Nat Cat-Risikomanagement in Echtzeit

Transcription

1 Nat Cat-Risikomanagement in Echtzeit Naturkatastrophen, Verträge und eine Datenbank Dr. Kai Haseloh, Group Risk Management, Hannover Re Dritter Weiterbildungstag der DGVFM Hannover, June

2 Real-time Exposure Management for a Reinsurer What this talk is about Reinsurers (and large insurers as well) face the following task They manage a book of hundreds, even thousands of reinsurance treaties exposed to catastrophe risk The portfolio shall make optimal use of available capital. This means: profitability and diversification are maximized within system of limits and thresholds which curbs the risk of overexposure Standard since the early 1990s for measuring nat-cat risk: Nat-Cat Models This talk is about the challenges of implementing a real-time exposure/risk reporting IT system for a reinsurance portfolio exposed to cat risk

3 Agenda Cat-Modelling Exposure data available Building blocks of a Cat-Model Cat-Model Output and Risk Metrics Cat Portfolio Management Portfolio Aggregation Challenges

4 Cat Modelling

5 Exposure Database for a Single Reinsurance Contract A large insurer may have 100,000s of locations re-insured against catastrophes 20,576 59,212 33,657 50, ,203 13, ,496

6 Primary Insurance Portfolios / Exposure Databases Can be as detailed as this... Office complex Replacement Value $100m 25 stories Earthquake retrofits Policy 2899A-1 Earthquake insurance: 10% of $50m with 5% deductible Filling station Replacement Value $250,000k Policy 6239C-1 Earthquake insurance: $200k with $10k deductible Single-familiy residential Replacement Value $500k 2 stories, built in 1979 Policy R-1A Earthquake insurance: $500k with 5% deductible

7 Primary Insurance Portfolios / Exposure Databases But sometimes are as sparse as this... Example 1: Surplus treaty Example 2: Per Risk treaty State Sums Insured Alaska 20,000 Alabama 162,850,000 Arkansas 12,970,000 Arizona 62,540,000 California 14,090,000 Washington 19,200,000 Wisconsin 125,000,000 West Virginia 51,140,000 Limit Range Number of Locations Premium Unknown 6,106 3,509,433 Under 500,000 77,851 64,995, ,001-1,000,000 20,556 39,775,647 1,000,001-1,500,000 7,456 20,965,224 1,500,001-2,000,000 4,255 14,309,799 2,000,001-2,500,000 2,622 10,331,667 2,500,001-5,000,000 5,454 28,681,663 5,000,001-10,000,000 2,807 20,091,749 10,000,001-20,000, ,249,410 20,000,001-30,000, ,735,154 30,000,001-40,000, ,407,222

8 Typical Reinsurance Coverages Perils, LOBs, Obligatory and Facultative Reinsurance Perils Covered Earthquake Flood Wildfire Storms Lines of Business Worker s Compensation Marine Business Interruption Terrorism, Life, Personal Accident Obligatory Reinsurance Types Proportional Quota Share Surplus Non-Proportional Catastrophe and Per Risk XL Stop Loss Facultative Reinsurance Coverage for very large individual risks

9 Components of Natural Catastrophe Models Typical Design of a Cat Model Hazard Eventset generation Vulnerability Financial module Frequency Intensity Local intensities Damage- Estimation Calculation of insured Losses Exposure Database of Insured Locations Policy and treaty conditions Loss evaluation Natural Catastrophe Modelling and Data Capture

10 Components of a catastrophe model - Event Set The hazard is described by a set of discrete events Hazard Eventset generation Frequency Local intensities Intensity Events are a stochastic representation of the catastrophe hazard Generated by extrapolating historical record years years, or more Historical databases: HURDAT (U.S. HU), JTWC (JP TY), USGS (North America EQ) Events are described by their characteristics Storm: Track, Intensity, Windfield, Duration Quake: Epicenter, Magnitude, Direction, etc. Where, how big, what type, and how likely? Nat Cat Know ledge for UWs

11 Historic Storm Tracks in the Atlantic Basin , Source: NOAA Best Track Archive

12 Components of a catastrophe model Event set - entire catalog Event Year Day Event Info Cen Pres Max Wind RMax Speed Angle Long Class 1 Hurr NC Class 1 Hurr GOM MX TX Class 1 Hurr TX Class 5 Hurr CU GOM BB JM MQ Class 1 Hurr ME BD Class 1 Hurr GOM TX Class 1 Hurr LA MS Class 1 Hurr LA Class 1 Hurr DR HT BF MQ CU Class 2 Hurr GOM CU JM CJ AN Class 1 Hurr NC Class 1 Hurr GOM BF CU FL Class 1 Hurr BF CU FL CJ Lat 293,203 10, Class 3 Hurr GOM FL ,220 10, Class 1 Hurr NC

