THE USE OF RISK ADJUSTED CAPITAL TO SUPPORT BUSINESS DECISION-MAKING

Transcription

1 THE USE OF RISK ADJUSTED CAPITAL TO SUPPORT BUSINESS DECISION-MAKING By Gary Patrk Stefan Bernegger Marcel Beat Rüegg Swss Rensurance Company Casualty Actuaral Socety and Casualty Actuares n Rensurance 1999 Call for Papers CARe meetng, Baltmore, Md. June 6-8, 1999

2 OUTLINE: 0. Abstract 1. Pressures on Captal (Surplus) 2. How Much Captal Do You Really Have? Rsk Bearng Captal (RBC) 3. How Much Captal Do You Really Need? Rsk Adusted Captal (RAC) 4. How To Estmate RAC: Underwrtng Model 5. Modelng Man-made Maor Catastrophes (Threats) 6. How To Estmate RAC: Investment Model 7. How To Estmate RAC: Credt Model 8. How To Estmate RAC: Puttng It Together 9. How to Allocate RAC to Lne, Product, etc. 10. Managng RAC To Optmze Rsk and Return 11. Concluson 12. Bblography 13. Appendces CARepaper\paperFN9.doc 2

3 0. Abstract Ths s partally a conceptual paper about the reasons why an nsurance company should address rsk and captal ssues n a methodcal manner and about the problems encountered dong so. But t also offers some mathematcal methods for dealng wth some of the problems. We do not offer the reader the fnal answer, snce we certanly don t have t. But we do offer some deas and some procedures for obtanng useful measurements. Wthout reasonably accurate parameter estmaton, the most sophstcated dynamc fnancal analyss model s smply a black box mappng nformaton accordng to the garbage n, gospel out syndrome (let us all bow down to our computers and worshp ther unarguable output!). Modelers of nsurance rsk may fnd value n the dscusson of modelng man-made maor catastrophes va the constructon of threat scenaros. The secton on modelng nvestment rsk dscusses possble ways of usng the prevalng alue at Rsk model and some problems n dong so. The secton on credt rsk outlnes the modelng problems encountered here. The reader may fnd the dscusson of captal allocaton to be partcularly enlghtenng. In the secton on managng rsk adusted captal (RAC), we attempt to show, as smply as possble, how the concept of RAC can be used by management to steer the course of busness decson-makng. The Bblography lsts some references whch the reader can use to learn more about the deas presented n ths paper. And the Appendces contan more mathematcs about some of the models and ther estmaton. At ths stage we also want to menton that the overall captal estmaton and allocaton CARepaper\paperFN9.doc 3

4 methodology descrbed n ths paper s ntended for a company s nternal rsk management. It cannot be used n the same way by external partes such as regulators, ratng agences, etc. These external partes need a standard model for the whole ndustry, and they must rely only upon publcly avalable nformaton. 1. Pressures on Captal (Surplus) We use the terms captal and surplus nterchangeably throughout ths paper. The pressures on nsurance ndustry captal are ntense and conflctng. Company shareholders, polcyholders, nsurance regulators and ratng agences are all pushng and pullng n dfferent drectons. The shareholders want ther captal to perform, that s, earn a hgher return. But there are many obstacles. Industry returns-onequty (RoE) have been weak hstorcally; most crtcs see them as beng less than commensurate wth the rsk level. In addton, long-latent clams are stll a drag upon the results of many companes. But yet, many people beleve there s excess capacty currently n the nsurance ndustry. Rates are decreasng, thus drvng down proft margns. It s a stuaton of too much captal chasng too lttle busness. To satsfy shareholders hopng to obtan a hgher return, there s an ntense compettve push to assume more rsk n order to use captal more effcently. Meanwhle, polcyholders, nsurance regulators and ratng agences are all pullng n the drecton of hgher captalzaton. They are concerned about nsurance company solvency n lght of the recent greater recognton of the ndustry s extreme exposure to natural catastrophes, the emergence of clams stemmng from many long-latent CARepaper\paperFN9.doc 4

