By: Alexander Pui

Dealing with Uncertainty in Catastrophe Modelling

Global Catastrophe Losses (1970 – 2013)

H. Katrina (2005)

Japan/NZ EQ, Thai Floods

(2011)

Northridge EQ (1994)

Source :Swiss Re Economic Consulting and Research

Global Catastrophe Losses (2015)

• Why perform Cat Modelling?

• How do Cat Models work?

• Interpreting Cat Model Output

• Uncertainty in Cat Modelling

Out

line

Outline

Why

per

form

cat

mod

ellin

g?Why perform Cat Modelling?

• Understanding risk exposure

• Direct Pricing

• Structuring and Pricing Reinsurance Programs

• Regulatory Requirements / Dynamic Financial Analysis (DFA)

• Pricing of Alternative Risk Transfer (ART) Mechanisms

How

do C

at M

odel

s wo

rk?

A Tool for Managing Catastrophic Risk

Catastrophe Modelling

(Probabilistic)

Data

Engineering

Financial Structures

Claims Experience

Science

How

do C

at M

odel

s wo

rk?

Key Model Components

Hazard

• Science, Simulation of many events

Vulnerability• How do buildings respond to events?

Financial Loss

• What is the cost given the damage?

Hazard – stochastic simulation of many eventsKe

y M

odel

Com

pone

nts

Simulated Hurricane Tracks Simulated Earthquake Events (Epicenters)

Sources : Franco, G. (2010) “Minimization of Trigger Error in Cat-in-a-Box Parametric Earthquake Catastrophe Bonds with an Application to Costa Rica” Earthquake Spectra, AIR

Vulnerability: response of a building to hazardKe

y M

odel

Com

pone

nts

Source: Latchman S, Quantifying the Risk of Natural Catastrophes (http://understandinguncertainty.org/node/622)

Vulnerability: Variation in building responseKe

y M

odel

Com

pone

nts

Wood Frame Masonry

Vulnerability: Variations in building responseKe

y M

odel

Com

pone

nts Earthquake

MDR

Peak Ground Acceleration

Wood Frame

Masonry

Cyclone

MDR

Peak Wind Gust

Wood Frame

Masonry

Financial LossKe

y M

odel

Com

pone

nts

• Combined loss distribution for 2 (or more) buildings in different locations is computed via convolutions, for each event.

Where: L = loss of amount L for event

P1(Li) = probability distribution for Location 1P2(Lj) = probability distribution for Location 2

Li (for P1)

Li + Lj

For e.g. , what is probability of loss of 10m for this event?

Lj (for P2)

Source : Latchman S., Quantifying the Risk of Natural Catastrophes, 2010

𝑷 (𝑳 )=∑ 𝑷𝟏 (𝑳𝒊 )×𝑷𝟐 (𝑳 𝒋 )

Return Period Losses (RPL)In

terp

retin

g Ca

t Mod

el O

utpu

t

• Return Period = 1 / Probability of Exceedance

• Hence, the 1 in 10 year Hurricane loss corresponds to 10% EP with a loss of 99m

Loss (m)

Source: Modelling Fundamentals : What is AAL? By Nan Ma and Greg Sly (AIR CURRENTS , March 2013)

Average Annual Loss (AAL)In

terp

retin

g Ca

t Mod

el O

utpt

ut

• AAL = (250*0.1) + (150*0.1) + (0*0.1) + (0*0.1)...... = 40m

Average Annual Loss (AAL): What is the expected loss from earthquakes this year for Japan EQ?

Source: Modelling Fundamentals : What is AAL? By Nan Ma and Greg Sly (AIR CURRENTS , March 2013)

Exceedance Probability (EP) CurveIn

terp

retin

g Ca

t Mod

el O

utpt

ut

Different EP curve shape

Identical AAL

Source: Modelling Fundamentals : What is AAL? By Nan Ma and Greg Sly (AIR CURRENTS , March 2013)

Applications of Model OutputIn

terp

retin

g Ca

t Mod

el O

utpt

utEx

ceed

ance

Pro

babi

lity

Loss

XSAAL

p

RP Loss (PML)

TCE (p) = E (L | L >= RPLp)

AAL

AAL Applications:• Direct Pricing• Understanding key drivers of loss• Underwriting Guidelines

PML Applications:• Pricing Cat Reinsurance Treaties• Rating Agency Reporting (APRA)

XSAAL & TCE• Help understand drivers of tail risk• Average severity of losses in tail

Types of UncertaintyUn

certa

inty

in C

at M

odel

ling • Epistemic vs Aleatory Uncertainty

– Epistemic : Imperfect science ; limited historical record; sampling errors– Aleatory: Intrinsic randomness ; irreducible

• Primary Uncertainty– Focused more on the hazard generation component– i.e. event occurrence, parameters that govern cyclone path

• Secondary Uncertainty– Focused more on vulnerability component– i.e. ground motions/ wind speeds at site, damage given particular ground

motion/ wind speed.

