The Management of Losses Arising from Extreme Events GIRO 2002 D E A Sanders (Chair) Anders Brix Paul Duffy Will Forster Tony Hartington Gavin Jones Charles Levi Paddy Paddam Dimitris Papachristou Geoff Perry Stephen Rix Fiona Ross Andy J Smith Anup Seth David Westcott Mark Wilkinson Contents 1. Introduction 2. Extreme Events 2.1 Weather Related Events 2.2 Geological Events 2.3 Man Made Events 3. Extreme Value Theory 3.1 Overview 3.2 Introduction 3.3 Extreme Value Distributions 3.4 Example and Application 4. Catastrophe Models 4.1 Structure of Catastrophe Models 4.2 Overview of Existing Models 4.3 Use Of Catastrophe Models In Direct Pricing 4.4 Advantages/disadvantages of cat models 4.5 Use of cat models in practice 5. Management and Control of Extreme Events 5.1 Before the event 5.2 Multi disciplinary underwriting groups 5.3 Underwriting Authorities 5.4 Realistic Disaster Scenarios (RDS) 5.5 After the Event 6 Coherent risk measures 7 Conclusions Appendix 1 Recent United States Extreme Weather Events Appendix 2 British Weather Extremes Appendix 3 Hurricanes Appendix 4 Tornadoes Appendix 5 European Windstorm Appendix 6 US Floods Appendix 7 UK Floods Appendix 8 El Niño Appendix 9 Earthquake Appendix 10 Tsunami Appendix 11 Volcanoes Appendix 12 Meteorite Collision Appendix 13 Man Made Events Explosion Aviation Oil Energy Marine Appendix 14 Review of EVT Literature Appendix 15 Example Underwriting Authorities Appendix 16 Realistic Disaster Scenarios Appendix 17 Extreme Value Data Appendix 18 Actuarial Governance 1. Introduction 1.1 This paper explores extreme events and their impact on the insurance market. There are 5 basic sections The first of these relates to a description of the types of events that we need to consider. The appendices give fuller details and data relating to the risks. These form an historic perceptive of the issues. This is followed by an explanation of Extreme Value Theory. Accompanying this paper is an Excel spreadsheet with worked examples. The next section deals with the various cat models that are used in the market. At the end of this section we consider the differences between the bottom up approach from cat modeling and compare with EVT as a top down approach. Finally we deal with the management of extreme events and look at realistic disaster scenarios and consider risk measures. 1.2 We conclude with a section that brings all these issues together. If the world’s to globalise then the final conclusion is that the growth of mega cities and mega risks combined with a limited number of ultimate risk takers will mean that there is insufficient world wide insurance capacity to deal with many of the realistic loss scenarios, and that matters will not improve as the process continues. The main alternative is to rely on the wealth of the financial sector to absorb these losses which are minimal compared with daily fluctuations in asset values. 2 Extreme Events 2.1 Weather Related Events Is it as bad as it can get? 2.1.1 We all complain about the weather and the fact that it is getting wetter, warmer, colder and so on. Summers in our youth were always better than those of today. We have great difficulty in predicting weather – in fact a good predictor for tomorrows weather is that it is the same as today’s! 2.1.2 We appreciate that the Earth’s weather is a hugely complex system, with multiple interacting elements. Because they defy simple expression, meteorologists rely on a “bottom up” approach to modeling the climate. They divide the world into boxes, model the forces on the atmosphere and oceans in each box, and then guess the overall effect. This is the approach used in Cat modeling. However to make the approach work you often need to include a number of “fudge factors” to make the models fit with known events. 2.1.3 Alternatively we have the top down approach. The entity that drives the complex system is the Sun. Solar energy warms the Earth, and it does so disproportionately, heating the tropics much more than the poles. This creates a temperature gradient with the effect that heat goes from low to high latitudes and drives the climate. 2.1.4 This heat flow from the tropics to the poles reflects the second law of thermodynamics, which states that heat flows from warm to cold regions and never the other way round. This heat flow produces mechanical work in the atmosphere and oceans. The dynamical system is lifting water to drop as rain or snow, whipping up waves and blowing sand into dunes. One critical element is that the second law of thermodynamics gives no indication of the speed that the process takes place. 