Natural Catastrophe Risk and the Changing Environment: Overview and Challenges

1. Natural Catastrophe Risk and the Changing Environment: Overview and Challenges Shree Khare, Senior Catastrophe Risk Modeller, RMS Ltd., London

2. Talk Outline • Focus: Hurricane Risk Modelling • Financial motivation • Catastrophe modelling basics: Event set framework • Components • Climate change • Model development project • Mathematical and scientific challenges  Opportunities for collaboration Confidential

3. Introduction to RMS “ At RMS, our goal is to help clients manage catastrophe risk through the practical application of the most advanced quantitative risk assessment techniques available.” - Hemant Shah, President & CEO • Founded at Stanford University in 1988 • Multi-disciplinary skills: Applied mathematics, statistics, physical sciences and engineering applied to insurance • Solely focused on risk management issues • Independent and objective information source • Global presence in major insurance markets Confidential

4. Top 10 Insured Cat Losses, 1990-2005 Insured Loss ($billions) Year Event Country 45.0 2005 Hurricane Katrina U.S. 31.7* 2001 Terrorist Attack on WTC U.S. 21.5 1992 Hurricane Andrew U.S., Bahamas 17.8 1994 Northridge Earthquake U.S. 11.0 2004 Hurricane Ivan U.S., Caribbean 8.0 2004 Hurricane Charley U.S., Caribbean 7.8 1991 Typhoon Mireille Japan 6.6 1990 Winterstorm Daria France, U.K. 6.5 1999 Winterstorm Lothar France, Switzerland 2005 Hurricane Wilma U.S., Bahamas 6.0-6.8 5.0 2004 Earthquake & Tsunami Indonesia, Thailand * Includes liability losses Swiss Re Sigma 2/2006; Triple I 1/2006 Confidential

5. Framework: Event Based Modelling Apply property exposure $ Loss Assess WindSpeed - Peak gusts experienced at each location Quantify FinancialLoss - Apply policy termsand Reinsurance structures Calculate Damage - Varies by structure type • Define Hurricane • Track • intensity • Using physical and statistical modelling - simulate events in time and quantify financial loss for each event • Model components are consistent with observed data Confidential

6. Framework: Event Based Modelling Apply property exposure $ Loss Assess WindSpeed - Peak gusts experienced at each location Quantify FinancialLoss - Apply policy termsand Reinsurance structures Calculate Damage - Varies by structure type • Define Hurricane • Track • intensity • Simulation of hundreds of thousands of years can be used to quantify modelled probabilities of financial loss Confidential

7. Framework: Event Based Modelling Apply property exposure $ Loss Assess WindSpeed - Peak gusts experienced at each location Quantify FinancialLoss - Apply policy termsand Reinsurance structures Calculate Damage - Varies by structure type • Define Hurricane • Track • intensity • Model output is used to inform Enterprise Risk Management: Rate setting, capital allocation, securities … Confidential

8. Hurricane Risk Model Components • ‘Rates’ (5-year view, long-term projections in a changing climate) • ‘Track modelling’: Trajectories of tropical vortices in space/time • ‘Windfield’ • Surface roughness and topography • Transitioning of tropical  extra-tropical storms • Vulnerability • Exposure • Financial Model • On the horizon: Parametric and model-choice uncertainty Confidential

9. Modelling Hurricane Rates Data source: NOAA NHC HURDAT “Best Track” 1950-2005: 597 time series for named North Atlantic TCs • Need to quantify expected number of landalling hurricanes: models are validated using historical data Confidential

10. Modelling Hurricane Rates Data source: NOAA NHC HURDAT “Best Track” 1950-2005: 597 time series for named North Atlantic TCs • Insurance/Re-insurance industry typically interested in 5-year projections Confidential

11. Modelling Hurricane Rates Cat 1-5 Storms Blue Basin Numbers Red Landfall Numbers HURDAT data Jarvinen et al. (1984) • RMS has built an exhaustive collection of statistical models for predicting this non-stationary time series • Annually, we gather world-leading hurricane experts to give us their recommendations as to which of our models are best for predicting future rates (expert elicitation) Confidential

12. HISTORICAL (1950-2005) SYNTHETIC (1000 YRS) Modelling Hurricane Tracks Evaluation criterion: historical TCs should be statistically indistinguishable from equal-sized samples of synthetic TC set. For most diagnostics in most regions (but not all) the historical TCs fall within the range of values in the synthetic TC set (Hall and Jewson, Tellus, 2007). On most coast regions track model’s landfall predictions “beat” predictions derived solely from local landfall events, based on out-of-sample likelihood analysis (Hall and Jewson, JAM, 2007). Confidential