5 man-made exposures and the threats of future clams from many smlar exposures. The recent savngs and loan crss n the US has made nsurance regulators and ratng agences aware that such a crss could also possbly occur n the nsurance ndustry f a clams shock s accompaned by a fnancal shock. In order to pull nsurance companes to a hgher, more conservatve captal base, the NAIC has formulated the concept of rsk-based captal to defne relatvely hgh captal thresholds for companes operatng n the US [ref. 1.1]. Wth these ntense, conflctng pressures, nsurers need a better concept of captal n order to measure captal adequacy and to help steer decson-makng throughout ther companes. We wll dscuss varous knds of captal. The three man types we dstngush are: (1.1) Types of captal Publcly-perceved captal: Ths has more than one value. These are the varous values of captal calculated by the statutory or GAAP fnancal statements, the NAIC, A.M. Best, Standard & Poors, etc. These are external vews. Rsk bearng captal (RBC): In secton 2, we wll defne a smple calculaton of the captal that the company has avalable to support ts busness. Note that the RBC gves an nternal vew, and s dstnctly dfferent from the NAIC rsk based captal concept, whch we would classfy as one of the publcly-perceved types of captal. CARepaper\paperFN9.doc 5

6 Rsk adusted captal (RAC): In secton 3, we wll defne a smple calculaton of the captal that the company needs to support ts busness. Agan, ths wll be an nternal vew. 2. How Much Captal Do You Really Have? Rsk Bearng Captal (RBC) The smplest answer to the queston of how much captal you really have s fnancal statement captal, ether statutory or GAAP. Ths of course equals fnancal statement assets mnus fnancal statement labltes. It has the advantage of beng very smple. It also has the advantage of beng audted; t s ndependently verfed and sgned-off by professonals who are potentally lable for neglgence f, for example, the future run-off of loss reserves turns out sgnfcantly dfferent from that stated. It s also publc nformaton, prnted n black and whte, for revew and comment by any crtcs or other nterested partes. A problem wth fnancal statement captal s that t doesn t gve a complete pcture of the value of an nsurance company. The tme value of money s generally not recognzed for property and casualty companes. It does not recognze varous hdden values such as goodwll. But worst of all, t s a snapshot pcture. It s not a dynamc vew of an ongong, actve company. It s not forward lookng. It looks backward only to prevous exposure. CARepaper\paperFN9.doc 6

7 A better vew of how much captal a company really has to support the rsk generated by ts busness s gven by the concept of rsk bearng captal, or RBC. A very smple, operatonal vew of RBC can be obtaned as follows. (2.1) RBC = fnancal statement captal plus any unrealzed captal gans not ncluded above plus the dscount nherent n the loss reserves plus other hdden values mnus latent taxes The latent taxes are those that would occur f the three plusses lsted above flowed through ncome. One can argue ad nauseam about whch fnancal statement to start wth: statutory or GAAP. Clearly, whole chapters of lengthy fnancal accountng books can be wrtten about the exact treatment of the other tems. And actuares can go on for days about how to dscount loss reserves, at what nterest rates, etc. We do not wsh to prescrbe too much here. Snce we ntend ths to be an nternal vew, we beleve t s up to the ndvdual companes and ther techncal staffs to decde how exact a measurement they want. The man thng s to do somethng along these lnes. Don t worry too much about dottng s and crossng t s. Snce there are so many fuzzy ssues and dffcult-to-measure varables n any endeavor lke ths, tryng to be overly exact s wasted effort. CARepaper\paperFN9.doc 7

