Handbook of Solvency for Actuaries and Risk Managers: Theory and Practice (Chapman & Hall Crc Finance Series)

1083 Pages·2010·17.19 MB·English

by  Arne Sandstrom

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Library of Congress Cataloging-in-Publication Data
Sandström, Arne.
Handbook of solvency for actuaries and risk managers : theory and practice / Arne Sandström.
p. cm. -- (Chapman & Hall/CRC finance series)
Includes bibliographical references and index.
ISBN 978-1-4398-2130-5 (hbk. : alk. paper)
1. Risk (Insurance) 2. Risk (Insurance)--European Union countries. 3. Asset-liability management.
4. Asset-liability management--European Union countries. 5. Risk management. 6. Risk
management--European Union countries. I. Title.
HG8054.5.S26 2011
368.001--dc22 2010042931
Visit the Taylor & Francis Web site at
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and the CRC Press Web site at
http://www.crcpress.com
Contents
Preface xxxvii
Reader’s Guide xxxix
Web Site Information xli
Future Information xliii
Abbreviations xlv
PARTA Solvency Introduction 1
CHAPTER 1 Solvency 3
CHAPTER 2 A Historical Review 9
2.1 CLASSICALAPPROACH 10
2.1.1 FluctuationinAggregateClaimsandRuinTheory 11
2.1.2 CombinedRatiosandOtherRatios 12
2.1.3 ChangeintheCapitalPosition 13
2.1.4 MultidimensionalSystems 15
2.2 ECONOMICAPPROACH 16
2.3 EUROPEAN SOLVENCY II PROJECT 21
2.3.1 BasicArchitectureofSolvencyII 21
2.3.1.1 GeneralIdeas 22
2.3.1.2 ValuationandInvestment 22
2.3.1.3 StandardFormulaofSCRandMCR 22
v
vi (cid:2) Contents
CHAPTER 3 Managing Risks and the Enterprise 25
3.1 STEPPING STONESTO MANAGINGASSETSAND LIABILITIES 25
3.2 RISK MANAGEMENTANDALM 28
3.2.1 ModelOfficeTools 29
3.2.2 ToolstoManageAsset–LiabilityInteractions 30
3.2.2.1 Cash-FlowTesting 31
3.2.2.2 Immunization 31
3.2.2.3 Cash-FlowMatching 34
3.2.2.4 Asset–LiabilityManaging 34
3.2.3 SimulationToolsandTesting 36
3.2.4 DFATools 36
3.3 ENTERPRISE RISK MANAGEMENT 38
3.3.1 COSO’sDefinitionofERM 40
3.3.2 SOA’sDefinitionofERM 41
3.3.3 ERM-II–CAS–SOADefinition 42
3.3.4 IAISERMStandardsandGuidance 44
3.3.5 IAA’sNoteonIAIS’KeyFeatures 47
3.3.6 EUSolvencyIIERMApproach 48
3.3.7 TheFinancialCrisisandERM 48
CHAPTER 4 Summary of the Development of ERM and Solvency 51
CHAPTER 5 Elements of SolvencyAssessment Systems 55
5.1 IAIS CAPITAL REQUIREMENTS STANDARDSAND GUIDANCE 57
5.2 MODELING CAPITAL REQUIREMENT 61
5.2.1 GeneralStructure 61
5.2.2 DiversificationandMitigation 63
5.3VALUATION OFASSETSAND LIABILITIES 63
5.4 CONSERVATIVEVALUATION REGIMES 66
PART B Valuation, Investments, and Capital 69
CHAPTER 6 Total Balance SheetApproach 71
6.1 MARKET–CONSISTENTVALUATION 74
Contents (cid:2) vii
6.2TIMEVALUE OF MONEY 76
6.2.1 PresentValue 76
6.2.2 DiscountingRates 77
6.2.3 LongMaturitiesandLiquidityConsiderations 79
6.2.4 LiquidityPremium 83
6.3 HEDGING 84
6.4 RISK MARGINS 84
6.5 ACCOUNTING 86