13. Long-Term Risk Management: Climate Change Confidential

14. Long-Term Risk Management: Climate Change • ‘Natural’ forcing can not explain 20th century warming Confidential

15. Rates and Track Modelling in a Changing Climate • Clients are increasingly interested in quantifying hurricane risk in future climates • Given the changing climate, quantifying future risk is a significant challenge (more later …) Confidential

16. Model Development Example: HurricaneWinds • Natural catastrophe risk models are comprised of components (rates, track, winds, …) • Need to generate millions of simulations • Need to explore efficient methods of generating windfields along the modelled tracks • Given some validation data set, can use cross-validation to perform model selection • Quick overview of hurricane vortex model comparison • Apologies in advance for jargon … Confidential

17. Model Development Example: Hurricane Winds • Goal: To model maximum 1-minute/3-second winds over ocean and land (10 m height with roughness) for a large number of simulated events • Given spatial scales of hurricanes, full 3-dimensional numerical modelling can not feasibly be used to generate the full stochastic set Confidential

18. Wind Modelling Basics • We need some approximations: Steady Pressure Field • Heating source ‘maintains’ a steady pressure gradient on time scales of 6 hours - also ignoring feedbacks, convection, vertical acceleration … • Approximate pressure distribution as radially symmetric: p(r) Confidential

19. Wind Models: PBL + Linear Analytical • Our interest is 10m winds: Consider the atmospheric boundary layer • Surface layer is ‘turbulent’: Ultimately arising from surface friction – has effect of slowing down winds at surface Confidential

20. Wind Models: PBL + Linear Analytical • Space/time scales of turbulent motions can be extremely small, hence difficult to model • Attempt to model larger scale flow by ‘Reynolds Averaging’ Confidential

21. Wind Models: PBL + Linear Analytical • The (approximate) momentum equations (in translating system) Confidential

22. Wind Models: PBL + Linear Analytical • PBL (Chow, Vickery, Cardone, FHLC): Vertical mean – friction parameterization Confidential

23. Wind Models: PBL + Linear Analytical • For Gradient Wind let H  ∞, and look at the steady state solution, which is the root (with the proper limiting property) of: Confidential

24. Linear Analytical Boundary Layer Model • Analytical theory developed in Kepert (2001) for 3-dimensional flow in a translating vortex for a prescribed pressure field • Model has friction, vertical diffusion, ‘slip’ boundary condition at surface Confidential

25. Linear Analytical Boundary Layer Model • Idea: Linearize equations about gradient wind, solve first order equations • Efficient (free) to run, encapsulates physics causing asymmetries • z, Cd and K can be optimized Confidential

26. Model Selection Study Using H*WIND • H*WIND is consists of 10 m, 1-minute mean winds over ocean which summarizes nearly all available data (surface obs, flight level …) • Put together by researchers at Hurricane Research Division of NOAA in Miami • We are the first group to perform such a thorough study … Confidential

27. Mathematical and Scientific Challenges: Collaboration • RMS is in a unique position, serving as an intermediary between academic/government research and the financial industry • Our models involve many components – some of which are developed through collaboration with the wider research community • This involves pure academic research and paid consultancies • Example institutions: LSE, NASA, University of Miami, National Center for Atmospheric Research, Oxford, … • Collaboration often leads to peer-reviewed journal publications • We work with PhD students, University Faculty, US Government Researchers, Post-Docs, … • We are very open to new collaboration … Confidential

28. Extreme Value Theory • EVT is not often used in catastrophe risk modelling • With event based mathematical modelling, spatially correlated extremes are naturally accounted for – a challenge in EVT • Output from cat models may provide a rich ‘data’ set to ‘play’ with • Can EVT be used to gain greater insight into cat model output? • Can EVT be used to build better cat models? Confidential

29. Use of Climate Models in Catastrophe Risk • General circulation models are used by research groups to simulate the evolution of future climates • Climate researchers and catastrophe risk modellers ask related, yet unique questions • It is challenging for catastrophe risk modellers to make best use of climate simulations • How we make best use of climate simulations will involve extensive research and statistical analysis Confidential

30. Model Choice Uncertainty • Catastrophe models are made of components • Components have parameters, which have been estimated using observed data • Financial loss can be sensitive to uncertain parameters – this kind of information will be included in future cat models • Financial loss is also sensitive to choice of model components (track model A vs. track model B) • How do we best quantify model choice sensitivity/uncertainty? • How do we optimally use ensembles of models? • Bayesian model averaging seems inadequate due to ‘double-counting’ (e.g. Hoeting et al., 1999, Statistical Science) • Cat modelling requires a proper statistical framework to answer these questions Confidential

31. QUESTIONS? Confidential