13 Components of a catastrophe model Size of event catalogue varies by region and peril Region Peril Years with Events Number of Events Australia Earthquake 4,027 5,122 Australia Cyclone 9,954 59,377 Chile Earthquake 9,447 28,977 Europe Earthquake 10, ,904 Europe Winterstorm 9,985 27,557 Hawaii Earthquake 5,623 9,757 Hawaii Cyclone 2,872 3,491 Japan Earthquake 9,998 83,608 Japan Cyclone 9,995 79,885 Canada Earthquake 4,938 6,820 Canada Tornado / Hail 10, ,017 Columbia Earthquake 9,375 27,335 Mexico Earthquake 9,946 51,483 South East Asia Earthquake 10, ,406 USA Earthquake 9,853 42,765 USA Tornado / Hagel 10, ,838 Currently active at 71 full models 6,388,024 events

14 Components of a catastrophe model - Vulnerabilities Intensity calculation at the sites of Exposure Vulnerability A set of rules to calculate the intensity of each event at the site of interest (i.e. where the exposure sits) Local intensities Exposure Database of Insured Locations Damage- Estimation Taking into account effects such as: EQ: ground motion attenuation, soil, liquefaction, WS: terrain roughness, surface friction, distance to coast, Requires knowledge about where the exposure is located (geocoding) Nat Cat Know ledge for UWs

15 Damage Ratio Components of a catastrophe model - Vulnerabilities Intensity calculation at the locations in exposure database 1 Building Content Vulnerability Functions describe the physical impact of an event on risks 0.75 Dependence on building characteristics Construction type (Concrete, Steel, ) 0.5 Occupancy type (Single Family, Office Tower, Filling station) Retrofits Wind Speed Age, Size, etc Further refinement: Secondary uncertainty modelling to capture uncertainty around the mean

16 Vulnerability Function Yields damage for given local hazard intensity 33,657 Damage to 9,496 building $24, Damage to building $5,000 50,734 Roof blown, Water damage $65,000 material damage $10,000 content damage $4,000 additional living expenses The vulnerability function combines the event intensity with the exposure at risk For any given event in the event set the model is able to produce the loss to each individual location The size of the loss depends on the replacement values encoded in the exposure database In aggregate models the exposure is disaggregated within the zones used using industry average assumptions

17 Components of a catastrophe model Insurance Structure Financial module Policy conditions are provided by the user (detailed models only) Limits, deductibles, franchises Multi-location policies Damage- Estimation Policy, Treaty conditions Calculation of insured Losses Loss evaluation The financial module converts the ground up losses into losses borne by the policy issuer (insurer) After aggregation across the portfolio losses for reinsurance can be calculated for RI treaty structures Both of these operations can be performed for each and every event Runtimes from minutes to hours on multiple CPU cores Nat Cat Know ledge for UWs

18 Event Loss Table Typical Cat Model Output Event Year Loss , , , , , , , , ,529, , , , , , ,900, , ,082 ELT contains losses for every modelled event Various loss perspectives can be generated ground up without primary policies gross of reinsurance reinsurance treaty loss net of reinsurance The order of the events and allocation to the years is the same for every model run allows correlation Multiple peril models may be combined

19 Event Loss Table Visualization for Atlantic Cyclone Model

20 Event Loss Table Typical Cat Model Output Event Year Loss , , , , , , , , ,529, , , , , , ,900, , ,082 Risk Measures can be derived the from ELT Average Annual Loss Sum of Loss column / # of simulation years Here: AAL = 4,194,198 Distribution function of Annual Loss (AEP) = sum of all losses within a year Maximal Annual Loss (OEP) = maximum loss occurring within a year

21 Event Loss Table Obtaining the OEP Distribution Event NEP Year Loss 99.99% 2 8, ,288, , % ,881, , % 32 1, ,765, , % 41 6, ,719, , % 70 9, ,700, , % ,645, , % 115 1, ,182, , % ,883, , % ,363,237 9,529, % 152 8,096 98,259, , % 156 9, ,387, , % 158 2, ,026, , % 160 8, ,529, , % 8,904 91,391, , % ,283 56,900,867 87,835, , ,082 Take the maximum loss per year and resort the resulting table in descending order The nth largest value then corresponds to the non-exceedance probability NEP = 1 n/10000 Example: 10th largest loss has a 0.1% chance of being exceeded Cat-Modeller lingo: The 1,000y event is 98m Similar for AEP, here losses per year are added before re-sorting

