Oasis approach to support correlation

Zürich, September 2017

Dag Lohmann

KatRisk LLC752 Gilman St.Berkeley, CA 94710510-984-0056www.KatRisk.com

KatRisk Deutschland GmbHWilhelmstr. 679098 Freiburg, Germany0761-5146-7600

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Non-Standard OASIS Implementation

Store flood and storm surge data dynamically: 80 billion grids in the USA would not fit in a OASIS-type event set, need flexible location level flood defenses

Location-aware sampling: enable coherent view of risk in cat modeling, always produce identical results irregardless of who runs the code. We need actuarial sound simulations.

Flexible secondary uncertainty correlation: spatial kernel with uncertainty correlation between 0% and 100% in steps of 1%

True multi-peril: wind, storm surge, inland flood. Flexible inuring order of contracts, multiple policy files (by peril)

→ replace OASIS ktools kernel with KatRisk kernel, but keep architecture

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Non-Standard OASIS Implementation

Performance: 30x improvement, 1 million locations in 4 minutes on 25 cores with 10 samples, 50k years event set

Loss convergence: repeatable sparse antithetic latin-hypercube sampling

Global correlation: driven between regions by SST event set VARMAX models

Global correlation: expose and enable user driven climate change sensitivity

Exposure and policy format: find OASIS format too convoluted, but haven’t checked in a while

→ replace OASIS ktools kernel with KatRisk kernel, but keep architecture

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What catastrophe models are missing in general

Many current catastrophe models do not support coherent measures of risk– Can you diversify your portfolio when hypothetically insuring the same building twice

and then take half the risk?● Coherent risk measure ρ on measurable function Z● Positive homogeneity: if α ≥ 0, then ρ(αZ) = αρ(Z)

– Can your risk measure go up when you diversify?● Sub-additivity: ρ(Z1 + Z2) ≤ ρ(Z1) + ρ(Z2)

– Can EP losses go down anywhere on the EP curve when adding e.g. a building?

Many catastrophe models cannot answer key questions about correlated losses– Is there “climate sensitivity” in catastrophe models?

– How about globally correlated losses?

– How about peril – peril correlations?

KatRisk Simplified Global Workflow

Probabilistic Deterministic Expensive Financial + Analysis + API

Probabilistic VARMA based Ocean SST model

Probabilistic Tropical Cyclone Track Model Probabilistic Precipitation and Temperature Model, Surface Meteorology

TC Precipitation Model

Land Surface Model River Routing Model

Hydraulic 2-d Flood Model

Tropical Cyclone Wind Model

Storm Surge Model, Tidal Model

2-d hydraulic

Exposure and GU Loss Model (API for third party data integration)

Insured Loss Model (Policies, Treaties)

Statistics, Analysis, Maps (WMS), Web Interface (GUI) and Web Service (API)

Probabilistically sampled vulnerability with correlated severity distributions

Global Teleconnections

Climate Change SLR

Peril-Peril CorrelationSpatial - Temporal

Uncertainty Correlation

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What have we built?

Peril Model Software (OASIS compliant streaming architecture)– High performance multi-peril location level loss sampling

● Location-aware sampling to enable coherent measures of risk

– In-memory multi-peril policy financial module (speed increase)

– Flexible model execution architecture to investigate model assumptions and sensitivities (climate change, correlations)

Global data sets that correlate events– 10,000 ensembles that are 5 years long for sea surface temperature

(SST) with VARMA model

Tropical cyclone track and wind field models for all basins

Flood and storm surge probabilistic models

Flood and storm surge hazard maps (6 to 10 return periods)

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IPCC Special Report (Floods, Sea Level)

Projected precipitation and temperature changes imply possible changes in floods, although overall there is low confidence in projections of changes in fluvial floods. Confidence is low due to limited evidence and because the causes of regional changes are complex, although there are exceptions to this statement. There is medium confidence (based on physical reasoning) that projected increases in heavy rainfall would contribute to increases in local flooding in some catchments or regions. [3.5.2]

Likely increase in heavy rainfall associated with tropical cyclones. [3.4.4]

It is likely that there has been an increase in extreme coastal high water related to increases in mean sea level. [3.5.3]

KatRisk Hurricane and Storm Surge Model A climate conditioned hurricane track set developed for the Atlantic Basin (1km

resolution, 10k * 5 years of events)

Combined with roughness, windfield, and vulnerability models, full wind loss modeling capabilities

Sample Tracks 100 Year Windspeed Map

Storm Surge and Inland Flood Storm surge (SS) has been simulated

for the entire 50k year track set and output on a 10m resolution grid

Inland flood simulation with TC and non-TC rainfall. 50k years of continuous simulation of pluvial and fluvial flooding

