcharge9
1.7Assumptions11
1.8Testingthemodel12
1.9Loanexposuremodels13
1.9.1Classicalmethods14
1.9.2Moderncreditriskanalysisbasedonfinancialtheory14
1.9.3Themodelpresentedhereseeninrelationtopreviousmodels16
2 Ratingsystem 19
2.1Theneedforaratingsystem19
2.2Definingshortfallriskintermsoffigures20
2.3Definingthecredit-worthinesskeyfigure21
2.4Exampleofaratingsystemintermsoffigures21
2.5Amplificationoftheratingsystemforverycompetitivemarkets23
PartIIMathematicalFoundationsoftheModel25
27
3 Probabilitymodel:Developmentofψ
j
3.1Determiningtheprobabilityofcashflowsbeingfulfilled27
3.2Maturitytransformation28
3.3Conclusions29
3.3.1Thecaseofaloanbeinggrantedindefinitely29
3.3.2Reflectionsonthesuccesschanceε(n)29
3.4Resultsandconclusions31
4 Calculationofthe shortfallrisk hedgingratein thespecial case
ofshortfallrisksbeingconstant33
4.1Fixedadvancewithoutrepayments33
4.2Fixedadvancewithregularrepayments36
4.3Loansonregularannualrepayment36
4.4Currentaccountcredit36
4.5Loanassessment40
4.6Conclusions41
4.6.1Minimumloaninterestrate42
4.6.2Effectiveprofitcontributionrate43
4.6.3Effectiveshortfallriskhedgingrate43
4.6.4Maximumshortfallriskcovered44
4.7Resultsandconclusions45
4.8Example455 Calculationofthe shortfallrisk hedgingratein thegeneral case
ofvariableshortfallrisk47
5.1Fixedinterestloanwithoutrepayments47
5.2Approximatesolutionforfixedinterestloanwithoutrepayments48
5.3Reliabilityoftheapproximatesolution49
5.4Fixedadvancewithcompleterepayment50
5.5Fixedadvancewithpartialrepayments51
5.6Currentaccountloans52
5.7Resultsandconclusions52
6 Shortfallriskon uncoveredloanson thebasis of statistics 53
6.1Privateclients53
6.1.1Unearnedincomeandincomefromself-employment53
6.1.2Incomefromsalariedemployment54
6.1.3Investmentincomeandassets54
6.2Companies55
PartIIIOption-TheoryLoanRiskModel57
7 Shortfall riskonuncoveredloans to companies on thebasis of an
option-theoryapproach59
7.1DifferenceinapproachbetweenBlack/ScholesandKMV,together
withfurtherelaboration59
7.2Derivationofbasicformulae60
7.3Derivationofrisk-adjustedvalues63
7.4Definitionofthevaluesforthesolutionformula67
7.4.1Thevalueofthecompanyanditsdebtrate67
7.4.2Volatility69
7.4.3Privatedebtors71
7.5Influenceofindividualparametersonthecreditshortfallrisk71
7.6Riskofbankruptcyandbreakdowndistribution78
7.7Loanassessment79
7.8Bonds80
7.9Considerationofprivilegedsalaryclaimsintheeventofbankruptcy80
7.10Limitstotheapplicationoftheoptiontheoryapproach82
7.11Resultsandconclusions84
7.12Examples85
7.12.1Exampleofacompanywithcontinuousbusinessdevelopment85
7.12.2Exampleofacompanywithapoorfinancialyear87
8 Loanscoveredagainstshortfall risk 91
8.1Shortfallriskofacoveredloanonthebasisoftheoption-theory
approach91
8.2Correlationbetweentheshortfallriskoftheborrowerandtheshortfall
riskofthecollateral93
8.2.1Derivationofthecorrelation93
8.2.2Valueareaoftheefficiencyofthecorrelation94
8.3Shortfallriskofthecoveredloan97
8.4Coveredanduncoveredloanstothesameborrower98
8.5Resultsandconclusions99
8.6Example99
9 Calculationofthecombinationofloanswith the lowest interestcosts 103
9.1Marginalinterestrate103
9.2Twoloans105
9.3Threeloans107
9.4Thegeneralcaseofseveralloans107
9.5Partiallycoveredloans108
9.6Maximumreturnonequity108
9.7Acceptabilityofdebtservicing112
9.7.1Acceptabilityofinterestrates112
9.7.2Acceptabilityofrepayment113
9.7.3Maximumdebt114
9.7.4Consequencesforcompanieswithdecliningearning114
9.7.5Consequencesforloansupervision114
9.8Resultsandconclusions115
9.9Example116
tIVImplementationinpractice119
Procedure—accordingtothemodel—forassessingtherisk
inlendingtoacompany121
10.1Overallviewoftheprocedure121
10.2Analysisofearningsstatements122
10.3Analysisofcashflowstatements122
10.4Analysisofbalancesheets123
10.5Determinationofthediscountrate123
10.6Determinationofrelevantloanterms124
10.7Determinationofvolatility124
10.8Determinationofcreditrisk124
10.9Prudenceinthecaseofnewloans/borrowers125
10.10Possiblecausesofconflictbetweenbankandborrowerwhenthe
modelisapplied125
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