Strictly Exam 5 Vocab- No formulas

Exposure

basic unit of risk underlying insurance premium, measures how much risk the insurer is subject to before losses

Exposure base

unit used to measure risk, price, and compare risk across policies

Criteria for Exposure Bases

Proportional—> scales directly with expected losses

Practical—> objective, easy and inexpensive to obtain and verify

Precedence—> considerate of historical precedence as it is costly for industry to change an existing exposure base

reported losses

incremental paid losses + change in case reserves during time period

Main Considerations for aggregating to appropriate time grouping

1.) Match premium and exposure to losses, need to be on like for like basis

2.) Use most recent data available

3.) Minimize cost of data collection retrieval

Time Grouping Analysis: Calendar Year Pros and Cons

Pros: results are final immediately after year is over

Cons: Poor matching in time between premiums/exposures and losses

Time Grouping Analysis: Calendar/Accident Year Pros and Cons

Pros: better match in timing between premium and losses. Best for short tailed business

Cons: future development must be estimated since AY losses develop over time

Time Grouping Analysis: Accident Year Pros and Cons

Pros: slightly better than calendar/accident year

Cons: premium and exposure data subject to development

Time Grouping Analysis: Policy Year Pros and Cons

Pros: true match between premium and exposures. best for long tailed business

Cons: longest of any grouping to develop

Time Grouping Analysis: Report Year Pros and Cons

Pros: # of claims at YE known, helpful in estimating IBNER

Cons: not useful for estimating IBNYR

Types of External Data

Statistical plans: aggregate data cross companies and produce analyses or rates that companies can use

Other aggregated industry data

Competitor rate filings+ manuals

Other 3rd party data: economic or geo-demographic data

Principles of P&C Insurance Ratemaking

1.) Rate is estimate of expected value of future costs

2.) Rate must be sufficient to pay claims, cover expenses, and provide return for taking on the risk

3.) Rate must be adequate at individual level

4.) Rate is appropriate if it is not excessive, not inadequate and not unfairly discriminatory

External Influences of Rates

traffic density, urbanization/population density, legal environment, medical costs, repair costs, weather/cat exposure, crime/fraud, economic conditions, infrastructure

Types of Adjustments to Historical Data (8)

Large events and anomalies

One time changes

Trends

Development

Load for UW expenses and ULAE

Set UW profit goal

Reinsurance costs

Credibility

Adjustments to Historical Data: large events and anomalies

replace large claims and cat events in historical data with long term average or modeled estimate

Adjustments to Historical Data: one time changes

adjust for known difference from future period due to rate changes, law changes, coverage changes and benefit changes

Adjustments to Historical Data: trends

forecast for changes in cost and mix of business

Basic limits

limits assumed in insurer’s basic rate when calculating premium. Losses above may be handled separately with ILFs or excess loss loadings

Rating Factors

used to bring premiums to basic limits when wanting losses to basic limits

basic limit premium = actual premium/ rating factor

Excess loss loading

need to decide on loading which accounts for portion of losses above the cap

Non pricing measures to deal with risks from cat losses

restrict writings in high risk areas

require higher deductibles in high risk areas

purchasing reinsurance

Rate changes

adjusting for price when cost or risk changes

changes indicate a change in price charged per unit of exposure

Direct Effect

obvious impacts on premium, losses, or expenses resulting from a change

Indirect Effect

impact to premium, losses, or expenses from changes in human behavior that are consequences of one time changes

difficult to quantify but is incorporated into trend adjustments

On-Leveling Premium

restates historical premium at current rate levels

want to charge same amount each time period regardless of ups and downs so premium is table and consistent

Methods to On Level Premium

Extension of Exposures

Parallelogram Method

Use Actual writing distributions and group data by rate level

Extension of Exposures

take old policies and pretend today’s rates were in effect back then. Then recalculate what the premium would have been

Pros: most accurate method

Cons: getting detailed data, computing power needed, hard to make assumptions for new rating variables with no historical data

Parallelogram Method

used to group policy data and adjust historical premium by average factor for each historical period

pretty much weighted avg of rate per each period on on exposure period graph then divide it from most recent rate

Pros: quick to calculate

Cons: assumes policies are written evenly throughout historical period and can be inappropriate for class ratemaking if effects vary by class

Trends

adjusting historical losses to future cost levels due to changes in underlying costs of claims

Overlap Fallacy

no overlap between development and trending

trending: reflects difference in ultimate from one historical period to the next (goes down triangle rows)

Development: brings data from each historical period to ultimate level ( goes across columns in triangle)

Development

changes overtime to costs or premiums within an exposure period

Reasons for Changes in Loss Triangles

Changes in case reserve adequacy

Changes in settlement rates

Changes in mix of business

Growing or shrinking book of business

Tort Reform

Chain Ladder/ Development Method: definition

uses past development patterns and applies to latest data forecast to estimate ultimates

do not apply trends to this method!!!!!!

