Catastrophe Modeling Boot Camp Jim Maher, fcas maaa
tarix 21.08.2018 ölçüsü 469 b. #73729
Jim Maher, FCAS MAAA Platinum Re Cat Modeling Basic Elements of Cat Models Similarities/Differences of Cat Models Data/Modeling Issues Portfolio Management Basic Elements of Cat Models Hazard Module Engineering Module (aka Vulnerability) Insurance (aka Financial) Module Event Set (and Year Set) Hazard Module Seismology Meteorology Terrorism Non random frequency Non random severity Non-modeled perils Tsunami Meteor strike Est. RP of 1,000 years for 10 megaton event Most recent Siberia (1908) River Flood Wildfire Winterstorm Non-modeled coverages Life/Health Personal Accident Group Life Disability Marine Yachts Offshore Oil Rigs Cargo Earthquake Major Types of Earthquake Location of Earthquake Hazard Major Historical US Earthquakes Recent US Earthquakes Vulnerability and Financial Models Earthquake prediction (?) Major Types of Earthquakes Strike-Slip Dip-Slip (subduction) Fault is at an angle to the surface of the earth Movement of the rock is up or down Great Kanto Earthquake (Japan 1923) Location of Earthquakes Plate Boundaries 90% of worlds earthquakes occur here Seven Major Crustal Plates on the Earth Rocks usually weaker, yield more to stress than Examples: California, Japan, etc. Ring of Fire Intra-plate Earthquakes New Madrid (1812) Newcastle, Australia (1989) Charleston (1886) Plate Boundaries & “Ring of Fire”
Modified Mercalli Scale IV Felt by many indoors but by few outdoors. Moderate V Felt by almost all. Many awakened. Unstable objects moved. VI Felt by all. Heavy objects moved. Alarm. Strong. VII General alarm. Weak buildings considerably damaged. Very strong. VIII Damage general except in proofed buildings. Heavy objects overturned. Modified Mercalli ctd. IX Buildings shifted from foundations, collapse, ground cracks. Highly destructive. X Masonry buildings destroyed, rails bent, serious ground fissures. Devastating. XI Few if any structures left standing. Bridges down. Rails twisted. Catastrophic. XII Damage total. Vibrations distort vision. Objects thrown in air. Major catastrophe. Major Historical US Quakes San Francisco (1906) Magnitude 7.8, 3000 deaths Significant fire following element Charleston (1886) Magnitude 7.3, 100 deaths New Madrid (1811/12) 12/16/1811 Northeast Arkansas 1/23/1812 & 2/7/1812 New Madrid, Missouri Estimated Magnitude 8.0 Destroyed New Madrid, severe damage in St. Louis, rang church bells in Boston Recent US Earthquakes Loma Prieta (1989) Northridge (1994) Nisqually/ (Seattle) (2001) Loma Prieta (1989) Magnitude 6.9 on San Andreas Fault 63 deaths, 3,757 injuries, $6 BN economic damage, $1.0 BN insured damage Severe property damage in Oakland and San Francisco Collapse of Highways, viaducts Loma Prieta ctd. Liquefaction San Francisco’s Marina district loosely consolidated, water saturated soils. Loosely consolidated soils tend to amplify shaking and increase structural damage. Water saturated soils compound the problem due to their susceptibility to liquefaction and corresponding loss of bearing strength. Unreinforced masonry construction Engineered buildings performed well Northridge (1994) Magnitude 6.8 earthquake Occurred on previously unknown fault 60 killed, 7,000 injured, 20,000 homeless, 40,000 buildings damaged Fires caused damage in San Fernando Valley, Malibu, Venice Liquefaction at Simi Valley Northridge-PCS Estimates
Nisqually/(Seattle) (2001) Magnitude 6.8, 400 people injured Major damage in Seattle-Tacoma area Insured Damage $305 Million Max. intensity VIII in Pioneer Square area Landslides in the Tacoma area Liquefaction and sand blows Earthquake vulnerability factors Building construction Unreinforced masonry vs. seismic designed Building height Taller buildings vulnerable to long-period waves Soft story (hotel lobby) increases vulnerability Building location Soil type is critical Fire following losses can be very significant Financial model factors CEA mini-policy Per policy Per location Regional sublimits (e.g. CA only) Interlocking clause Reduces event loss across multiple treaty years Hard to model Differences between models Detailed vs. Aggregate Detailed models better capture these vulnerability and financial considerations Fire Following Significant difference in modelers New Madrid Significant difference in return period Earthquake prediction Earthquakes not a Poisson process Poisson implies inter-arrival times are exponentially distributed (memory-less) 1999 Izmit (Turkey) Earthquake Increased risk for a quake in Istanbul San Andreas Fault Is an earthquake due? Where on fault? Izmit Quake ctd. 60% chance of Istanbul earthquake in next 30 years - Thomas Parsons, USGS Researchers took into account the stress transfer from a magnitude 7.4 earthquake in Izmit, Turkey in August 1999. San Andreas Fault Over the past 1,500 years large earthquakes have occurred at about 150-year intervals on the