Kirsten Mitchell-Wallace, PhD is EMEA Regional Head of Catastrophe Management at SCOR, Zürich, Switzerland Matthew Jones, PhD is Director at Cat Risk Intelligence, UK John Hillier, PhD is Senior Lecturer in Physical Geography at Loughborough University, Loughborough, UK Matthew Foote is Group Head of Exposure Management at Argo Group International Holdings, London, UK

• List of Contributors and Acknowledgements xiiiForeword xxv1 Fundamentals 1Matthew Jones, Kirsten Mitchell-Wallace, Matthew Foote, and John Hillier1.1 Overview 11.1.1 What Is Included 11.1.2 What Is Not Included 11.1.3 Why Read This Chapter? 11.2 Catastrophes, Risk Management and Insurance 21.3 What Are Catastrophe Models? 51.4 Why Do We Need Catastrophe Models? 61.5 History of Catastrophe Models 71.6 Who Provides and Uses Catastrophe Models? 101.7 What Are Catastrophe Models Used For? 111.8 Anatomy of a Catastrophe Model 121.8.1 Hazard 131.8.2 Vulnerability 141.8.3 Exposure 151.8.4 Loss and Financial Perspectives 151.8.5 Platform 171.9 Model Input 191.9.1 Exposure 201.9.2 Financial Structure 241.9.3 Portfolio Hierarchy 251.10 Model Output: Metrics and Risk Measures 261.10.1 Common Metrics 261.10.2 Exceedance probability curve characteristics 271.10.3 More Advanced Metrics 291.10.4 Event Loss Tables and Year Loss Tables 291.10.5 Event Loss Table (ELT) 291.10.6 Year Loss Table (YLT) 361.11 Statistical Basics for Catastrophe Modelling 381.11.1 Discrete Distributions 401.11.2 Continuous Distributions 421.11.3 Coherent Risk Measures 44Notes 44References 452 Applications of Catastrophe Modelling 47Kirsten Mitchell-Wallace2.1 Overview 472.1.1 What Is Included 482.1.2 What Is Not Included 482.1.3 Why Read This Chapter? 482.2 Introduction 482.3 Risk Transfer, the Structure of the (Re)insurance Industry and Catastrophe Modelling 492.4 Insurance and Reinsurance 522.4.1 What Is Insurance? 522.4.2 What Is Reinsurance? 532.5 Catastrophe Risk Management and Catastrophe Modelling 60Kirsten Mitchell-Wallace and Matthew Foote2.5.1 What Are Catastrophe Risk Management and Exposure Management? 602.5.2 Catastrophe Risk Management Metrics 612.5.3 Catastrophe Risk Management Data 622.5.4 Exposure Data 632.5.5 Common Tools Used in Catastrophe Risk Management 702.6 Underwriting and Pricing 70Kirsten Mitchell-Wallace and Matthew Jones2.6.1 What Is Underwriting? 702.6.2 What Is Pricing? 732.6.3 Practicalities of Using Catastrophe Model Output for Pricing 812.6.4 Pricing Specifics for Insurance and Reinsurance 832.7 Accumulation, Roll-Up and Capacity Monitoring 97Claire Crerar and Kirsten Mitchell-Wallace2.7.1 What Is Accumulation? 972.7.2 Use in Underwriting and Risk Management 1012.7.3 Practicalities of Accumulation 1042.8 Portfolio Management and Optimization 105Kirsten Mitchell-Wallace and Guillermo Franco2.8.1 What Is Portfolio Management? 1052.8.2 What Is Portfolio Optimization? 1072.8.3 Using Catastrophe Models in Optimization 1082.8.4 Optimization Methods 1092.9 Event Response and Integration with Claims Team 111Kirsten Mitchell-Wallace2.9.1 Early Estimation of Claims 1112.9.2 Claims Stresses and Inflation 1142.9.3 Lessons Learnt Analysis 1152.10 Capital Modelling, Management and Dynamic Financial Analysis 116Junaid Seria2.10.1 Risk Appetite and Risk Tolerance 1162.10.2 Why Capital Models? 1172.10.3 What Is a Capital Model? 1182.10.4 The Structure of Capital Models 1182.10.5 Capital Models and Catastrophe Models 1202.10.6 What is Dynamic Financial Analysis (DFA)? 