1、Research Working Party on the Public - Access DFA ModelPhase I Work Product:Documentation and Evaluation of Componentsof Existing ModelMorgan H. Bugbee, Co-ChairmanPatrick J. Crowe, Co-ChairmanJoel E. Atkins, MemberRobert J. Azari, MemberThomas P. Conway, MemberWilliam D. Hansen, MemberAbstractThe R
2、esearch Working Party on the Public Access DFA Model has published the attached report to document and evaluate the components of an existing DFA model which has been available over the internet. Under the supervision of the CAS-Dynamic Risk Modeling Committee (DRMC), the working group was formed to
3、 evaluate, update and correct the DFA model which was out of date and required thorough documentation. The underlying goal of the working group is to create an accepted, documented and widely available DFA model template. The revised DFA model and its documentation are the basis for future call pape
4、rs and research projects involving DFA modeling.The attached paper is the documentation of the revised DFA model. The first section provides an overview of model functionality. In the subsequent sections, additional documentation is provided for each MS Excel model worksheet which describes the func
5、tionality, assumptions and errata. After reading the paper a user should have an understanding of the inner workings of the model, how to input starting assumptions, trigger model simulation runs and generate output. The documentation should enable the user to research and develop enhancements to th
6、e model.- 1 -Table of ContentsSECTION PAGEINTRODUCTION .2ORGANIZATION OF DOCUMENTATION.9UNDERWRITING INPUT SHEETS: XYZ COMPANY HMP-I; XYZ COMPANY WC-I.10UNDERWRITING OUTPUT SHEETS: XYZ COMPANY HMP-O; XYZ COMPANY WC-O15UNDERWRITING OUTPUT SHEET: LINE SUMMARY .18REINSURANCE INPUT.19CAT LOSS GENERATOR
7、.21INVESTMENT INPUT WORKSHEET .24BOND 1 THRU BOND 5 WORKSHEETS.27BOND SUMMARY WORKSHEET.30STOCKS WORKSHEET .31GENERAL INPUT WORKSHEET .33TAX CALCULATOR WORKSHEET.35SIMULATION DATA WORKSHEET.38RANDOM NUMBERS WORKSHEET.40INVESTMENT DISTRIBUTION WORKSHEET .41OUTPUT SHEET .43STATUTORY SUMMARY.47GAAP SUM
8、MARY.49APPENDIX A. 51- 2 -IntroductionThe Dynamic Risk Modeling committee has established goals for Dynamic Financial modeling, which are outlined in the four phases below. The CAS Working Party on the Public Access DFA Model has been formed to document and evaluate the public access dynamic financi
9、al modeling tool that is available for download from the internet. This modeling tool was built in the mid nineties by the actuarial firm of Miller, Rapp, Herbers and Terry along with a team from the University of Illinois. The working group has agreed to update and enhance the model through several
10、 phases of work described as follows:Phase 1: Documentation and evaluation of the components of the existing modelThe current components being evaluated and documented include:1. Interest rate and inflation generator2. Investment module3. Financial statement development4. Loss development and paymen
11、t patterns5. New business6. Jurisdictional risk7. Catastrophe module8. Underwriting cycle9. Taxation10. OutputPhase 2: Identification of selected enhancements to the modelPhase 3: Implementation of selected enhancementsPhase 4: Ultimately, consider an “open source” framework for the public-access mo
12、delThe following document is the first step in addressing the working groups first phase. This paper describes the cumulative work done to review and document the current public access DFA model.General Description of Model FunctionalityThe Public Access DFA model is a spreadsheet based stochastic s
13、imulation model which simulates and property casualty insurance companies financial conditions over a five year time horizon. The model generates financial statements including balance sheets, income statements - 3 -and IRIS ratios. The model can also capture and display expected values and distribu
14、tions of any variable included in the model.The model relies on input assumptions for a series of financial and underwriting variables listed below:Investment Assumptions1. Short-term interest rate2. Term structure3. Default potential4. Equity performance5. Inflation6. Mortgage pre-payment patternsU
15、nderwriting Assumptions1. Loss frequency and severity2. Rates and exposures3. Expenses4. Underwriting cycle5. Loss reserve development6. Jurisdictional risk7. Policyholder aging phenomenon8. Payment patterns9. Catastrophes10. Reinsurance Terms11. TaxesModel outputs can be produced in a variety of fo
16、rms but standard output includes:1. 5-year projections2. Balance sheets3. Income statements4. Loss ratio reports5. IRIS tests- 4 -The flow of information through the public access model is illustrated through the flow chart below:Public Access Model Approach to Modeling Risk The following section is
17、 an excerpt from a paper presented at the 1997 CAS DFA Seminar by DArcy, Gorvett, Herbers, Hettinger, Lehmann and MillerThe risks facing insurers can be classified into two major categories: one for items listed on the balance sheet, and the other based on continuing operations (which would appear i
18、n the operating statement). Furthermore, each of these categories can be subdivided into two further categories. Balance sheet risk consists of asset risk and liability risk. Operating risk consists of underwriting risk and investment risk.Asset risk involves the change in value of an existing asset
19、. For a bond, this could result from a change in interest rates, a change in the debt rating, or default on interest or principal. For an equity, asset risk involves a change in the market price, which could be caused by some of the same factors affecting bond values, or by other changes affecting c
20、ompany profitability or operations. Other assets, such as agents balances, are exposed to default risk.Liability risk is primarily related to the adequacy of the loss reserves. As statutory valuation requires loss reserves to be carried as the nominal value of all future payments, this risk involves
21、 the possibility that total payments will ultimately differ from the indicated estimate. Based on market valuation of loss reserves, however, the risk also includes timing and discount rate components as well as the total payment amount. In addition, liability risk includes the adequacy of the unear
22、ned premium reserve to cover losses that will emerge on existing policies.Underwriting risk is the risk associated with business that the insurer will write in the future, either as new business or renewals of existing policies. This risk includes pricing risk - the ability to obtain adequate premiu