CHAPTER 7 AssetValuation 87
7.1 ASSET RISK MARGIN:A DEDUCTION OF NONHEDGEABLEASSETS 89
CHAPTER 8 LiabilityValuation 91
8.1 CE OF LIABILITIES 93
8.2 DISCRETIONARY PARTICIPATING FEATURES (dpf) 95
8.3VALUATIONTECHNIQUES 96
8.3.1 ReplicatingPortfolios 97
8.3.2 ValuationPortfolio 99
8.3.2.1 VaPoforLifeInsurance 100
8.3.2.2 VaPoforNonlifeInsurance 106
8.3.2.3 SomeGeneralAspectsontheVaPoTechnique 109
8.3.3 ValuatingtheLiabilities 110
8.4 LRM:ANADDITIONTO NONHEDGEABLE LIABILITIES 110
8.5 CoCAPPROACHTO ESTIMATETHE RM 114
8.5.1 ExamplefromCEA(2006a) 117
8.6 OTHER LIABILITIES 118
CHAPTER 9 OtherValuation Issues 119
9.1 RISK MITIGATION 119
9.1.1 In-HouseRiskMitigation 119
9.1.1.1 Pooling 119
9.1.1.2 Diversification 120
9.1.1.3 Hedging/OffsettingRisks 121
9.1.2 ExternalRiskMitigation 121
viii (cid:2) Contents
9.1.2.1 Reinsurance 121
9.1.2.2 AlternativeRiskTransfer 123
9.1.2.3 Hedging 126
9.2 RISK ENHANCING 126
9.3 SEGMENTATION 127
CHAPTER 10 Investments and Own Funds 131
10.1 INVESTMENTS 131
10.1.1 PrudentPersonRule 131
10.2 AVAILABLE CAPITAL: ELIGIBLE OWN FUNDS 132
CHAPTER 11 AccountingValuation 137
11.1 BACKGROUND 137
11.2 INTERNATIONAL DEVELOPMENTS 137
11.3 INSURANCE CONTRACTS, REVENUE RECOGNITION,AND
FINANCIAL INSTRUMENTS 139
11.3.1 ServiceContracts 140
11.3.2 FinancialInstruments 140
11.3.3 InsuranceContracts 141
11.4 AN ESTIMATE OFTHE FUTURE CASH FLOWS 142
11.4.1 EffectoftheTimeValueofMoney 147
11.5 A MARGIN: IASB’S DISCUSSION 147
11.6 A MARGIN: DISCUSSIONS BY IAISAND IAA 149
PART C Modeling and Measuring 157
CHAPTER 12 Developing a Model 159
12.1 ANALYTICAPPROXIMATION OFAN EXACT MODEL 159
12.1.1 FirstApproximationoftheExactModel 160
12.1.2 SecondApproximationoftheExactModel 160
12.2 LINEARIZATION 160
12.3 HOMOGENEOUS FUNCTIONS 161
12.3.1 Euler’sTheorem 161
12.3.2 CorollarytoEuler’sTheorem 162
Contents (cid:2) ix
12.4 NONLINEARAPPROXIMATIONS 162
12.4.1 Second-OrderApproximation 162
12.4.2 Higher-OrderFunctions 163
12.4.2.1 QuadraticApproximation 163
12.4.2.2 Higher-OrderApproximation 164
12.5 RISK MODELS 164
12.5.1 HomogeneousModelsofDegreeOne 164
12.5.2 Second-OrderRiskModels 165
CHAPTER 13 Dependence 167
13.1 DEPENDENCE STRUCTURE 168
13.1.1 MoreonCopulasandDependence 170
13.2 DEPENDENCE STRENGTH: RANK CORRELATION 172
13.2.1 Spearman’sRho 173
13.2.2 Kendall’sTau 174
13.3 TAIL DEPENDENCE 174
13.4 COPULA CLASSESAND FAMILIES 175
13.4.1 CopulaClass:Archimedean 176
13.4.2 CopulaClass:Elliptical 181
13.4.3 OtherClassesofCopulas 185
13.4.3.1 Extreme-ValueCopulas 185
13.4.3.2 TheMarshall–OlkinCopulas 186
13.4.3.3 FréchetCopulas 187
13.4.3.4 Farlie–Gumbel–Morgenstern 187
13.4.4 ASummary 187
13.5 ESTIMATIONANDTESTING 188
13.5.1 EmpiricalCopula 188
13.5.2 EstimatingDependence 188
13.5.3 EstimatingCopulaFamilies 190
13.5.4 Goodness-of-FitTests 192
13.5.5 EstimatingRegressionFunctions 193
CHAPTER 14 Risk Measures 195
14.1 PROPERTIES OF RISK MEASURES 196