1202.11 Regulation and Best Practice in Catastrophe Modelling 121Junaid Seria, Claire Souch, and Paul Nunn2.11.1 The Evolution of Catastrophe Modelling as a Profession and Best Practice 1212.11.2 Rating Agencies 1252.11.3 Regulation and Catastrophe Modelling 1262.11.4 Case Study: Catastrophe Models and Solvency Regulation, Solvency II 1282.11.5 Case Study: Regulation of Catastrophe Models for Ratemaking 1352.12 Case Study: Catastrophe Modelling for Reinsurance and Retrocession Purchase 137Juan England2.12.1 Introduction 1372.12.2 Determining the Total Limit Required 1382.12.3 Layering of a CAT XL Programme 1402.12.4 Price 1402.12.5 Cost Allocation 1412.12.6 Conclusion 1412.13 Government Schemes and Insurance 142Matthew Eagle2.13.1 Introduction 1422.13.2 Government Schemes with Standalone Products Managed by a Central Organization 1442.13.3 Government Schemes Where Catastrophe Cover Is Provided as an Add-on to Fire 1442.13.4 Government-Backed Reinsurance/Pooling Schemes 1442.13.5 Private Insurance Company Pools Supported by Government Legislation 1442.13.6 Case Study: UK Flood Re 1522.14 Catastrophe Models and Applications in the Public Sector 154Rashmin Gunasekera2.14.1 Introduction 1542.14.2 Public Sector Catastrophe Models 1542.14.3 Applications of Public Sector Catastrophe Models 1552.14.4 Case Study: Country Disaster Risk Profiles (CDRP) 1562.15 Insurance Linked Securities 158Arnab Chakrabati2.15.1 What Are Insurance Linked Securities? 1582.15.2 From Insurance to Reinsurance to ILS 1592.15.3 Common ILS Instruments 1602.15.4 Preliminaries of ILS Instrument: Measurement and Layering of Losses 1602.15.5 Pricing an ILS Contract 1622.15.6 Pricing Cat Bonds with the Thin Layer Model 1632.15.7 Growth of the Market for ILS 1642.15.8 Conclusion 1662.16 Effective use of Catastrophe Models 167Ian Cook, Matthew Jones, Adam Podlaha, and Kirsten Mitchell-Wallace2.16.1 Treatment of Uncertainty in Catastrophe Models 1672.16.2 Importance of Framework: A Tool, Not an Answer 179Notes 181References 1813 The Perils in Brief 187John Hillier3.1 Overview 1873.1.1 What Is Included 1873.1.2 What Is Not Included 1913.1.3 Why Read This Chapter? 1913.X Structure of the Sections 1923.X.1 What Is the Peril? 1923.X.2 Damage Caused by the Peril 1923.X.3 Forecasting Ability and Mitigation 1923.X.4 Representation in Industry Catastrophe Models 1933.X.5 Secondary Perils and Non-Modelled Items 1933.X.6 Key Past Events 1933.X.7 Open Questions/Current Hot Topics/Questions to Ask Your Vendor 1933.X.8 Non-Proprietary Data Sources 193METEOROLOGICAL PERILS (I.E. ‘WIND-DRIVEN’) 1943.2 Tropical Cyclones 194James Done and Brian Owens3.2.1 What Is the Peril? 1943.2.2 Damage Caused by the Peril 1983.2.3 Forecasting Ability and Mitigation 1983.2.4 Representation in Industry Catastrophe Models 1993.2.5 Secondary Perils and Non-Modelled Items 2003.2.6 Key Past Events 2003.2.7 Open Questions/Current Hot Topics/Questions to Ask Your Vendor 2013.2.8 Nonproprietary Data Sources 202Acknowledgements 2023.3 Extra-Tropical Cyclones 202Len Shaffrey and Richard Dixon3.3.1 What Is the Peril? 2023.3.2 Damage Caused by the Peril 2053.3.3 Forecasting Ability and Mitigation 2063.3.4 Representation in Industry Catastrophe Models 2063.3.5 Secondary Perils and Non-Modelled Items 2073.3.6 Key Past Events 2073.3.7 Open Questions/Current Hot Topics/Questions to Ask Your Vendor 2083.3.8 Nonproprietary Data Sources 2093.4 Severe Convective Storms 209Michael Kunz and Peter Geissbuehler3.4.1 What Is the Peril? 