EAA series - Textbook

Transcription

1 EAA series - Textbook Editors D. Filipovic (Co-Chair) M. Koller E. Pitacco C. Hipp A. Pelsser U. Orbanz (Co-Chair) EAA series is successor of the EAA Lecture Notes and supported by the European Actuarial Academy (EAA GmbH), founded on the 29 August, 2005 in Cologne (Germany) by the Actuarial Associations of Austria, Germany, the Netherlands and Switzerland. EAA offers actuarial education including examination, permanent education for certified actuaries and consulting on actuarial education. actuarial-academy.com For further volumes:

2 Michael Koller Life Insurance Risk Management Essentials

3 Michael Koller Mathematics Department ETH Zurich Rämistr. 101 Zurich 8092 Switzerland ISSN ISBN DOI / Springer Heidelberg Dordrecht London New York e-issn e-isbn Library of Congress Control Number: Springer-Verlag Berlin Heidelberg 2011 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: deblik, Berlin Printed on acid-free paper Springer is part of Springer Science+Business Media (

4 For Luisa, Giulia and Anna

5 Introduction Fig. 0.1 Risk Management in a Nutshell

6 viii Introduction When starting to write a book, one always needs to ask oneself why one wants to do that and who is the target audience. Furthermore one needs also to know what is required from his audience. To start with the first question. I have performed quite a wide range of jobs in different international insurance groups and found that some patterns always repeat and that there is a need for education in relation to risk management. So at every place there were pieces missing and the overall risk management structure had to be improved. Over time I had to repeat parts of this educational process again and again. So I decided that it would be worthwhile to gather and compile all these different facts and leanings in order that other people can profit from it. I thought that it would be in particular valuable to have a book which covers a wide range of different topics in relation to risk management in such a way and tangible enough to be readily applicable. Hence the book does not focus on abstract concepts for the sake of mathematical beauty, but rather with the aim to concretely solve problems and in order to be able to set up a top performing risk management organisation. I have put considerable focus in order to make the book as practical and applicable as possible and I have tried to show a lot of concrete reporting templates including methodology and examples, in order to better understand the context. My intention was, that one could read this book in order to afterwards be able to solve and implement some 80 % of the typical questions which occur when setting up a concrete risk management organisation. Two things need to be stressed: on one hand there are always a lot of different ways which lead to Rome, hence there might in some instances exist better solutions than those presented in this document. On the other hand I believe that this book is also suited for the advanced reader due to its aim to be quite extensive. The overall focus of this book is mainly on financial risk management, insurance risk management, economic steering of an insurance company, insurance processes and products. I would also like to mention, that the methods presented in this book are not only applicable to life insurance companies, but also to pension funds, applying them mutatis mutandis.

7 Introduction ix I wrote this book because I believed this would be fun and help me to better understand risk management. This book is intended for both those who want to learn risk management starting at a beginner s level, but also for readers who want to widen their horizon. I have also tried to include more practical questions, such as what can go wrong with particular products in order to help to avoid them. The book is aimed to be self contained and I expect the reader to understand the basics of analysis and some probability theory, such as [JP04]. Since the application of the theory and methods is in the centre, we use different types of mathematical approaches without proof. The required mathematics has been placed in different appendices. Some of them require advanced mathematics such as measure theory, functional analysis and stochastic integration. Here we refer to the following text books for the underlying theory: measure theory [DS57], functional analysis [DS57], [Con91], [Ped89], stochastic integration [IW81], [Pro90]. Finally I would like to give some references in respect of arbitrage free pricing theory [Pli97], [KM03], [Duf92] and interest rate and equity models [BS73], [CIR85], [Hul97], [BM01]. For the relevant actuarial life literature we refer to [Ger95] and [Kol10]. Finally I would like to thank the many people who helped me to make this project happen. In particular I would like to thank my wife Luisa and my children who always support me. Michael Koller, 2010