Examples of P. and S. UncertaintyUn

certa

inty

in C

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ling

Primary Uncertainty (Hazard) : EQ Ground Motion attenuation

Secondary Uncertainty(Vulnerability) : Cyclone Damage

Source: RMS

Combining Uncertainty …from different model componentsUn

certa

inty

in C

at M

odel

ling

CV =

SD/

MDR

Mean Damage Ratio, MDR

Dam

age

Ratio

, D

Peak Wind Gust, v

= damage ratio distribution, at PWG v

Prob

abili

ty

Peak Wind Gust, v

= wind speed distribution, at PWG v

Prob

abili

ty

Damage Ratio,D

f(d) = overall damage ratio distribution =

X

X

The larger the event,MDR ↑ while CV ↓

Unce

rtain

ty in

Cat

Mod

ellin

gCombining Uncertainty… across different locations

. . . .

If Location losses are perfectly correlated (,

𝑺𝑫𝒕𝒐𝒕𝒂𝒍 ,𝒄𝒐𝒓𝒓𝒆𝒍𝒂𝒕𝒆𝒅=∑𝒊

𝑵𝑺𝑫𝒊

. . . .

If Location losses are perfectly uncorrelated (,

𝑺𝑫𝒕𝒐𝒕𝒂𝒍 ,𝒊𝒏𝒅𝒆𝒑𝒆𝒏𝒅𝒆𝒏𝒕=√∑𝒊𝑵𝑺𝑫𝒊❑

𝟐+¿

+¿

𝑺𝑫𝒑𝒐𝒓𝒕𝒇𝒐𝒍𝒊𝒐=𝒘 ∗𝑺𝑫𝒕𝒐𝒕𝒂𝒍 ,𝒄𝒐𝒓𝒓𝒆𝒍𝒂𝒕𝒆𝒅+(𝟏−𝒘 )∗𝑺𝑫𝒕𝒐𝒕𝒂𝒍 , 𝒊𝒏𝒅𝒆𝒑𝒆𝒏𝒅𝒆𝒏𝒕

Hence, overall portfolio standard deviation,

Where w is correlation weights (i.e. more geo-concentrated portfolio will have larger w than one that is more diverse)

How to express uncertainty in results?Un

certa

inty

in C

at M

odel

ling

Source: RMS

Example showing how uncertainty is incorporated into return period loss estimates.

BootstrappingAd

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Unce

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ty

• Repeated resampling of Event List Table (ELT)

• Plot new EP curve with each realization, and sort them

• Build confidence intervals for desired percentiles

Model BlendingAd

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Unce

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• Reduce model risk from reliance on single vendor opinion• May diversify away ‘independent imperfections’• But, may introduce new uncertainties in the process!

Model A

Model B

Blended Model

Severity BlendingAd

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Unce

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ty

Source: Ian Cook, Using Multiple Catastrophe Models, 2011

• If we have good reason to believe that, say at 400 year RP:– Greater chance the ‘true’ 1 in 400 year loss to be below B than above B– Greater chance the ‘true’ 1 in 400 year loss to be above A than below A

• Then weighted average of A and B may be ‘less wrong’ than pure A or B alone.

Frequency BlendingAd

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• Invokes a Bayesian approach, i.e. :

• Preserves event sets for other uses such as being fed into capital models.

Source: Ian Cook, Using Multiple Catastrophe Models, 2011

Other MethodsAd

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Unce

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• Sensitivity testing/ Stress Testing of model assumptions

• Historical Event validation

• Expert Judgment / Consultation with model vendors

• Bias Correction Methods

Alexander PuiEmail: alexpui8@gmail.com

Linkedin : https://au.linkedin.com/in/alexander-pui-94a33821

Contact DetailsCo

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