Natural Catastrophe Risk and the Changing Environment: Overview and Challenges Shree Khare, Senior...

Natural Catastrophe Risk and the Changing Environment: Overview and Challenges

Shree Khare, Senior Catastrophe Risk Modeller, RMS Ltd., London

2Confidential

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

3Confidential

Introduction to RMS

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

“ 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

4Confidential

Top 10 Insured Cat Losses, 1990-2005

* Includes liability losses

CountryEventYearInsured Loss ($billions)

Indonesia, Thailand

U.S., Bahamas

France, Switzerland

France, U.K.

Japan

U.S., Caribbean

U.S., Caribbean

U.S.

U.S., Bahamas

U.S.

Earthquake & Tsunami

Hurricane Wilma

Winterstorm Lothar

Winterstorm Daria

Typhoon Mireille

Hurricane Charley

Hurricane Ivan

Northridge Earthquake

Hurricane Andrew

Terrorist Attack on WTC

2004

2005

1999

1990

1991

2004

2004

1994

1992

2001

5.0

6.5

6.6

7.8

8.0

11.0

17.8

21.5

31.7*

U.S.Hurricane Katrina200545.0

6.0-6.8

Swiss Re Sigma 2/2006; Triple I 1/2006

5Confidential

Framework: Event Based Modelling

Assess WindSpeed

- Peak gusts experienced at each location

Calculate Damage

- Varies by structure type

Define Hurricane

-Track-intensity

Quantify FinancialLoss

- Apply policy termsand Reinsurance

structures

90%

$ Loss$ Loss

Apply property exposure

Using physical and statistical modelling - simulate events in time and quantify financial loss for each event

Model components are consistent with observed data

6Confidential


Assess WindSpeed


Calculate Damage


Define Hurricane

-Track-intensity



structures

90%

$ Loss$ Loss


Simulation of hundreds of thousands of years can be used to quantify modelled probabilities of financial loss

7Confidential


Assess WindSpeed


Calculate Damage


Define Hurricane

-Track-intensity



structures

90%

$ Loss$ Loss


Model output is used to inform Enterprise Risk Management: Rate setting, capital allocation, securities …

8Confidential

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

9Confidential

Need to quantify expected number of landalling hurricanes: models are validated using historical data

Data source: NOAA NHC HURDAT “Best Track” 1950-2005: 597 time series for named North Atlantic TCs

Modelling Hurricane Rates

10Confidential

Insurance/Re-insurance industry typically interested in 5-year projections

Data source: NOAA NHC HURDAT “Best Track” 1950-2005: 597 time series for named North Atlantic TCs


11Confidential


Cat 1-5 Storms

Blue Basin NumbersRed 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)

12Confidential

Modelling Hurricane Tracks

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).

Evaluation criterion: historical TCs should be statistically indistinguishable from equal-sized samples of synthetic TC set.

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).

HISTORICAL (1950-2005) SYNTHETIC (1000 YRS)

13Confidential

Long-Term Risk Management: Climate Change

14Confidential

Long-Term Risk Management: Climate Change

‘Natural’ forcing can not explain 20th century warming

15Confidential

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 …)

16Confidential

Model Development Example: Hurricane Winds

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 …

17Confidential

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

Model Development Example: Hurricane Winds

18Confidential

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)

19Confidential

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

20Confidential


Space/time scales of turbulent motions can be extremely small, hence difficult to model

Attempt to model larger scale flow by ‘Reynolds Averaging’

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21Confidential


The (approximate) momentum equations (in translating system)

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22Confidential


PBL (Chow, Vickery, Cardone, FHLC): Vertical mean – friction parameterization

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23Confidential


For Gradient Wind let H ∞, and look at the steady state solution, which is the root (with the proper limiting property) of:

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24Confidential

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

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25Confidential

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

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26Confidential

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 …

27Confidential

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 …

28Confidential

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?

29Confidential

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

30Confidential

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

31Confidential

QUESTIONS?

Natural Catastrophe Risk and the Changing Environment: Overview and Challenges Shree Khare, Senior...

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