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Correlated Wind fields, storm surge, and TC precipitation

Storm Surge Modeling

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Storm surge has been analyzed for 50,000 years of hurricane tracks

Houston

Chesapeake Bay

New Orleans

New York

Images show KatRisk Score (1-10)

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Short Story about Sea Levels and SLR

Representative Concentration Pathways

LIG127k

11k

Lohmann, AWI

KatRisk Surge Climate Change Study

Compares USA surge losses with current conditions and 30 cm sea level rise– Current speed of SLR is about 2.8 to 3.6 mm/year (could speed up),

and was about 1.8 mm/year in the 20th century

Use high resolution exposure of $6.88 trillion along the coasts results summarized on 200m gridded resolution

Buildings, contents, time element and appurtenant structures modeled

Ground-up AAL increased from $5.0 billion to $6.9 billion, implying an increase of about $60 million per centimeter SLR, or currently about $20 million per year (although the increase is not linear), equal to 0.4% of the AAL – but also with potential to accelerate.

Model Area #1 (#2 no shown)

Exposure By State

AAL by State

Increase in AAL

Sea Level Rise

EP curves base and SLR (30cm)BASE

Loss / RP 2 5 10 20 50 100 200 500 1000

BASE [$billion] 0.65 4.8 10.8 20.9 39.5 56.4 92.2 108 141

SLR [$billion] 1.0 7.1 15.2 27.6 49.6 69.6 75.9 128 161

AAL = $5.0 Bn AAL = $6.9 Bn

Southern Florida Exposure

Southern Florida AAL base

Southern Florida AAL SLR

Southern Florida change (SLR – base)/SLR

Teleconnections and Peril – Peril Correlation

Probabilistic Deterministic Expensive Financial + Analysis + API

Probabilistic VARMA based Ocean SST model

Probabilistic Tropical Cyclone Track Model Probabilistic Precipitation and Temperature Model, Surface Meteorology

TC Precipitation Model

Land Surface Model River Routing Model

Hydraulic 2-d Flood Model

Tropical Cyclone Wind Model

Storm Surge Model, Tidal Model

2-d hydraulic

Exposure and GU Loss Model (API for third party data integration)

Insured Loss Model (Policies, Treaties)

Statistics, Analysis, Maps (WMS), Web Interface (GUI) and Web Service (API)

Probabilistically sampled vulnerability with correlated severity distributions

Global Teleconnections

Climate Change SLR

Peril-Peril CorrelationSpatial - Temporal

Uncertainty Correlation

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Climate Conditioned TC / Storm Surge / Flood Models

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US Hurricane Wind Results Total AAL using our industry

exposure is $12.1 B

The model has also been run against the Florida CAT Fund exposure set used in the submittal process to the Florida Hurricane Commission

Geographic Distribution of AAL

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US Hurricane Model Comparison

Masonry Loss Costs by county:

Based on exposure specified by the Florida Commission on Hurricane Loss Projection Methodology

USA AAL by Atlantic SST and ENSO

Hurricane losses dependency on Atlantic SST Anomaly and ENSO

AAL by Atlantic SST

AAL by ENSO

Introduction of SST leads to clusteringfor TCs that cause losses in the USA

# Atlantic TCs with SST Dispersion = 1.15# Atlantic TCs Poisson

Flood Global Correlations with TCs Impact of teleconnections on global precipitation

– Combine TC and non-TC precip

– Base hurricane model and global precipitation model on same data set of global SST expressing natural variability and global correlations

– Correlate events between perils and continents based on SST

TC precip

ENSO AMOThree month lag anomaly correlation with PCAs

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Fraction of Tropical Cyclone Rain [%]

Tropical cyclones create a large fraction of the total precipitation amount in some parts of the world

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Return Periods TC vs. non-TC50 year 24h precipitation RP difference [mm/day] between TC and non TC

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Peril – Peril Correlation: Harvey

Loss estimates based on KatRisk footprints

8.8 million point IED in Texas– $45 Billion GU Inland Flood Loss

– Large demand surge (1.4?) + wind and storm surge (~$2 Billion) + other areas

~ $80 Billion

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Harvey Slides

Harvey cat response based on flexible model setup to compute wind, storm, and inland flood model footprint given observed data.