southern San Andreas fault. As the last large earthquake on the southern San Andreas occurred in 1857, that section of the fault is considered a likely location for an earthquake within the next few decades The San Francisco Bay area has a slightly lower potential for a great earthquake, as less than 100 years have passed since the great 1906 earthquake Cat Models and Earthquake Pred. At least one cat modeling firm has variable earthquake rate (changes with calendar date) Annual model updates allow for changing earthquake rate with time. Hurricanes Meteorology of Hurricanes Frequency of Hurricanes by category Recent Hurricane Activity Hurricane Andrew Vulnerability and Financial Models Hurricane prediction (?) Meteorology of Hurricanes Occur in both Northern and Southern Hemispheres Don’t occur on the equator Factor in the 2004 Tsunami tragedy Coriolis Force spin clockwise in southern hemisphere spin counter-clockwise in northern hemisphere Need warm sea surface temperatures Always travel from east to west Safir-Simpson Scale
Atlantic Basin Hurricanes
US Landfalling Hurricanes
2004 Season
2003 Season
2004 Hurricanes Charley: 8/9-14, Small storm- strengthened rapidly to Cat 4 just before FL landfall Frances: 8/25-9/8, Larger storm, weakened from Cat 4 to Cat 2 before FL landfall Ivan: 9/2-9/24, Long-lived, Cat 5 storm, weakened to Cat 3 before AL landfall Jeanne:9/13-9/28, Crazy Cat 3 storm, same landfall as Frances but smaller & faster 2004 Hurricanes ctd.
Modeling Issues raised by 2004 storms Storm Surge Demand Surge Offshore oil rig losses Caribbean Clash modeling Hurricane Andrew Period: 8/16-8/28 1992 Small, intense CAT 5 Cape Verde storm Affected Bahamas, S. Florida, Louisiana Damage $25 BN, $15.5 Insured US damage Central Pressure 992 mb, third lowest since 1900 Vulnerability model factors Construction Concrete bunkers vs. mobile homes Location Properties near ocean very vulnerable to storm surge Secondary modifiers Financial model factors percentage deductibles can be very significant New season deductible in FL What is a risk? Issue for per-risk treaties For hurricanes, widely dispersed buildings on one policy often considered one “risk” E.g. school district Differences between models Detailed vs. Aggregate models Northeast Hurricane Significant difference between modelers Caribbean clash Not all modelers facilitate this analysis Hurricane Prediction
Data/Modeling Issues Need for completeness Reinsurers need compensation for all risks being accepted Model all exposures Model all perils Run multiple models Missing exposures Sometimes only get tier 1 wind counties Sometimes only certain states E.g. CA, Pacific NW, New Madrid only Other shake exposure ignored (e.g. East Coast) Fire following exposures ignored Sometimes entire books of business are missing Must cross-check cat model exposure data Premium often n.a. , policy counts (?) Modeling Tricks Failing to load for LAE Failing to consider demand surge “Really, all my policyholders have roof tie-downs!” Running all the models and providing the lowest different modeling firms Aggregate vs. detailed models Portfolio Management Event Set framework is a powerful tool for portfolio management Ability to model portfolio’s risk vs. return Determine portfolio capital and allocate to individual deals Portfolio Framework Example Consider two countries 5 possible events for each country Industry losses specified Goal-determine risk vs. return for various reinsurance portfolios Event Sets
Create a set of Simulation Years
Check against Poisson
Contracts
Calc. Contract Losses by year
Compute AAL and expected profit for each contract
Distribution of profit/(loss)
Calculate return on capital
Portfolio Effects Now assume that the reinsurer’s portfolio consists of certain shares of these 3 contracts Want to calculate the overall portfolio capital and Portfolio Consider the following portfolio: Then consider 3 other portfolios P+0.1% A P+0.1% B P+0.1% C Portfolio ctd.
Allocating Portfolio Capital The portfolio capital can be allocated as follows: Cap[20%A]= 20%/0.1% * (422.89-422.02)=174 Cap[10%B]= 10%/0.1% * (422.56-422.02)= 54 Cap[5%C] = 5%/0.1% * (425.90-422.02)=194 -------------- -------- Cap[Portfolio] = 422 Return on Allocated Capital
Tail oriented Capital Metrics Approach also works for tail oriented capital metrics- e.g. TVAR Define capital = 3 x TVAR (80%) Tail oriented ROAC
Allocated Capital Calcs As before, alloc. capital based on marginal For example, for the 20%A contract: 450 = (793.5-791.25)/0.1% * 20% Portfolio Cap = Sum of Alloc. Capitals N.B. according to this capital metric, 10%B has the highest ROAC in the portfolio Summary CAT Models provide a powerful tool for portfolio management Can be used to derive capital for a contract within a portfolio and ROC There is no “contract order” issue as is sometimes thought Portfolio can then be optimized to maximize ROC Dostları ilə paylaş:
