oasis approach to support correlation - swiss re41768f7d-6c59-48df... · oasis approach to support...
Post on 27-May-2020
5 Views
Preview:
TRANSCRIPT
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
Confidential 2
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
Confidential 3
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
Confidential 4
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
C
C
C C
C
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)
Confidential 7
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
Confidential
Correlated Wind fields, storm surge, and TC precipitation
Storm Surge Modeling
Confidential 10
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)
Confidential 11
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
C
C
C C
C
Climate Conditioned TC / Storm Surge / Flood Models
Confidential 24
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
Confidential 25
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
Confidential 28
Fraction of Tropical Cyclone Rain [%]
Tropical cyclones create a large fraction of the total precipitation amount in some parts of the world
Confidential 29
Return Periods TC vs. non-TC50 year 24h precipitation RP difference [mm/day] between TC and non TC
Confidential 30
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
Confidential 31
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)
CONFIDENTIAL© 2008 Risk Management Solutions, Inc.32
CONFIDENTIAL© 2008 Risk Management Solutions, Inc.33
CONFIDENTIAL© 2008 Risk Management Solutions, Inc.34
CONFIDENTIAL© 2008 Risk Management Solutions, Inc.35
CONFIDENTIAL© 2008 Risk Management Solutions, Inc.36
CONFIDENTIAL© 2008 Risk Management Solutions, Inc.37
Confidential 38
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
Confidential 39
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
Confidential 40
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
Confidential 41
What is the effect of uncertainty correlation?
Confidential 42
What is the effect of uncertainty correlation?
Confidential 43
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
Confidential 44
OASIS RMS AIR Corelogic Impact Forecasting
KatRisk
1
2
3
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
Confidential 45
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 ?
Confidential 46
Some examples
Confidential 47
Some examples
Confidential 48
Some examples
Confidential 49
Some examples
Confidential 50
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
Confidential 51
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
Basic Copyright Notice & Disclaimer
©2017 This presentation is copyright protected. All rights reserved. You may download or print out a hard copy for your private or internal use. You are not permitted to create any modifications or derivatives of this presentation without the prior written permission of the copyright owner.
This presentation is for information purposes only and contains non-binding indications. Any opinions or views expressed are of the author and do not necessarily represent those of Swiss Re. Swiss Re makes no warranties or representations as to the accuracy, comprehensiveness, timeliness or suitability of this presentation for a particular purpose. Anyone shall at its own risk interpret and employ this presentation without relying on it in isolation. In no event will Swiss Re be liable for any loss or damages of any kind, including any direct, indirect or consequential damages, arising out of or in connection with the use of this presentation.
top related