Chain Ladder/ Development Method: assumptions

-future claim development is similar to prior development

-claims observed for immature period tell you something about claims yet to be observed

-consistent claims processing
-stable mix of claims types, policy limits and deductibles, reinsurance limits

Ways to determine a tail factor

specialty study

Industry benchmarks

fitting curve to LDFs and extrapolating tail

using best judgement

Methods for Pricing UW Expenses

All Variable Expenses

Premium Based Projection Method

Exposure/Policy based Projection

All Variable Expense

treat all UW expenses as variable to premium

find ratios(variable and fixed) of all expenses and to get variable expense ratio. By doing this you’re assuming all expenses are variable

Pros: easy to apply and works best when expenses vary with premium
Cons: inaccurate results if some expenses are truly fixed

Premium Based Projection Method

separately calculates fixed and variable expense ratios

pros: more accurate then all variable expense, simple and recognizes fixed costs exist

cons: historical expenses may not reflect future expectations, changes in premium expenses can distort ratios, allocating countrywide fixed expense by prem can unfairly charge states with increased avg premium more

Permissible Loss Ratio

maximum LR an insurer can have while still achieving its target profit

Rate Indication Methods

Pure Premium Method

Loss Ratio Method

Overall Rate Indication Purpose

determine whether current rates are adequate, excessive or inadequate and to calculate the needed rate change

Indicated rate

rate level that covers expected losses+ expenses + target profits

Types of Coverage Triggers

Occurrence

Claims Made

Occurrence

coverage depends on when accident occurs regardless of reported date (subject to statute of limitations)

Claims Made

coverage depends on whether claim is reported during the policy period, does not care about when the claim actually happened as long as event happens after specified retroactive date

reduces report lag from pricing risk compared to occurrence

Tail coverage

policy covering accident occurring during the claims made term but reported later

usually used when switch from claims made to occurrence policy

Report Year Diagram

used to understand which ultimate loss costs are covered by which policies

Report Year—> signifies when claim was reported
Report Lag—> Report Year - Accident Year

Claims Made Ratemaking Principles

Claims made will cost less than occurrence as long as cost increases

Claims made adjust to trend changes faster so pricing errors from sudden trend shifts are usually smaller

Shift in reporting patterns are less likely to affect cost of a mature claims made vs occurrence

Claims made reduce risk of reserve inadequacy

Investment income is less under claims made vs occurrence policies

Risk Classification

group risks with similar risk characteristics for purpose of setting price, helps mitigate adverse selection

Adverse Selection

insurer underprices high risk insured relative to competition causing risker individuals to concentrate in that insurers poll and lead to losses

Favorable selection

insurer attracts lower risk insured than average

Skimming the cream

identifying a lower cost group of insured that has not been identified by competition, and recognizing identifying difference in underwriting or marketing instead of rates

Criteria for evaluating rating variables

Statistical Criteria

Operational Criteria

Social Criteria

Legal Criteria

Statistical Criteria

difference in loss costs between classes is real, different groups have truly different risk levels

risks within same class should have similar expected loss levels

need enough stable data to produce reliable estimates

Operational Criteria

classes clearly defined, practical to administer, and easy to verify without excessive cost or manipulation

Social Criteria

classification should be fair, socially acceptable, affordable, behaviorally relevant and respectful of privacy

Legal Criteria

in compliance with laws and regulations

Univariate Classification

covers how to determine indicates rates for a single variable at a time

how much more or less different risk groups should pay relative to each other

studying one risk factor at a time

Relativity

measure how much more or less a risk group is expected to cost compared to a baseline group

Univariate Pricing Approaches

goal: find indicated relativity to a base class

methods- performed with and without credibility

pure premium approach

loss ratio approach

adjusted pure premium approach

Pros and Cons of Univariate Analysis

pros: simple to calculate and intuitive

cons: does not properly account for impact of correlated variables

Multivariate Classification

analysis incorporates impact of multiple variables at a time

most common method is Generalized Linear Models (GLMs)

Generalized Linear Model

create formulaic relationship between multiple predictor variables and a response variable

GLM Diagnostics

standard errors

deviance tests

time consistency

validation test

GLM Diagnostics: Standard Errors

measures how much that estimate would vary from sample to sample

smaller error—> more precise

GLM Diagnostics: Deviance Tests

compares models, commonly used in deciding whether to fit GLM with or without the variable in question

GLM Diagnostics: Time Consistency

estimated parameters consistent overtime

GLM Diagnostics: Validation test

measure model performance on unseen data

Data Mining Techniques: definition

help identify, evaluate, and quantify relationships between risk characteristics and loss experience

Data Mining Techniques: methods

Factor Analysis

Cluster Analysis

CART( Classification and Regression Trees)

MARS( Multivariate Adaptive Regression)

Neural Networks

Factor Analysis

reduce number of variables needed in classification

most common types is principle components

Cluster Analysis

combine similar risks into groups

MARS( Multivariate Adaptive Regression)

turn continuous variables into categorical variable

Neural Networks

can help identify unknown interactions between variables

Challenges of Territorial Ratemaking

highly correlated with other rating variables

Set territories to small areas which have limited credibility

Increased Limit Factors (ILF) Purpose

used to determine how much premium should increase as policy limit increases

Increased Limit Factors (ILF) Assumptions

-all UW expenses and profits are variable and don’t vary by limit

-frequency and severity independent

-frequency is the same for all limits

Limited Average Severity at limit H

severity assuming every loss regardless of actual policy limit is capped at H

Reasons for Deductibles

lower premium for insured because less coverage
eliminates claims below deductible
incentive for insured to mitigate losses since they pay amount below deductible
reduces cat exposure

Loss Elimination Ratio (LER) definition

measure percentage of expected losses that are eliminated by applying a deductible

Loss Constant

flat charges applied to WC premium to cover expected small losses that are not fully reflected in experience rating. This equalizes loss ratios between small and large risk

Insurance to Value (IVT)

ensures a property is insured for an amount close to its replacement value

coverage amount/ replacement cost

Issues when properties are insured less than full replacement cost amount

1.) Insured will not be covered in the event of a total or near total loss

2.) If insurer assumes every home is insured to full replacement value but some home are underinsured
- insured value used in rating is too low
-actual potential loss is based on full replacement cost
-insurer charges too little premium relative to risk

Coinsurance

used to deal with underinsurance

insurer requires property to be insured a minimum percentage of its value, if not there will be a penalty which will be the insurer only paying a fractions of the loss (pays ITV%)

Complements of Credibility Criteria

Accurate: has low variance

Unbiased: on average, equal to what you are estimating

Statistically independent from own data to prevent compounding errors

Easy to compute: otherwise hard to explain

Logical relationship to base statistic: easy to justify to others

Complements in First Dollar Ratemaking Methods

1.) use loss costs from larger group that includes group being rated

2.) Use loss costs from larger group that is related to (but does not include) the subject

3.) rate change from larger group applied to present rates

4.) Harwaynes Method

5.) Trended Present Rates

6.) Competitor rates

Experience Rating

adjust premium based on insureds past claim history on prior policy terms

Experience modification factor

multiplier that adjusts policy’s premium based on insured past loss experience

Experience Rating Plans

ISO CGL

NCCI

Complements in Excess Ratemaking Methods

Increased Limits Analysis

Lower Limits Analysis

Limits Analysis

Schedule Rating

adjust premium for individual risk that are not in premium calculations

premium calculations only capture quantifiable systemwide factors

captures hard to measure, not in data, or unique to individual risk

Large Deductible Policies Considerations

Who will handle claims?

Application of deductible

Deductible processing; who will pay for losses and how

Risk margin

Insured handles claims implications

may hire TPAs

insurer should be cautious insured has less incentive to keep losses below deductible

Insurer paying for all losses implications

will seek reimbursement from insured for loss below the deductible

as a result of paying all losses first:

• insurer will get extra cost for billing and processing

• credit risk in case insured is unable to pay

-both of these are included in expenses in premium calculations

Insurer risk margin implications

insurer is taking on more risk uncertainty, will charge higher margin for this

Retrospective Rating

use insured’s loss experience during the current policy period to determine the current policy period

Premium flow chart

Manual premium —> Standard premium —> Basic Premium —> Retrospective Premium

Manual Premium

premium based on manual rates and exposures before any individual risk adjustments

Standard premium

premium after applying all rating modifications, before retrospective adjustments

Basic Premium

portion of premium that covers fixed costs (not losses)