8 The man pont s to devse for your company some measure of rsk bearng captal n order to gve management a reasonably accurate pcture of the amount of captal they have avalable to support current and possble future busness. 3. How Much Captal Do You Really Need? Rsk Adusted Captal (RAC) Perhaps the queston that should be asked frst s: Why must we have any captal at all? If we were dealng wth a stuaton where run-off of current labltes and the earnngs on current assets were completely predctable and where the company was not about to assume addtonal labltes and assets n the comng year, there would be no need for captal. The concept of captal makes no sense wthout the concept of rsk. And rsk has entrely to do wth the unpredctablty of future events. The clams run-off wll never be the same as predcted; the future earnngs on and the future values of current assets wll be, except n unusual crcumstances, also unpredctable. And of course future assumed rsk-transfer busness by defnton s unpredctable. Captal s necessary for the future. It s not a statc concept for ether clams run-off or for ongong busness. Ths tells us why NAIC rsk-based captal or most ratng agency models do not gve us good answers to the queston of how much captal do you really need. These are relatvely smple models; they are quck n drty, geared to adequacy, not CARepaper\paperFN9.doc 8

9 optmzaton. They usually have faulty thermostats, employng smple ratos of premum or loss reserves whch ndcate less requred captal when rates or reserves are nadequate, whch s of course exactly when you need more captal. They also don t recognze management or shareholder rsk-level preferences. Lke fnancal statement captal, they are retrospectve, not prospectve. Fnally, they are not easly translatable to lnes of busness, types of contracts, proft centers, etc., n a manner that s useful for supportng busness decson-makng. We may classfy the rsks we should consder when defnng rsk adusted captal for an nsurance company. (3.1) Insurance company techncal rsks Underwrtng rsk Clams Ratng system bases: parameters, formulas, etc. Some actuares would further splt ths accordng to the concepts of parameter rsk versus process rsk, or splt even further wth the concept of model specfcaton rsk. Underwrtng cycles Investment rsk Market rsk: stock market, nterest rate, foregn exchange Default CARepaper\paperFN9.doc 9

10 Lqudty Etc. Credt rsk Rensurance Accountng balances due Letters of credt Etc. Note that we consder only techncal rsks, gnorng softer concepts whch mght be gathered under the rubrc management rsk. These other knds of rsks are better handled outsde of a techncal model. What crtera do we want our defnton of rsk adusted captal to satsfy? We want RAC to be the level of captal an nsurance company needs to wrte ts busness. Among many possble crtera, we select the followng. (3.2) Crtera for RAC It must meet specfed management rsk and survval crtera. It should quantfy the rsk/return trade-off for all rsk exposures. It must be useful for makng approprate rsk-based busness decsons. Management rsk crtera have to do wth the publc statements of the company s results. These crtera may have to do wth year by year fluctuaton of results or wth downsde potental. Although fluctuatons are annoyng, the real fear of management CARepaper\paperFN9.doc 10

11 s downsde potental. They fear that an event or a seres of events may occur that mght cause the company s publcly-perceved captal to fall far enough to nterfere wth the company s ablty to contnue normal busness and also to rase serous questons about the company s contnuaton. Snce t s absolutely crtcal that the model reflects management rsk tolerance, t s absolutely crtcal for management to understand enough of the model so that they can understand what s beng asked of them, so that ther opnons are translated accurately nto the model structure and parameterzaton. Thus we propose a very smple, non-black box model for RAC. There are three steps n constructng our very smple RAC model. (3.3) A very smple RAC model Management specfes a smple rsk tolerance rule. The probablty dstrbuton of the company s result s estmated for the tme perod specfed by the management rsk tolerance rule. RAC s set to be the mnmum RBC necessary at the begnnng of the tme perod so that the RBC at the end of the tme perod satsfes the management rsk tolerance rule. As an example, n ths paper we wll use a very smple management rsk tolerance rule. (3.4) A very smple management rsk tolerance rule CARepaper\paperFN9.doc 11

