mitchell wallaceraa hurricane risk - final f.pdf

8/12/2019 Mitchell WallaceRAA Hurricane Risk - final f.pdf

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Hurricane Risk: A

Reinsurer's Perspective

Kirsten Mitchell-Wallace, PhD


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1 Introduction

2 Hurricane Sandy

3 Deductibles and political risk

4 Rates and Clustering

6 An example of using hurricane footprints

7 From model to real world

8 Conclusions


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We have a choice of options

(bnUSD)

Model B

current

outlookModel B long

term

with

SS

w/o

SS

with

SS

w/o

SS

AAL 16.86 15.21 14.27 12.92SD 36.63 34.43 32.80 30.83

(bn USD)Model C

current

outlookPCS

with SS with SS

AAL 13.15 11.60SD 28.25 20.04

(bn

USD)

Model A

current

outlookModel A long

term

with

SS

w/o

SS

with

SS

w/o

SSAAL 21.92 18.50 15.46 13.12SD 44.02 39.06 34.90 31.17


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But we need our own view of risk

Follows from Article 126, External models and data

The use of a model or data obtained from a third party shall not be considered justification for

exemption from any of the requirements for the internal model set out in articles 120 to 125

The view of the risk embedded in the cat model shall be understood and validated internally

The models are getting ever more complicated

can you really have your own view without

building your own model?

Model methodology/characteristics, flat behaviour,

industry behaviour, portfolio behavior


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6

NAHU Model Output Comparison

Model A vs. Model BOEP curves for North-East

Implications of Model Change on IED Basis: OEP Curve

Above 20y RP: Model A < Model B Below 20y RP: Model A > Model B

This effect has its origin in the landfall rates,not in the storm surge component

(B-A)/A

(A-B)/B


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1 Introduction

2 Hurricane Sandy




7 Conclusions


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Cedant losses by cause of loss


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Keep in mind that there is a lot of scatter


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Damage ratio by construction type


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Damage ratio by age range shows patterns


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Damage ratio distribution differs for high and low windspeeds

0%

5%

10%

15%

20%

25%

30%

35%

40%

0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0% 4.5% 5.0%

ProportionofCla

ims

Damage Ratio

Distribution of Claims in Damage Ratio Bands for differentWindspeeds

50-60

60-70

70-80

80-90

90-100


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Auto Physical Damage

APD data often notincluded in modellingsubmissions

Underwriters always

check directly withbrokers

Sandy a case in point


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Loss adjustment expenses vary by location and by cause of loss


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1 Introduction

2 Hurricane Sandy





8 Conclusions


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for the industry

As expected, different behaviour bygeographical regionrelated to hazard


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1 Introduction

2 Hurricane Sandy





8 Conclusions


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Or in more detail

0

0.5

1

1.5

2

2.5

3

Texas Gulf xTX Florida Georgia,

North

Carolina

and South

Carolina

Coastline

from

Virginia to

Maine

All U.S.

Rates

Comparison of LF Rates for all HU Categories

v9 MTR

v11 MTR

v13 MTR

v11 LTR

EQECAT

HURDAT - NOAA

Model 1 (C)

Model 2 (C)

Model 3 (C)

Model 4

Model 5


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Can compare proportions too

Model


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Landfall history

US hurricane landfalls peaked in years 1916, 1985 and 2004.

In the recent years since 2000 there is obvious clustering. Two years with unusually high number oflandfalls and six years without any hurricane-strength landfalls have occured.


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Some definitions

The presence of clustering can be formally assessed by calculating the ratio of variance over meanin a given timeseries of count data:

=2

The ratio is called index of dispersion.

= 0: constant random variable

0 < < 1: under-dispersed variable

= 1: equi-dispersed variable

> 1: over-dispersed (i.e. clustered) variable

The classic averaging period to define climate characteristics is 30 years. The dispersionparameter of hurricane landfalls for the last 30 years is 1.7, which indicates over-dispersion.

We investigate the magnitude and statistical significance of the dispersion parameter for variousaveraging periods.


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Clustering considering different time windows

The following plots show the dispersion parameter of the time-series of hurricane landfalls for allpossible combinations of starting years and time-series lengths.

Both plots are the same. Black color on the right hand side plot indicates significant over-dispersionat the 95% level of significance.


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Discussion

Significant over-dispersion is observed for averaging periods of 50 years or less, when the latestdecade is included.

Individual years with high activity have a strong influence on the result: The averaging periods thatinclude the peak years 1916, 1985 and 2004 have markedly larger dispersion parameter than theperiod between 1937 and 1965, where no such peaks occurred.


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Relationship with NAO

Elsner et al (2000) suggest a link between hurricane track and NAO.

An excited (relaxed) NAO is associated with higher (lower) latitude recurving (nonrecurving)storms.

Periods of under-dispersion coincide with positive NAO conditions and vice-versa.


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Presence in cat models

Model vendors have investigated hurricane clustering. Variation of clustering properties in different

parts of the North Atlantic has also been taken into account. Comparing the overall US landfall rates from two vendor models to a Poisson distribution (equi-

dispersed assumption), there is no significant departure from equi-dispersion:

Clustering may still be present in Cat Model 1 in subsets of hurricane events in certain parts of theUS.

Clustering properties in the Cat Model 1 have been estimated from data from the 1950-2008 period.