8 Contents 1 What is Risk Management Introduction Raison D être of Risk Management The Role of Risk Management Three Lines of Defence in Risk Management Principles RiskCategories Risk Management Process Risk Management Policies and Risk Landscape The Role of the Balance Sheets and of Capital The Balance Sheet of an Insurance Company RoleofValuation Valuation Methods PrincipleofNoArbitrage Reconciliation of Balance Sheets Bonds Shares OtherAssets Insurance Liabilities Life Insurance Model Capital Insurance PureEndowment Annuities CashFlowsandValuation Primer on Life Insurance Risks Shareholders Equity and Capital

9 xii Contents 3 Accounting Principles Statutory Accounting IFRS and US GAAP Accounting Embedded Value and Economic Accounting Economic Valuation / Market Consistent Embedded Value Valuation Methodology Revisited Formulae Examples Annuity CapitalProtection Risk Appetite and Tolerance Risk Capacity and Risk Appetite LimitSystems Hedging Strategies and Response Strategies Introduction: Use of Capital Definition of the Risk Factors Considered Probability Density Functions per Risk Factor Valuation Methodology RiskMeasures RiskMeasures ValueatRisk(VaR) TailValueatRisk(TVaR) Relationship Between Value at Risk and Expected Shortfall What Is a Stress Scenarios Mathematically Key Insurance Processes and Their Risks Capital Allocation and Planning Process Economic Capital Calculation Process ALM and Bonus Setting Process Product Design Process Financial Risks and Their Modelling The Model Underlying Financial Risks Approximations Concrete Implementation InterpretingtheResults Notation Scenarios What Can and What Cannot Be Done with This Reporting Example

10 Contents xiii Summary Decomposition of VaR Figures Scenarios ICACapital StressTests Limits Summary Reporting Example Insurance Risks MethodforAllocationofCapital Steps Required Probability Density Functions per Risk Factor Diversification Stochastic Models Used Mortality Longevity Concrete Example: An Annuity Portfolio Formulae Application to Insurance Linked Securities Statistics Allocation of Risk Capital in Proportion to Premium Reporting Templates Operational Risks Introduction Risk Appetite Risk Measurement and Exposure Controlling Process in General and Embedding Risk Policies Strategy & Planning Distribution Management Brand & Marketing Communications Corporate Social Responsibility Environment Regulatory Information Technology Financial Crime BusinessProtection People Outsourcing Communications...157

11 xiv Contents Legal Financial Reporting ExternalAuditor Taxation General Insurance Reserving LifeReserving Capital Management Credit Market Derivatives Liquidity Foreign Exchange Mergers & Acquisitions Risk Management & Internal Control Life Insurance Risk Life Insurance Product Development & Pricing UnitPricing General Insurance Underwriting General Insurance Reinsurance General Insurance Claims Capital Models and Integrated Risk Management Introduction Bringing the Puzzle Together Diversification Risk Adjusted Performance Metrics Introduction Performance and Value Metrics IBNRReserves Financial Options Frictional Capital Costs DurationofProjection Formulae Example Examples Capital Allocation Process Risk Management in a Group and Intra-group Transactions Introduction RiskandCapitalTransferInstruments...191

12 Contents xv Internal Loans InternalHybrids Cashpools Guarantees GI / Life Reinsurance Contracts Ranking of RCTI s Modelling Products and Their Risks Nuptualite Index Linked Products and Other Contractual Issues Variable Annuities Investment Guarantees and Bonus Rates Longevity and the Ability to Forecast LongTermCare ImperfectCashFlowsMatching Emerging Risks What Are Emerging Risks and Why Are They Important? What Process Is Needed for Emerging Risks? Regulatory View on Risk Management: Solvency II Introduction WhatIsSolvencyII? Economic Balance Sheet and Prudence Risk Modelling and Internal Models GoodRegulation SwissSolvencyTest Solvency II Standard Model Structure of the Model Market Submodule QuoVadis? Governance and Organisation Governance Definitions Generic Governance EscalationProcesses Effective Governance Risk Governance and Oversight Framework PrinciplesofEffectiveOversight...247