12 Defne the management Rsk Tolerance Level (RTL) to be that value of RBC necessary to mantan a gven external ratng, e.g., A.M. Best A ratng, S&P BBB ratng, etc. Wth a specfed probablty, e.g., 90%, 95% or 99% At the end of a tme perod of one, two or n year(s). You can see that ths s ndeed a very smple management rsk tolerance rule. To smplfy our dscusson, let us assume that the probablty s 99% and the tme perod s one year. A tme perod of one year s not long enough to completely model the effects of potental shocks to captal caused by the manfestaton of long-latent clams. And of course a sngle probablty level s also very smplstc: why not use 99.5%? 98%? And of course management has more on ther mnd than the company s A.M. Best ratng. However, let us walk wth management before we make them (and ourselves) run. Ths defnton of RTL s the same as the defnton of u C, the early warnng lmt of captal n Daykn, Pentakänen and Pesonen s Practcal Rsk Theory for Actuares [ref. 3.1, p.365]. Note that the RTL s defned to be a mnmal level of RBC, but yet the frst crteron refers to a company s selected external ratng that utlzes one of the publcly-perceved types of captal. Thus we must construct a mappng of the RTL level of RBC onto the selected external ratng s captal level. Rather than gettng bogged down n ths constructon, we leave ths detal to the reader (remember not to worry too much about s and t s.). CARepaper\paperFN9.doc 12

13 By the company s result durng the tme perod (n our case, one year), we mean smply the change n RBC from begnnng to end. (3.5) Company s Result CR = { endng RBC} mnus { begnnng RBC} Note that CR s a calendar year concept. CR may be thought of, and modeled, as the sum of three components. (3.6) CR = company s calendar year underwrtng result plus plus company s calendar year nvestment result company s calendar year credt result A smple graph of the probablty densty functon of CR s llustrated n (3.7). CARepaper\paperFN9.doc 13

14 (3.7) CR probablty densty functon 1% $0 Expectaton $Result Note that the dstrbuton, whose random varable s essentally calendar year premum plus nvestment result mnus expenses mnus ncurred clams, s decdedly non-normal. It s skewed to the left snce the dstrbuton of ncurred clams s skewed to the rght [ref ] and the dstrbuton of the nvestment result s usually modeled to be essentally normal [ref. 3.4]. What else can we say about the dstrbuton of CR? The expectaton s the expected (planned?) result for the calendar year. The dstrbuton obvously depends upon the degree of dversfcaton n the company s underwrtng, nvestment and credt rsk portfolos: the more dversfed (lower correlaton), the narrower the spread. We can now construct a smple pcture of how RAC s defned. CARepaper\paperFN9.doc 14

15 (3.8) Defnton of RAC RBC Expected RBC RAC RTL Tme 1% (year) 0 1 year Gven ths smple model and defnton of RAC, we have the followng relatonshps. (3.9) RTL = RAC + CR 1% or RAC = RTL - CR 1% where CR 1% s the frst percentle of the dstrbuton of CR. In order to test our understandng of RAC (may we say RACology?), we can ponder the followng results. (3.10) Some smple RAC results As dversfcaton ncreases (lower correlaton among rsk portfolo segments), RAC decreases. Thus the amount of RAC relatve to rsk CARepaper\paperFN9.doc 15

16 volume, e.g., premum, loss reserves, assets, etc., provdes one measure of dversfcaton. As RTL decreases, RAC decreases. As the probablty (99%) decreases, RAC decreases. As the tme perod decreases, RAC decreases. As RAC decreases, the company s RBC can be reduced or addtonal busness can be wrtten. As a consequence, the company s needed target prcng margns wll decrease. 4. How To Estmate RAC: Underwrtng Model Our smple RAC depends upon the dstrbuton of CR, the company s calendar year result, and CR has three components: underwrtng, nvestment and credt results. The frst step s to estmate the dstrbuton of the company s calendar year underwrtng result. We defne the underwrtng result, CR U, as follows: (4.1) CR U = calendar year net earned premums mnus calendar year net expenses mnus calendar year net ncurred losses all dscounted at selected rsk-free nvestment returns The net result should however not be modeled drectly, but va a model for the gross result and a separate rsk transfer model for ceded rensurance. Ths approach then CARepaper\paperFN9.doc 16