2.1.5 We know that if the process is fast then temperature throughout the world would be the same, and if it were slow then Northern Europe would be in an ice age. The reality is somewhere in between. 2.1.6 Garth Paltridge, an Australian climatologist now at the University of Tasmania, experimented with a model of the Earth divided into latitude zones with different amounts of sunlight and cloud cover. One of the free parameters of his model was the heat flow between the zones. Paltridge found that if he set this factor so it maximised the production of the thermodynamic quantity called entropy, the results modeled Earth’s climate well. Entropy production is a measure of the generation of disorder, and it is closely related to a system’s capacity for mechanical work. Both quantities peak at about the same heat flow. The same theory has been tested and appears to work on the moons of Jupiter. 2.1.7 Most orthodox meteorologists dismiss the result as an uninteresting fluke. There’s no reason why the climate should maximize entropy, or the work done. However, if it is not a fluke then we can see that the earth’s dynamical weather system has limits on the extreme events. This top down approach is equivalent to an Extreme Value approach to weather events, whereas the bottom up approach is equivalent to Cat Modeling. The theory is being tested on other bodies in the solar system with positive conclusions. 2.1.8 In the appendices we set out a number of weather events that give rise to large insurance claims. These include Hurricanes, Tornadoes and Floods. If the historic hurricanes were repeated today, then the largest one would potentially give rise to a loss of $90 billion. In the 1980’s the industry was concerned with two $6billion hurricanes hitting in one year. 2.1.10 Europe has been hit by storms – the recent European storms in France have been estimated from Cat models as being “as bad as it can get”. However we often fail to recognise that the losses may arise from other sources. It has been estimated that the Floods following the 1947 winter, if repeated, would give losses twice as high as Storm 90A at about $4bn. 2.1.11 Finally we need to consider the impact of climate change, and the two key weather driver, the Southern Ocean Oscillation (and EL Nino) and the North Atlantic Oscillation. 2.1.12 All of these events are all summarised in the various appendices. 2.2 Geological events Uncertainty v Predictability 2.2.1 Geological events differ from weather events. We know that earthquakes occur at tectonic boundaries, we know where volcanoes are and earthquake Tsunami tend to impact on coasts. However meteorite or comet collisions can occur anywhere. 2.2.2 What has proven to be more difficult is to determine when an event is likely to occur with sufficient time to minimise loss. 2.2.3 Prediction in respect of volcanoes has improved considerably in recent years. The factor appears to be long period events or resonance in magna discovered by seismologist Bernard Chouet from the US Geological Survey in Menlo Park. Using these techniques, on 16 December 2000, a warning was issued that the Popocatepetl volcano in Mexico would explode in exactly two days’ time. On 18 December, Popocatepetl unleashed its largest eruption for a thousand years. 2.2.4 The approach, however, gives no indication of the size of the eruption. With Earthquakes, there is no predictive formula. The predictive Parkfield quake, which is supposed to occur regularly every 20 years, is now well overdue. Chouets Volcano Predictions – (New Scientist 12 January 2002) 2.2.5 Most theories regarding earthquake predictability are controversial, found wanting and untested. A recent method has come from geophysicist Didier Sornette, who claims that there is a subtle underlying signal, common to many catastrophes, that can sound the alarm before it’s too late. Sornette, in analyzing the rupture of materials such as concrete, has modelled the breakdown as a network of growing and interacting microcracks that finally result in rupture. Sornette found that the rate at which these growing cracks released energy was correlated with the time left before the material suffered catastrophic failure. In other words, the cracks-even the seemingly insignificant ones-give you a countdown to disaster. The pattern is a little trill appearing at intervals in the recording, a bit like the chorus in a song that grows higher and higher, with ever smaller gaps between repeats, until suddenly the material breaks. This is similar to the volcanic analysis, and should be in the seismic data, 2.2.6 The most dangerous geological event is the meteorite/comet collision. It has been shown that, on average, 3,900 people die each year as a result of meteorite collision (See Appendix 13).