22 Event Loss Table Typical Cat Model Output Loss Distribution unit: millions OEP AEP VaR 99.5% approx. 57m (AEP) Insurers often base their reinsurance buying on VaR 99.5% or similar Regulatory requirements are often formulated using VaR % 98.5% 99.0% 99.5% VaR 99% approx. 35m (OEP)

23 Reinsurance Portfolio Management

24 Portfolio Management of a Reinsurer The portfolio of a reinsurer contains thousand of treaties and is constantly changing Treaties are usually underwritten on an annual basis shared between multiple reinsurers Key questions when treaty is newly offered or comes up for renewal: How much share do I underwrite this year? Do I underwrite the treaty at all? Decision needs to take into account the impact of the treaty on overall risk position Capital consumption Diversification Limit and Thresholds

25 Portfolio Analysis for a RI portfolio Event Loss Table Aggregation by Summation per Event Event Yr Loss TTY 1 Share 5% Loss TTY 2 Share 10% Loss TTY n Share 1% Sum of all treaty losses ,082 3,748,714 2,328,360 11,859, ,694 2,648,593 1,369,912 7,527, ,376 5,497,345 2,791,043 17,576, ,950 2,310,288 1,046,783 6,735, ,054 11,511,951 8,732,334 46,173, ,637 1,381, ,212 3,972, ,074 17,134,595 8,627,970 51,610, ,073 12,391,297 7,542,775 41,686, ,529, ,684,313 73,672, ,192, ,433 3,786,295 1,891,014 10,291, ,547 6,096,586 2,359,949 17,655, ,053 8,100,430 4,529,365 27,356, ,172 4,856,102 2,786,358 15,934,921

26 Portfolio Analysis for a RI portfolio Event Loss Table Aggregation by Summation per Event Event Yr Loss TTY 1 Share 5% Loss TTY 2 Share 10% Loss TTY n Share 1% Loss TTY n+1 Share 2% Sum of all treaty losses ,082 3,748,714 2,328, ,685 12,295, ,694 2,648,593 1,369, ,553 7,674, ,376 5,497,345 2,791, ,146 18,271, ,950 2,310,288 1,046, ,147 6,940, ,054 11,511,951 8,732,334 1,022,725 47,196, ,637 1,381, , ,701 4,143, ,074 17,134,595 8,627,970 1,292,664 52,902, ,073 12,391,297 7,542,775 1,428,358 43,114, ,529, ,684,313 73,672,402 11,688, ,880, ,433 3,786,295 1,891, ,117 10,526, ,547 6,096,586 2,359, ,874 18,437, ,053 8,100,430 4,529, ,004 28,027, ,172 4,856,102 2,786, ,558 16,504,478

27 The Global Reinsurer's Conundrum For a small portfolio of XL treaties in a single county the problem is well-behaved Impact analyses and reporting can be done with some effort in Excel On a global basis the problem becomes much more complex: Portfolio consists of several thousand treaties 200 countries need to be monitored for multiple perils (EQ, WS, TC, FL, FI, TH) Dozens of underwriters are active and changing the portfolio at the same time Choice of risk measure Non-modelled treaty types Sparse data Integration with treaty management system and underwriting/modelling workflows

28 Global Exposure Management (GEM) Treaty Management System Excel Worksheets Scope / Users Group cat business worldwide Treaty Data Exposure Data Cat Models GEM Frontend and Reporting Real-time Reporting Database Gross/Net views for Internal Model underwriting centres worldwide exposure Underwriters: 150 Modelers/Actuaries: 30 Development / Technology GEM Front-End: Silverlight Reporting Database: ORACLE BI/Reporting: MicroStrategy Development time: 6 years

29 Challenge: 200 countries need to be monitored Focus on most important scenarios Challenge Global reinsurer underwrites treaties in most countries of the world Small perils can have considerable significance to the (re)insurance industry 2011 Thailand flood 2016 Canada Bushfire have In many cases no vendor models / event sets are available to model the peril Solution Neglecting the perils is not an option! Very small scenarios can be monitored with a reduced event set Events are suitably chosen to represent a 10, 20,, year event in the region For larger second tier scenarios proxy models can fill the gap