17 allows us to address separately n the credt result model the mpact of the credt rsk arsng from the ceded rensurance. In the followng we wll descrbe the modelng of the gross result. Why complcate the underwrtng model by reflectng rsk-free nvestment ncome? Why not smply leave all the nvestment ncome n the nvestment result? The reason s that once you have a model for RAC, nevtable questons arse about the rsk/return contrbuton of the varous components of the model. Management wll qute rghtly want to know whch busness segments are contrbutng ther far share and whch are not. To push the RAC model of returns down to busness segment level requres a corporate-wde busness evaluaton system reasonably consstent wth the RAC methodology. It s easy to see that f such a busness evaluaton model s to properly evaluate underwrtng results, t must reflect some knd of nvestment ncome to be able to accurately evaluate the relatve values of the varous short and longer-tal busness segments. Many actuares consderng ths ssue have opted to reflect some knd of rsk-free nvestment ncome only. The thought s that addng n total nvestment ncome would unduly dstort the dstrbuton of underwrtng results because of the ncluson of too much nvestment rsk. It s thought that t s better to account for ths addtonal rsk elsewhere, n the nvestment model. But how should nvestment ncome be reflected n calendar year results? In order to have a good underwrtng evaluaton model, calendar year results must be modeled by frst modelng accdent year or polcy year results, so that premums, expenses and losses can be ted together for dfferent exposure perods. Rsk-free nvestment CARepaper\paperFN9.doc 17

18 returns are used to dscount all cash flows arsng from each accdent or polcy year to a sngle evaluaton date. These rsk-free returns may dffer for each year. For the calendar year result, the calendar year dscounted cash flows can reflect any changes n each accdent or polcy year s results durng the calendar year that were not expected at the begnnng of the calendar year. For the smplcty that arses from havng non-overlappng exposure perods, you mght choose to model accdent years nstead of polcy years, as we do. So now we are n the stuaton of modelng the dstrbuton of the dscounted change n result durng the next calendar year for each past accdent year, and also for the next accdent year. A stochastc model for premum and loss development s most helpful here. The premum model s smpler than the loss model except for the ncluson of retrospectve or other later premum adustments and payments. But snce the really sgnfcant premum changes rely upon changes n loss evaluaton, and can thus be modeled as a functon of the losses, let us concentrate upon the modelng of the losses. We want a stochastc model for accdent year losses and the calendar year ncurred loss development thereof. There are many such models n the actuaral lterature to choose from [ref ]. Whchever model s selected, we need a reasonably good parameterzaton n order to produce reasonably good answers remember the garbage-n-gospel-out syndrome? A reasonably good parameterzaton for the accdent year loss dstrbuton can be obtaned from hstorcal nformaton sutably adusted to future level by the followng steps. CARepaper\paperFN9.doc 18

19 (4.2) Loss dstrbuton modelng steps 1. Defne future potental maor catastrophes. 2. Flter the maor cats out of the hstorcal loss data. 3. Model the fltered, non-maor cat losses, adusted to future level. 4. Model the future maor cat scenaros. 5. Glue them back together. The maor cats are those large loss events whose presence or absence from the hstorcal loss data dstorts the estmaton of future loss occurrence or loss run-off potental. These maor cats can be ether natural or man-made catastrophes. Examples of realzed maor cats dstortng recent loss data are Hurrcane Andrew, the Kobe earthquake, asbestos and polluton clean-up. Dependng upon the company s nsurance portfolo, there may be others. Ths s an mportant pont: what consttutes a maor cat event for a partcular company depends upon the company s partcular nsurance portfolo. An example of a maor cat whose absence dstorts the hstorcal loss data, and thus the extrapolaton to the estmate of future loss potental, s the non-occurrence of an earthquake centered on the New Madrd fault. The future occurrence of ths event s beleved to be very possble and of very large loss potental, but yet there has not been an occurrence snce CARepaper\paperFN9.doc 19