2093.4.2 Damaged Caused by the Peril 2133.4.3 Forecasting Ability and Mitigation 2143.4.4 Representation in Industry Catastrophe Models 2153.4.5 Secondary Perils and Non-modelled Items 2163.4.6 Key Past Events 2163.4.7 Open Questions/Current Hot Topics/Questions to Ask Your Vendor 2163.4.8 Nonproprietary Data Sources 217HYDROLOGICAL PERILS (I.E. ‘RAIN-DRIVEN’) 2183.5 Inland Flooding 218Jane Toothill and Rob Lamb3.5.1 What Is the Peril? 2183.5.2 Damage Caused by the Peril 2213.5.3 Forecasting Ability and Mitigation 2213.5.4 Representation in Industry Catastrophe Models 2233.5.5 Secondary Perils and Non-Modelled Items 2283.5.6 Key Past Events 2283.5.7 Open Questions/Current Hot Topics/Questions to Ask Your Vendor 2293.5.8 Nonproprietary Data Sources 229Acknowledgements 2303.6 Shrink-Swell Subsidence 230John Hillier3.6.1 What Is the Peril? 2303.6.2 Damage Caused Caused by the Peril 2313.6.3 Forecasting Ability and and Mitigation 2313.6.4 Representation in Industry Catastrophe Models 2323.6.5 Key Past Events 2323.7 Earthquakes 232Joanna Faure Walker and Guillaume Pousse3.7.1 What Is the Peril? 2323.7.2 Damage Caused by the Peril 2373.7.3 Forecasting Ability and Mitigation 2393.7.4 Representation in Industry Catastrophe Models 2403.7.5 Secondary Perils and Non-Modelled Items 2423.7.6 Key Past Events 2433.7.7 Open Questions/Current Hot Topics/Questions to Ask Your Vendor 2433.7.8 Nonproprietary Data Sources 2443.8 Mass Movement 245Tom Dijkstra, Craig Verdon, and John Hillier3.8.1 What Is the Peril? 2453.8.2 Damage Caused by the Peril 2463.8.3 Forecasting Ability and Mitigation 2463.8.4 Representation in Industry Catastrophe Models 2473.8.5 Secondary Perils and Non-Modelled Items 2473.8.6 Key Past Events 2483.8.7 Open Questions/Current Hot Topics/Questions to Ask Your Vendor 2493.8.8 Nonproprietary Data Sources 2493.9 Tsunami 250Anawat Suppasri and Yo Fukutani3.9.1 What Is the Peril 2503.9.2 Damaged Caused by the Peril 2513.9.3 Forecasting Ability and Mitigation 2523.9.4 Representation in Industry Catastrophe Models 2523.9.5 Secondary Perils and Non-Modelled Items 2523.9.6 Key Past Events 2533.9.7 Open Questions/Current Hot Topics/Questions to Ask Your Vendor 2533.9.8 Nonproprietary Data Sources 2533.10 Volcanoes 254Sue Loughlin, Rashmin Gunasekera, and John Hillier3.10.1 What Is the Peril? 2543.10.2 Damage Caused by the Peril 2563.10.3 Forecasting Ability and Mitigation 2563.10.4 Representation in Catastrophe Models 2573.10.5 Secondary Perils and Non-Modelled Items 2573.10.6 Key Past Events 2573.10.7 Open Questions/Current Hot Topics/Questions to Ask Your Vendor 2583.10.8 Non-Proprietary Data Sources 258References 2584 Building Catastrophe Models 297Matthew Foote, Kirsten Mitchell-Wallace, Matthew Jones, and John Hillier4.1 Overview 2974.1.1 What Is Included 2974.1.2 What Is Not Included 2984.1.3 Why Read This Chapter? 