Possible changes in the dispersion properties with time have not been considered.


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1 Introduction

2 Hurricane Sandy





8 Conclusions


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Model footprints: database

Complete set of footprints for HURDAT losses

Not entirely easy to reconcile to HURDAT list, especially for older storms

Other modelling vendors estimates

Pielke and HURDAT loss estimates

Aggregatemodel/Agg

regatePCS


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El Nio and hurricane (in)activity

El Nio has a strong impact on hurricane activity (Gray, 1984).

During El Nio years, increased convection associated with strong rainfall is observed in theEaster Pacific.

The Caribbean, being in the outflow of this convection, experiences stronger than usualWesterly upper level winds.

Increased wind shear in turn inhibits the development of hurricanes.

Conversely, more hurricane activity is observed during La Nia years.

Pielke and Landsea (1999, hereafter PL99) linked El Nio directly to economic losses.

Are El Nio conditions reflected in modeled losses?


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Reproducing publication using modelled footprints

Comparison between PL99 and losses estimated using a cat model PL99 refers to 1997 values. Model data have been adjusted accordingly.

PL99 refers to economic losses. As a first approximation, model insured losses have been scaled bya factor of 2 to make them comparable to economic losses.

Data limited to the 1925-1997 period (which is covered by PL99)

PL99 and the model estimates have some similarities

As expected, median losses increase as we move from El Nio to La Nia.

Mean losses are maximum for neutral conditions. This reflects the fact that the standarddeviation for neutral conditions is much larger.

and some differences: median losses in the model are much lower than economic losses.

median mean standard

deviation

PL99 model PL99 model PL99 model

La Nia 3.3 0.7 5.9 4.0 7.0 7.0

Neutral 0.9 0.2 7.0 6.0 15.9 18.0

El Nio 0.2 0.02 2.0 2.0 4.3 5.9


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We see the same

The discrimination between El Nio and La Nia conditions present in the economic losses is alsoseen in the modeled losses.

La Nia Neutral

PL99 model PL99 model

Neutral 94% 86%

El Nio >=99% 98% 81% 71%

Table: Level of confidence of two-sampled t-tests testing the difference inthe mean values of log-losses for different El Nino conditions


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Loss frequency

La Nia/neutral years also have a higher loss frequency compared to El Nio years.

La Nia (22 years) Neutral (29 years) El Nio (22 years)

PL99 model PL99 model PL99 model

> 1 billion 17 15 14 16 7 5

> 5 billion 8 10 8 9 3 3

> 10 billion 4 5 6 8 3 3


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Significance

Differences in PL99 losses for various El Nio conditions become weaker as we go to higher lossthresholds.

Patterns in behaviour of model differences less clear

Unlike PL99, there is no significant contrast between La Nia and El Nio in the model estimates.

La Nia Neutral

PL99 model PL99 model

Neutral

> 1 billion 96% 89%

> 5 billion 48% 97%

> 10 billion 22% 91%

El Nio

> 1 billion >99% 37% 74% 73%

> 5 billion 90% 63% 74% 90%

> 10 billion 27% 38% 48% 93%

Table: Level of confidence of two-sampled t-tests testing the difference in the mean

values of log-losses for different El Nino conditions


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What have we learned?

La Nia years have more hurricane activity than El Nio years. This isreflected in the frequency and severity of losses.

This result persists if different time periods are used

This can also be seen using the PCS losses

The effect is also seen is model footprints are used

A clear decrease in loss frequency is seen for La Nia years also if weconsider higher thresholds only.


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1 Introduction

2 Hurricane Sandy





8 Conclusions


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From modelling to real world

Hard vs soft factors?

ALAE Exposure growth Multi-model factorshow and

where?

Cedant specificities e.g. notwell-modelled Pool participations Comparison with loss history

vailidity? Data for adjustmentson specific cedants

Underwriting judgement?

Compare range of loadings withwhat we believe about models

Min to Max Loading


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Client quality - which criteria should we measure?

Criterion 3

Criterion 5

Criterion 6

Criterion 2

Criterion 4Criterion 5

Criterion 7

Criterion 1

Business PlanViability and

Strategic

Direction

e.g. managementstrength, buyingphilosophy


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Comments on CQI

It is possible to score clients objectively

Measuring leads to clarity and repositioning

There is more to our decision making than modeling

It matters what information the broker provides us with

The strategic direction of our clients, and their business execution, are importantdecision drivers for SCOR

Capacity is prioritised to core clients but there are always opportunistic/diversificationplays

Terms and Conditions are considered


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1 Introduction

2 Hurricane Sandy





8 Conclusions


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Conclusions

Model evaluation is hard (through a glass, darkly)

Model comparison and understanding is an essential component

Other sources are critical to supplement our view, e.g.

Claims

HURDAT

Science

We need to differentiate between model generalities (research) and cedantspecificities (underwriting)

Working closely with underwriters is essential

Finally, modelling our best view of risk must be integrated into our riskmanagement and underwriting framework


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With special thanks to

Ronny Abplanalp

Jacky Andrich

Iakovos Barmpadimos, PhD

Markus Gut, PhD

Thomas Linford

SCOR Global P&C Guide toHurricanes:http://www.scor.com/images/stories/pdf/

library/newsletter/pc_nl_hurricanes_en.PDF

mitchell wallaceraa hurricane risk - final f.pdf

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