20 Maor cats are very rare events that may be dffcult to dentfy and are certanly dffcult to quantfy. Yet these events are the key to understandng and measurng nsurance company underwrtng rsk. Let us separate the maor cat scenaro modelng nto two types: natural and manmade. Natural maor cats are easer to model than man-made. Much data exsts for smaller and medum-szed natural catastrophes, and data exsts for some larger events lke Hurrcane Andrew and the Kobe earthquake. Rensurers especally have devoted much tme and effort analyzng nsurance exposure to natural catastrophes, and there are some reasonably good, commercally avalable models to quantfy the exposure of any nsurance portfolo. The models seem to be dong a reasonably good ob estmatng loss severty. The man problem s the estmaton of loss frequency, the nverse of whch s sometmes referred to by underwrters as return perod. The more dffcult problem s the modelng of man-made maor cats. These are loss events arsng from the unknown rsks of technologcal, economc, legal and socal development. Ths development may nclude the expanson of nsurance coverage for what had been consdered to be busness rsks. If we take asbestos and polluton clean-up as canoncal examples, we can say that man-made maor cats have the followng characterstcs. CARepaper\paperFN9.doc 20

21 (4.3) Characterstcs of man-made maor cats Arsng from technologcal, economc, legal and socal development No sngle, well-defned event causng all the clams Long clams dscovery perods Unknown number of clamants No geographcal lmtaton Modelng man-made maor cats s very dffcult. There s great uncertanty regardng approprate model structures and realstc parameter values. Hstorcally, we have had so far only two maor events whch mght be consdered to be man-made maor cats: asbestos and polluton clean-up, and the ultmate nsurance losses from these two events are stll very much unknown [ref. 4.4]. But snce these man-made maor cats are so mportant to the evaluaton of future loss occurrences and loss run-off, and thus to the evaluaton of rsk adusted captal, we must do somethng. The modelng of these man-made maor cats s so complex and yet so mportant that t deserves a secton to tself. So we wll put off ths modelng dscusson untl the next secton. Let us temporarly assume that we have successfully modeled these man-made maor cats, and thus contnue the dscusson of the underwrtng model. The fltered loss dstrbutons may be modeled usng standard actuaral methods. We wll want to create the dstrbutons of the next calendar year ncurred losses arsng from each prevous or current accdent year and also the next accdent year. The standard methodologes tell us to segment the company s nsurance portfolo nto ts CARepaper\paperFN9.doc 21

22 maor components. Some of these components may be sngle contracts large enough and sgnfcant enough to be analyzed and modeled separately. In addton to lne of busness, a well-dversfed company may also need to consder geographc area. Sutable hstorcal exposure and loss data must be analyzed, model structures determned and parameters estmated. The models can then be extrapolated to the next calendar year. Note that ths extrapolaton tself ncreases uncertanty because of future nflaton and market rsks. Most actuares would say that ths ncreases parameter rsk. It s mportant to also model and estmate correlaton among the busness segments, both loss event correlaton and prcng or rate-level correlaton. The loss modelng obvously depends upon the exposure estmates by year. And let us not forget that the modelng of premums and expenses depends upon the ratng/underwrtng cycle and the degree of prcng or rate-level correlaton among the lnes. The model for the fltered losses s combned wth the models for natural and manmade maor cats to yeld the dstrbuton of gross ncurred loss for the next calendar year. Combne ths wth the model for premums and expenses and rsk-free nvestment ncome on the cash flow to obtan the dstrbuton of the underwrtng result for the next calendar year. Now let us return to the modelng of man-made maor cats. CARepaper\paperFN9.doc 22