2984.2 Introduction 2984.3 Hazard 3014.3.1 Deterministic Versus Probabilistic Hazard Models 3024.3.2 Representing the Hazard Severity 3074.3.3 Understanding the Historical Hazard 3084.3.4 Deterministic Hazard Models: Historical Reconstructions 3154.3.5 Site-Based Extrapolation: A Local Solution 3164.3.6 Building a Probabilistic Event-Set 3194.3.7 Secondary or Consequent Perils 3314.3.8 Time-Dependent Hazard Modelling and Clustering of Catastrophe Events 3334.4 Exposure Models and Databases 3344.4.1 Economic or Insured Exposure Data? 3364.4.2 Economic and Insurance Industry Exposure Database Development Approaches 3374.4.3 Bottom-Up Industry Exposure Database Development 3394.5 Vulnerability 3414.5.1 Vulnerability Function Development 3434.5.2 Empirical Vulnerability Approaches 3484.5.3 Analytical Vulnerability Approaches 3554.5.4 Use of Design Codes in Vulnerability Function Development 3574.5.5 Using Buildings Damage to Determine Other (Non-Structural) Types of Loss 3624.5.6 Vulnerabilities for Non-Standard Exposures 3634.5.7 Validating Vulnerability Models 3654.6 Integrating Model Components and the Geographical Framework 3674.6.1 Relative Spatial Resolution/Nominal Scale of Source Data 3674.6.2 Geodetic and Coordinate Bases of Data Sources 3684.6.3 Relative Vintage of Source Data 3684.6.4 Point Representation Versus Cell, Area Geographies 3684.6.5 Data Generalization, Interpolation and Smoothing 3694.7 The Financial Model 3694.7.1 Why We Need a Financial Model 3694.7.2 Uncertainty 3714.7.3 Case Study: Combining Distributions: Convolution 3734.7.4 Applying Financial Structures 3774.7.5 Case Study: Back-Allocation 3784.7.6 Financial Model Output 3784.8 Model Validation 3794.9 Conclusion 381Note 381References 3815 Developing a View of Risk 389Matthew Jones5.1 Overview 3895.1.1 What Is Included 3895.1.2 What Is Not Included 3895.1.3 Why Read This Chapter? 3895.2 Introduction 3905.2.1 Why Develop a View of Risk? 3905.2.2 What Developing a View of Risk Involves 3925.2.3 Practical Considerations in a Resource-Constrained World 3925.2.4 Insurance Versus Reinsurance 3935.3 Governance and Model Change Management 3945.3.1 Governance 3945.3.2 The View of the Risk Process 3955.3.3 Prioritization 3965.3.4 Vendor Selection and High-Level Model Evaluation 3975.3.5 Detailed Model Evaluation 3975.3.6 Non-Modelled Peril Evaluation 3985.3.7 Sign-off 3995.3.8 Implementation 3995.3.9 Review Triggers and Frequency 4005.3.10 Other Governance Aspects 4005.4 How to Develop a View of Risk 4015.4.1 Understanding What Is in the Model 4015.4.2 Analysing Model Output (Including Sensitivity Testing) 4055.4.3 Actual Versus Modelled, Comparing to Own Company Experience 4195.4.4 Comparing Multiple Models 4275.4.5 Using Industry Data 4295.4.6 Considering the Time Period of Risk 4345.4.7 Understanding What Is Not in the Model: Non-Modelled Risk 4355.5 Implementing a View of Risk 4425.5.1 Different Uses in a Company 4425.5.2 Consistency in an Organization 4435.5.3 Methods of Implementation: Single Model 4435.5.4 Methods of Implementation: Multiple Models 4465.6 Conclusion 452Notes 452References 4526 Summary and the Future 455John Hillier, Kirsten Mitchell-Wallace, Matthew Jones, and Matthew Foote6.1 Overview 4556.2 Key Themes in the Book 4556.2.1 Chapter 1 Introduction 4556.2.2 Chapter 2 Applications of Catastrophe Modelling 4566.2.3 Chapter 3 The Perils in Brief 4566.2.4 Chapter 4 Building a Catastrophe Model 4576.2.5 Chapter 5 Developing a View of Risk 4576.3 The Future: Progress, Challenges and Issues 4586.3.1 Future Changes in Climate 458Clare Souch6.3.2 Modelling Dependency between Perils 460Rick Thomas6.3.3 Open Modelling and Open Architectures 461Dicke Whitaker6.3.4 The Role of Modelling in Disaster Risk Financing 463Rashmin Gunasekera6.3.5 Changing Global Demographics and Growing Insurance Penetration 464John HillierReferences 464Glossary 467Index 495

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