Compare flood footprint with FEMAand point observations (Pensacola 2014)

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Correlation of Secondary Uncertainty The correlation of secondary uncertainty is probably one of the most misunderstood

features of catastrophe models

High return period losses are significantly impacted by this

The GU AAL is not impacted by this, but GU EP curves

The GR AAL and EP curves are impacted – “Deductible erosion” without it

Dependent on how you do this, it can result in a non-coherent measure of risk

– https://en.wikipedia.org/wiki/Coherent_risk_measure (Monoticity, Sub-additivity, Positive Homogeneity, Translation Invariance)

The following slides present currently used methods

– analytical

– “semi” analytical

– simulation

Source: Keogh, RAA 2011

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Secondary Uncertainty “Secondary Uncertainty” is often parameterized or stored in a non-parametric

table around a mean loss that comes from a vulnerability function

The result is a “smeared out” loss event, where the event has a probability of being more or less costly than the mean

It has a profound impact on losses

http://www.casact.org/community/affiliates/camar/1012/uncertainty.pdf

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What is the effect of uncertainty correlation?

Model setup– KatRisk probabilistic Canada flood model (released July 2017)

– 50k years of modeled pluvial and fluvial flood events (more than 1 million events) down to 10 year return period local small floods

– OASIS compliant compute kernel with enhanced features (see table later)

– Flexible defense assumptions for location and regional level (fully editable defense failure fragility curves)

See full document on http://www.katrisk.com

AAL = $1.36 Billion CAN

Total Exposure = $6.67 trillion CAN

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What is the effect of uncertainty correlation?

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What is the effect of uncertainty correlation?

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Uncertainty Correlation References Dong: Building a More Profitable Portfolio. Modern Portfolio Theory with Application to

Catastrophe Insurance. Reactions Publishing Group, 2001

Foote, Mitchell-Wallace, Jones, Hillier: Building Catastrophe Models: in Natural Catastrophe Risk Management and Modelling, Wiley, 2017, p. 373ff.

Lohmann, Yue: Correlation, simulation and uncertainty in catastrophe modeling. Winter Simulation Conference, 2011

Shome, Jayaram, Rahnama: Uncertainty and Spatial Correlation Models for Earthquake Losses, 15WCEE, 2012

Wang, Hofmann, Park: Distance based correlation in earthquake loss simulation, RAA 2016

Keogh: Correlation: Catastrophe Modeling’s Dirty Secret, RAA 2011

Calder et al: Catastrophe Model Blending: Techniques and Governance, GIRO - UK Actuarial Profession, 2012 (not directly related, but relevant information about uncertainty)

Strassburger: Risk Management and Solvency – Mathematical Methods in Theory and Practice, Ph.D. Thesis, University Oldenburg, Germany, 2006 (good treatment of copula usage, some errors though) and other publications from Prof. Pfeiffer’s (retired) group

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OASIS RMS AIR Corelogic Impact Forecasting

KatRisk

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Overview of Model Vendor Complexity

1) Aggregating mean and standard deviation to fit a parametric aggregate distribution 2) Using FFT (or other) methods to convolve location loss distributions (implies 0% correlation)3) Use Monte-Carlo simulation to sample from individual distributions a) either 100% or 0% uncertainty correlation b) uncertainty correlation between 0% and 100% c) distance based uncertainty correlation between 0% and 100% d) account based uncertainty correlation e) repeatable antithetic latin-hypercube multi-peril sampling

I’d rather not sayb, c, ea, d

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Aggregation examples

Workflow– Specify correlation (rho), and marginal loss distributions (beta)

– Compute ● the aggregate distribution for analytical distribution

– Check what kind of model you are using, these should be factor model equivalent for normal distributions (adding variances), even though the marginal distributions are often different

● “semi” analytical 0% (convolution) and 100% (addition) correlated● full simulation with factor model

– Compare● Aggregate distribution based on different analytical method● “semi” analytical method with factor model● Analytical result with factor model: Is a beta + beta = beta ?

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Some examples

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Some examples

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Some examples

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Some examples

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Quick summary secondary uncertainty

Individual locations always need to have the same sampled loss by event and peril (100% correlated). Otherwise we diversify without wanting to do so. This is especially important for tail risk and individual high value buildings (fac). We need location aware sampling.

Correlation of uncertainty is a driver of tail risk, and should not be either 0% or 100%

Impact of current implementation in many cat models is a non-coherent view of risk

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Summary

Non-standard implementation needed for flood models

Need to enable coherent view of risk

Showed results of global correlation = sea level rise– 0.4% of AAL per year increase in AAL, mainly in low return periods

Global teleconnections through SST modeling feasible way to correlate cat models globally

Harvey demonstrated (again) that peril – peril correlations are important

Secondary uncertainty is a misunderstood concept, has a large impact on tail losses. Simulation effects how we sum up losses

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