23 5. Modelng Man-made Maor Catastrophes Before descrbng an approach to the modelng of man-made maor cats, we want to pont out the goal once more. Both the natural and man-made maor cats have a sgnfcant mpact on the company s result, affectng the tal of the loss dstrbuton, and thus the calculaton of RAC. But snce they occur wth such low frequency, they cannot be modeled approprately on the bass of hstorcal loss records only. Ths s especally true for the man-made cats. So nstead, we model them usng addtonal nformaton. Thnk of t ths way. Instead of usng only statstcal and actuaral methods to model the tal of the loss dstrbuton, we want to take nto account as much nformaton as possble. Ths nformaton comprses hard data such as past loss experence, portfolo nformaton and market nformaton, but also soft factors such as expert-knowledge and gut feelng. In addton, qute a bt of pure guesswork s necessary. Some mportant ssues related to the modelng of man-made maor cats are llustrated wth followng example. Suppose we ask ten experts to estmate the frequency of an ol tanker polluton event wth an mpact comparable or worse to the Exxon aldez accdent. We wll probably get more than ten answers! Ths s not only because of dfferent opnons among experts, but also because of a dfferent understandng of the queston: what do we mean by comparable mpact? Is t the mpact on the envronment, on the socety, on the economy or on the nsurance ndustry? Are we askng for the expected frequency n the next year, n the next 10 years or n the next 100 years? Are we askng for the frequency of ol tanker accdents only, or do we CARepaper\paperFN9.doc 23

24 want to nclude ol platforms as well? Are we askng for the frequency ust for Alaska or are we nterested n the worldwde number of smlar events? Because of ths ambguty, we must accept the fact that there cannot be a sngle correct answer. We wll always end up wth a set of possble solutons. Obvously, there s not only uncertanty related to the stochastc nature of the modeled events. The dstrbutons used to descrbe ths stochastcty are also uncertan. Ths s usually descrbed as model and/or parameter rsk. Whenever possble, ths uncertanty should also be ncluded n the overall RAC model. The tal of the loss dstrbuton to be modeled should represent all events whch mght have a maor fnancal mpact on the company. In order to derve a reasonably accurate dstrbuton, we want to quantfy the mpact (severty) and the occurrence probablty of all relevant events. Ths s mpossble. Therefore we must restrct the evaluaton to a lmted number of representatve scenaros. In dong so, we can exactly defne whch events we want to consder and whch assumptons we want to make. For each such specfc event, t s then possble to quantfy the fnancal mpact on the company (ths s a sort of stress testng). Much more dffcult s the estmaton of the occurrence frequency of the events represented by each representatve scenaro. We could of course also start wth the frequency of the events and then try to quantfy ther severty n a second step (what s the mpact of an event expected to occur wth a frequency of 0.01?). It should be clear that there s not a unque methodology for modelng man-made maor cats. The modelng method depends on the nature of the rsks, the lne of CARepaper\paperFN9.doc 24

25 busness, the avalable nformaton, etc. A model for man-made maor cats wll never be complete, but wll have to be adapted and modfed over tme n an ongong process. The modelng of future man-made maor cats nvolves underwrters, actuares, scentsts, engneers, clams people and fnancal analysts. The steps nvolved are as follows. (5.1) Modelng man-made maor cats Defne the characterstcs of a maor cat event Identfy potental maor cat exposures Estmate the frequency probablty of each maor cat event Estmate the severty dstrbuton of each maor cat event Translate all ths nto nsurance coverage We have already dscussed some defnng characterstcs of man-made maor cats. But let us restate them somewhat dfferently. (5.2) Characterstcs of man-made maor cats No sngle, trggerng event Unknown temporal duraton (development of loss exposure over many years) Unknown geographcal boundares (geographc development from local to global) CARepaper\paperFN9.doc 25

26 Lmted knowledge of event frequency and severty probabltes Lmted knowledge of nsured values because of unknown: - lnes of busness exposed - types of clams (BI, PD, fnancal) - number of clams, plantffs, nsureds - amount of compensaton per clam Lmted knowledge of the reacton of socety and nsurance markets (If losses are to be pad only n the future and f the ndustry can collect enough addtonal premums and f the losses need not be reserved too quckly, there may be less calendar year mpact.) The frst step n dentfyng the maor cat exposures s to hold branstormng sessons of underwrters, actuares, clams people, scentsts, engneers and fnancal analysts to lst scenaros whch mght generate maor cats. Let us call these scenaros threats. An example of such a lst mght look somethng lke ths. CARepaper\paperFN9.doc 26