Risk-adjusted Lending Conditions
 An Option Pricing Approach
By WernerRosenberger

Published by Wiley,2003.

Contents
Preface1xiii
Preface2 xv
PartIOutline1
1Introduction3
1.1Theproblem3
1.2Narrowingthesubjectdown,settingtheobjectiveandsubdividingit3
1.3Theinsuranceconcept5
1.4Typesofprobleminthecontextofloanbusiness7
1.5Loaninterestratemodel8
1.6Modelforcalculatingrisksurcharge9
1.7Assumptions11
1.8Testingthemodel12
1.9Loanexposuremodels13
1.9.1Classicalmethods14
1.9.2Moderncreditriskanalysisbasedon?nancialtheory14
1.9.3Themodelpresentedhereseeninrelationtopreviousmodels16
2Ratingsystem19
2.1Theneedforaratingsystem19
2.2De?ningshortfallriskintermsof?gures20
2.3De?ningthecredit-worthinesskey?gure21
2.4Exampleofaratingsystemintermsof?gures21
2.5Ampli?cationoftheratingsystemforverycompetitivemarkets23

viiiContents
PartIIMathematicalFoundationsoftheModel25
27
3Probabilitymodel:Developmentof
j
3.1Determiningtheprobabilityofcash?owsbeingful?lled27
3.2Maturitytransformation28
3.3Conclusions29
3.3.1Thecaseofaloanbeinggrantedinde?nitely29
3.3.2Re?ectionsonthesuccesschance(n)29
3.4Resultsandconclusions31
4Calculationoftheshortfallriskhedgingrateinthespecialcase
ofshortfallrisksbeingconstant33
4.1Fixedadvancewithoutrepayments33
4.2Fixedadvancewithregularrepayments36
4.3Loansonregularannualrepayment36
4.4Currentaccountcredit36
4.5Loanassessment40
4.6Conclusions41
4.6.1Minimumloaninterestrate42
4.6.2Effectivepro?tcontributionrate43
4.6.3Effectiveshortfallriskhedgingrate43
4.6.4Maximumshortfallriskcovered44
4.7Resultsandconclusions45
4.8Example45
5Calculationoftheshortfallriskhedgingrateinthegeneralcase
ofvariableshortfallrisk47
5.1Fixedinterestloanwithoutrepayments47
5.2Approximatesolutionfor?xedinterestloanwithoutrepayments48
5.3Reliabilityoftheapproximatesolution49
5.4Fixedadvancewithcompleterepayment50
5.5Fixedadvancewithpartialrepayments51
5.6Currentaccountloans52
5.7Resultsandconclusions52
6Shortfallriskonuncoveredloansonthebasisofstatistics53
6.1Privateclients53
6.1.1Unearnedincomeandincomefromself-employment53
6.1.2Incomefromsalariedemployment54
6.1.3Investmentincomeandassets54
6.2Companies55

Contentsix
PartIIIOption-TheoryLoanRiskModel57
7Shortfallriskonuncoveredloanstocompaniesonthebasisofan
option-theoryapproach59
7.1DifferenceinapproachbetweenBlack/ScholesandKMV,together
withfurtherelaboration59
7.2Derivationofbasicformulae60
7.3Derivationofrisk-adjustedvalues63
7.4De?nitionofthevaluesforthesolutionformula67
7.4.1Thevalueofthecompanyanditsdebtrate67
7.4.2Volatility69
7.4.3Privatedebtors71
7.5In?uenceofindividualparametersonthecreditshortfallrisk71
7.6Riskofbankruptcyandbreakdowndistribution78
7.7Loanassessment79
7.8Bonds80
7.9Considerationofprivilegedsalaryclaimsintheeventofbankruptcy80
7.10Limitstotheapplicationoftheoptiontheoryapproach82
7.11Resultsandconclusions84
7.12Examples85
7.12.1Exampleofacompanywithcontinuousbusinessdevelopment85
7.12.2Exampleofacompanywithapoor?nancialyear87
8Loanscoveredagainstshortfallrisk91
8.1Shortfallriskofacoveredloanonthebasisoftheoption-theory
approach91
8.2Correlationbetweentheshortfallriskoftheborrowerandtheshortfall
riskofthecollateral93
8.2.1Derivationofthecorrelation93
8.2.2Valueareaoftheef?ciencyofthecorrelation94
8.3Shortfallriskofthecoveredloan97
8.4Coveredanduncoveredloanstothesameborrower98
8.5Resultsandconclusions99
8.6Example99
9Calculationofthecombinationofloanswiththelowestinterestcosts103
9.1Marginalinterestrate103
9.2Twoloans105
9.3Threeloans107
9.4Thegeneralcaseofseveralloans107
9.5Partiallycoveredloans108

xContents
9.6Maximumreturnonequity108
9.7Acceptabilityofdebtservicing112
9.7.1Acceptabilityofinterestrates112
9.7.2Acceptabilityofrepayment113
9.7.3Maximumdebt114
9.7.4Consequencesforcompanieswithdecliningearning114
9.7.5Consequencesforloansupervision114
9.8Resultsandconclusions115
9.9Example116
PartIVImplementationinpractice119
10Procedureaccordingtothemodelforassessingtheri
inlendingtoacompany121
10.1Overallviewoftheprocedure121
10.2Analysisofearningsstatements122
10.3Analysisofcash?owstatements122
10.4Analysisofbalancesheets123
10.5Determinationofthediscountrate123
10.6Determinationofrelevantloanterms124
10.7Determinationofvolatility124
10.8Determinationofcreditrisk124
10.9Prudenceinthecaseofnewloans/borrowers125
10.10Possiblecausesofcon?ictbetweenbankandborrowerwhenthe
modelisapplied125
11Applications127
11.1Specialistclothingbusiness:Turn-aroundsituation127
11.2Companytradinginmachinetools:Provisionforsuccessorcompany129
11.3Shipmortgages:Risklimitation130
11.3.1Startingposition130
11.3.2Thebanksloandecision13
11.3.3Assessmentoftheloanriskbythebanks131
11.3.4Determinationofloanriskaccordingtothemodel131
11.3.5Comparisonofassessmentbetweenthebankandthemodel134
11.3.6Limitationofloanrisk134
11.4Mortgagebusiness1985¨C9913
12Finalconsiderations139
12.1Testsofhypotheses139
12.2Implementationinpractice141
12.2.1Specialistpersonnel141
12.2.2Statisticalbases142

Contentsxi
12.2.3ITsupport143
12.2.4Organisationalmeasures143
12.3Applicabilityofthemethodpresented144
12.4Customerconsiderations145
12.5Openquestions145
12.6Closingremarks146
Appendix1:Notation147
Appendix2:Excelworksheet149
Appendix3:Propertypriceindex151
Appendix4:Chapter3Derivations15
Appendix5:Chapter4Derivations15
Appendix6:Chapter5Derivations15
Bibliography163
Index 167