13 xvi Contents 15.5 BoardOversight Management Oversight Why Risk Management Committees Are Important How Do Risk Management Committees Work Terms of Reference of a Risk Committee Roles and Responsibilities Duties of the Line Management Duties of the Chief Risk Officer Duties of the Group Internal Audit Risk Relevant Parts Within Job Descriptions Decomposition of the Risk Management Process DataandSystems A Stochastic Processes A.1 Definitions A.2 Markov Chains with Countable State Space A.3 Mean Excess Function A.4 DeterministicCashFlowStreams A.5 Random Cash Flows B Application of the Markov Model to Life Insurance B.1 Traditional Rating of Life Contracts B.2 Life Insurance Considered as Random Cash Flows B.3 Reserves, Recursion and Premiums C Abstract Valuation C.1 Framework C.2 CostofCapital C.3 Inclusion in the Markov Model C.4 Asset Liability Management D An Introduction to Arbitrage Free Pricing D.1 PriceSystems D.1.1 Definitions D.1.2 Arbitrage D.1.3 Continuous Case D.2 The Black-Scholes Set Up D.2.1 EndowmentPolicies D.2.2 Term Insurance D.3 Thiele sdifferentialequation...308

14 Contents xvii E An Introduction to Stochastic Integration E.1 Stochastic Processes and Martingales E.2 Stochastic Integral E.3 Properties of the Stochastic Integral F CERA Comparison F.1 Enterprise Risk Management Concept and Framework F.2 ERM Process (Structure of the ERM Function and Best Practices). 324 F.3 RiskCategoriesandIdentification F.4 Risk Modelling and Aggregation of Risks F.5 RiskMeasures F.6 Risk Management Tools and Techniques F.7 Economic Capital References Index...331

15 List of Figures 0.1 Risk Management in a Nutshell vii 1.1 Overview RiskMap Risk Management Process Frequency vs. Severity Risk Landscape Yield curves as at Credit spreads over time Possible Trajectories of Shares Probability density function for the future life span and hazard rate Value of the benefits of a whole life insurance Value of a term insurance Value of different annuity covers ReplicatingPortfolio Required capital over time Development of Mortality over Time Comparison of different years Mortality by Ages for Sweden Risk Identification Process ComparisonVaRandTailVaR Value Chain of an Insurance Company Overview over Capital Allocation Process Example Capital Allocation Process Capital Allocation Process

16 xx List of Figures 5.5 Economic Capital Calculation Process ALM and Bonus Setting Process Investment Process Product Design Process Models and Model Risk CorrelationMatrix DistributionofLosses CashFlowProfile Diversification Required Capital CreditRiskbyRating Δ SHE for the scenarios BS for Scenarios Required ICA Capital by Risk Financial Risk Reporting Evolution of death rate at age 40 for males from Sweden Evolution of death rate at age 40 for males from England Evolution of death rate at age 40 for males from France Distribution of the present value of the future cash flows SampleofCFTrajectories Probability Density Function of the Present Values MarketValuesbyTimeBuckets Example of a covered layer CDS structuring for longevity ILS Operational Risk Reporting Required Economical Capital Reporting CashFlows Details Example Profitability of three products Example Capital Allocation Process Exampleofanintra-grouprelationship δ Hedging Policyholder shareholder split Development of mathematical reserves LevelPremiumsforLTCcover...215

17 List of Figures xxi 12.5 Relative Mathematical Reserves for LTC cover Distribution of Mathematical Reserves for LTC cover LTC Mathematical reserves when reducing mortality LTC expected losses when reducing mortality Modifiedyieldcurves Cash Flow Pattern of Annuities in Payment Cash Flow Pattern of Deferred Annuities Cash Flow Pattern of Endowment Policies Example of a Risk Radar Supervision Intensity MarketValueMarginfortheSST Solvency II Standard Model Solvency II Partial Internal Model Generic Governance Process Allocation of Responsibilities