23、m levels on this business - as well as the risk associated with stochastic losses and expenses.- 5 -Investment risk relates to investment income and capital gains to be earned on existing assets and new assets resulting from continuing operations. This is dependent on interest rates and other econom
24、ic conditions.The four risk components are complexly interrelated. An increase in interest rates, for example, would lead to a decline in the value of existing assets (especially bonds), but higher investment income on new investments. Adverse development on loss reserves would generate the need for
25、 premium increases, and impact future underwriting experience. The advantage of a DFA model is that it can allow for this type of interaction. However, a drawback is that these relationships are difficult to quantify. This leads to the need to develop answers to some basic modeling questions before
26、proceeding.Pricing RiskProperty-liability insurers have the opportunity to change the premium level prior to writing new or renewal business. Thus, as expenses or expected losses change, insurers can reflect these changes in the new rate levels. However, two problems can affect the ability of insure
27、rs to charge the correct price. First, since most insurance premiums are set prior to the policy being written, the insurer may incorrectly estimate future experience, causing the price to be either inadequate or excessive. Second, the freedom of insurers to set premium levels varies by state, with
28、some states allowing relatively unrestricted pricing and other states having extensive restrictions. Thus, there are two components to pricing risk. The first component is handled in this model by having the loss ratio (exclusive of catastrophes - see next subsection) be a random variable with the m
29、ean value and standard deviation based on company experience. Loss ratios are simulated by line, with appropriate consideration given in the simulations to correlations of contemporaneous loss experience between lines. The second component of pricing risk is handled by a factor imposing a restrictio
30、n on the ability of a company to make rate changes which are indicated by changes in loss frequency or severity. In our model, a factor of 1 would represent complete freedom to adjust rates in accordance with indications, while lower values are used when companies write in states with restrictive ju
31、risdictional forces.Catastrophe RiskIn addition to normal pricing risk and the inherently stochastic nature of the loss process, property-liability insurers face the risk of a catastrophic loss. Hurricanes, earthquakes, winter storms, and fires all have the potential to significantly affect the fina
32、ncial condition of an insurer. This risk is separated out from the normal pricing risk described above. In this model, catastrophes are handled as follows, for each simulated year:1. The number of catastrophes (by our definition, events of any type causing industry-wide losses in excess of $25 milli
33、on) during the year is determined based on a Poisson distribution, with the parameter based on historical experience.2. Each catastrophe is assigned to a specific geographical area, or “focal point,“ again based on historical tendencies.3. Once assigned to a focal point, the aggregate-industry size
34、of each catastrophe is - 6 -determined, based on a lognormal distribution. The size of the event is affected by the location, as both the type of loss and the amount of insured property exposed to a loss is a function of where the catastrophe occurred. The parameters of the lognormal distribution ar
35、e based on historical industry experience, appropriately adjusted to future cost levels.4. The geographical distribution of the event by state is determined, based on a state-by-state frequency correlation matrix determined from historical patterns.5. The loss is allocated to the company based on ma
36、rket share in the lines exposed to catastrophic risk.Loss Reserving and Adverse Development RiskThis is the major component of liability risk, and one that distinguishes, and complicates, dynamic financial analysis for property-liability insurers. The starting value used for the loss reserve in this
37、 model should be the value indicated by an analysis of the companys historical experience, not just the loss reserve stated in the latest financial report. However, even though the loss reserve is based on an actuarial analysis, it cannot be assumed to be exact - there is likely to be some random de
38、ficiency or redundancy. In addition to the stochastic nature of the loss reserve and payout processes, a complication is the correlation between loss reserve development and interest rates, since both are correlated with inflation. However, whereas the relationship between inflation and interest rat
39、es is well recognized and has been extensively documented, the relationship between inflation and loss development is much harder to quantify. Loss reserving techniques traditionally assume that past inflation rates will continue. If inflation increases over historical (or other forecasted) levels,
40、then future loss payments are likely to exceed the amount reserved. The relationship between inflation and loss development is one area that needs additional research.As mentioned, loss development is subject to further variability unrelated to inflation. This variability is factored into the model
41、by a normal random variable that allows for either favorable or adverse development. The volatility parameter is selected based on the companys size and past development patterns, as well as industry considerations (however, any tendency on the part of management - or the industry - to consistently
42、over- or under-reserve is considered separately, i.e., in the analysis of the appropriate beginning loss reserve level). In years in which the uncertainty regarding court decisions affecting loss payments is higher than usual or when other economic conditions generate greater volatility, this additi
43、onal uncertainty would be reflected by an increase in the loss development parameters. Loss reserve development may also affect rate adequacy. Significant under-reserving, in addition to impacting surplus directly, generates the need for additional rate increases that may, depending on the jurisdict
44、ional environment (as discussed below), be difficult to obtain. Also, rate increases can affect the renewal rates on business, causing an additional effect on a companys operations.- 7 -Jurisdictional RiskIn addition to having the potential to affect the responsiveness of rates to changes in economic conditions, the jurisdictions in