30 Stochastics to the Rescue Mathematical Models may be helpful where not nat cat models are available General Idea The presented approach of Nat Cat model building may be infeasible in many secondary markets availability of relevant scientific data access to insurance coverage or claim details Stochastic/mathematical models may be helpful in these occasions These are informed by the sparse data that is available Example: Winterstorm Peril in Japan Winterstorms are regular events in Japan, esp. in the north In rare circumstances, these can cause significant damage E.g February winterstorm in Japan caused 2.5 bn USD insured loss

31 Stochastics to the Rescue Mathematical Models may be helpful where not nat cat models are available Modelling the hazard as a sum of compound models Y = n i=1 Y i N i k, Y i = Y i k=0, with Y i k i.i.d. for fixed i Japan Winterstorm Example Japan is divided into a number of uncorrelated regions (subscenarios) For each subscenario i mathematical loss distributions for the frequency N i and severity Y i k are chosen These can be fitted to the available loss history, where available If Y i is expressed as a loss ratio a universal model for aggregate exposure E i (sum insured in region i) results: Y i = N i k=0 E i Y i k

32 Challenge: Choice of risk measure VaR does not work for the ELT approach Challenge Assign a suitable risk measure ρ( ) to each treaty X i and the portfolio X = X i It shall be used to measure and limit the risk contained in the overall portfolio ρ X What are desirable features? Subadditivity ρ X 1 + X 2 ρ X 1 + ρ X 2 +ve Homogeneity ρ αx = αρ X, α 0 VaR does not satisfy the first property! Easy to construct examples where VaR X 1 + X 2 > VaR X 1 + VaR X 2 Also VaR(X) may be zero while has X a very high risk in the tail of the distribution A better risk measure is the tail value at risk (TVaR)

33 Event Loss Table Typical Cat Model Output Loss Distribution unit: millions Definition TVaR E.g. for NEP = 99% TVaR 99% (X) E X X VaR 99% TVaR 99% approx. VaR 99.5% 65m (AEP) approx. 57m (AEP) With ELTs the TVaR contribution can be easily calculated as well: 60 Average of worst 100 years % 98.5% 99.0% 99.5% Advantages of TVaR over VaR: Takes tail into account Stability against perturbations Subadditivity

34 Portfolio analysis for a RI portfolio Correlation comes for free as it is implicit in the assignment of losses to events Event Yr Loss TTY 1 Loss TTY 2 Loss TTY n NEP Year Sum of all Sum of Treaty Losses Share 5% Share 10% Share 1% treaty losses per year ,082 3,748,714 2,328, % 11,859,892 1,009 7,307,159, ,694 2,648,593 1,369, % 7,527,418 6,053 6,261,320, ,376 5,497,345 2,791, % 17,576,262 9,138 6,153,631, ,950 2,310,288 1,046, % 6,735,673 8,096 5,219,283, ,054 11,511,951 8,732, % 46,173,624 7,755 4,311,811, ,637 1,381,777 aggregate 563, % 3,972,285 4,979 4,152,177, ,074 17,134,595 8,627, % 51,610,261 2,624 4,119,869,853 and sort ,073 12,391,297 7,542, % 41,686, ,103,179, ,529, ,684,313 73,672, % 434,192, ,057,460, ,433 3,786,295 1,891, % 10,291,979 8,904 4,052,764, ,547 6,096,586 2,359, % 17,655,984 8,056 3,977,655, ,053 8,100,430 4,529,365 27,356, ,172 4,856,102 2,786, % 15,934,921 1,921 1,868,418,580 average TVaR 99% = 2,777,452,233

35 TVaR as Risk Measure Practical Considerations Recalculation of the portfolio TVaR is computationally expensive Calculation of portfolio TVaR requires a consideration of whole event loss table The worst 100 years change in the sorting process Changing a single treaty requires full recalculation to view impact on group risk very expensive operation Current event loss table size > 1bn rows minutes to hours on a standard ORACLE enterprise database could benefit from in-memory technologies For underwriting decision making and practical purposes ρ X i TVaR 99% X i does not depend on X j,j i However, ρ X i should be reflective of diversification benefit of X i wrt the portfolio X On the other hand ρ X i should be stable if other parts of the portfolio change

36 Recalculation the portfolio TVaR Very expensive database operation, can be simplified by switch to TVaR-Contrib Both problems can be tackled as follows Initially the calculation of the portfolio TVaR is carried out above Years contributing to TVaR values are fixed, say y 1, y 2,, y 100 Each X i is assigned the risk measure ρ X i average loss in the fixed simulation years y 1, y 2,, y 100 ( instead of ρ X i = average loss in the worst 100 simulation years ) This is called the TVaR contribution of X i It measures the contribution of X i to the worst 100 simulation years for X

37 TVaR-Contrib - Advantages TVaR-Contrib is good and stable approximation of TVaR Changing the risk measure to ρ has many advantages ρ X i for a single treaty can be calculated using the treaty ELT only Changing a treaty X i do not affect ρ(x j ),i j TVaR-contrib is additive and homogeneous: ρ X = ρ( X i ) = ρ(x i ) important for segmentation ρ αx i = αρ X i treaty share can be calculated directly It allows very efficient reporting and as-if / impact analysis In practice, for a large reinsurer: ρ X ρ X even after busy renewal seasons with lots of portfolio changes quarterly re-calculation of y 1, y 2,, y 100

38 Sample Report for a Single Treaty for UW Decision Making Reports are available immediately after data is entered Scenario TVaR Contribution ρ for 10% share (Capacity consumption) Remaing Capacity for UW Center Group Capacity Atlantic Hurricane ,234.4 US Earthquake ,345.1 Europe Winterstorm Europe Earthquake Japan Earthquake Australia Cyclone Australia Earthquake all values in mn, fictional data

39 Challenge: Non-Modelled Treaties Challenge A considerable portion of business may not be modelled using cat models nature of the business (marine, personal accident, etc.) lack of exposure data To obtain comprehensive view on risk this business also needs consideration Solutions RDS scenarios help identifying those treaties Bespoke encoding functionalities are available in the GEM Front End Models for certain classes of business (Exposure data wizards) Per Risk XL, Marine, Worker s Compensation Third party model results for models not directly connected to GEM Last resort: Loss Estimations Output: Event loss tables stored in the reporting database

40 Beyond Probabilities Other methods of risk measurement - Realistic Desaster Scenarios (RDS) Idea Stress test a company by as-if analysis of a specific event Breadth rather than depth: Uncover hidden pockets of exposure Procedure Prescribe / describe a hypothetical set of catastrophe events Events should be of considerable magnitude, and well described Gather potential losses from all involved underwriting departments, even those with remote exposures Consider unexpected sources of loss Standard approach in the Lloyd s market

41 Extrapolation Methods Used to Map Losses to Events Simplest Case: Estimation of the 100 Year Event Market Losses (mn) 60,000 50,000 40,000 30,000 20,000 10, % 98.5% 99.0% 99.5% Treaty Loss (mn) % 98.5% 99.0% 99.5% User Input Treaty Type Quota Share Event Limit 150,000,000 Estimated 100y loss 120,000,000 Event Treaty Loss 2 1, , ,332

42 Integration with TMS and workflows Seamless interfaces ensure smooth workflow and limited extra efforts Challenge The system needs essential treaty and exposure data in real time during very busy renewal times to produce sensible output for decision makers Solutions System only captures data essential for the modeling / underwriting process Renewal functionalities make it easy to work off last year s data Full integration with treaty management system underwriting worksheets modelling worksheets Data needs to be keyed in only once (not thrice) Modelling / Quotation process fully supported Consistency between pricing and accumulation control Treaty Management System Excel Worksheets GEM Frontend and Reporting

43 Real-time Exposure Management for a Reinsurer Big Data!? Big data Vs Volume: Thousands of treaties, each generates 100,000s rows of data, but data used for reporting is structured Velocity Variety Veracity Portfolio is constantly changing, reporting in real-time Exposure data comes from different unstructured and structured sources; peril/region specific data/models; various treaty types However, data only enters the system in structured form Input data and model output may be sparse, unreliable or both While the described system meets some of the criteria it can be considered a Business Intelligence rather than a Big Data system. But there is no doubt about the fifth V!

44 Real-time Exposure Management for a Reinsurer The Fifth V Value! GEM has automatized many process steps which required onerous manual interaction before Great improvements to speed and quality of risk management reports GEM has become invaluable in underwriting decision making Underwriting close to assigned limits Optimal use of capital Immediate reactions to external market disruptions are possible Large cat events; Disruptions to the capital markets Timely and granular data delivery to the internal model