Workers compensation excess of loss pricing
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Workers Compensation Excess of Loss Pricing. CAS Reinsurance Pricing Seminar Moshe D. Goldberg, FCAS July 29, 2005. Workers Compensation. Workers Compensation characteristics that cause it to differ from other lines of business Extremely long tail Annuity-type benefits

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Workers Compensation Excess of Loss Pricing

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Workers compensation excess of loss pricing

Workers CompensationExcess of Loss Pricing

CAS Reinsurance Pricing Seminar

Moshe D. Goldberg, FCAS

July 29, 2005


Workers compensation

Workers Compensation

  • Workers Compensation characteristics that cause it to differ from other lines of business

    • Extremely long tail

    • Annuity-type benefits

    • Benefits defined by statute, not by courts

      • Indemnity and Medical benefits

      • Benefits, to some degree, vary by state

    • No policy limits

      • Essentially unlimited medical coverage!!

    • True No-Fault system (Or is it?)

Moshe D. Goldberg, FCAS

CAS Reinsurance Pricing

July 29, 2005


Wc s long tail

WC’s Long Tail

  • Discounting of case reserves prevalent

    • Explicit (lifetime pension cases)

    • Implicit (by not inflating projected future payments)

  • Mortality assumptions used in setting reserves

  • Effect of unwinding of discount can be quite large on an excess layer

  • Claims often develop adversely quite late

    • Family stops taking care of claimant

    • Back injuries “creep” into the layer

Moshe D. Goldberg, FCAS

CAS Reinsurance Pricing

July 29, 2005


Example of impact on reinsurer

Example of Impact on Reinsurer

  • An injured worker is expected to live 10 years.

  • Weekly indemnity benefits are 500/wk = 26,000/yr

  • Initial stabilizing medical expenses are 150,000

  • Annual medical expenses are 50,000/yr

  • Initial case reserve = 150k+(26k+50k)*10 = 910k

  • One would expect the loss to the 1Mx1M reinsurer to be zero.


Implicit discount effect

Implicit Discount Effect

  • Suppose that instead of the ongoing medical expenses being 50k/yr, they are really inflating at 6% per annum.

  • The primary company still books the ongoing medical loss at 500k, implicitly discounting them at 6%/yr.

  • Total undiscounted ongoing medical expenses are really 659k = 50k*(1.0610-1)/.06, instead of the booked 500k

  • The total undiscounted loss is 1,069k, and the 1Mx1M reinsurer will see 69k of development

  • Imagine if the time horizon was longer!


Mortality assumption effect

Mortality Assumption Effect

  • Back to the original example (no growth in medical costs), however, instead of a certain 10 year survival, there was a 50% probability of this worker living only 5 years and 50% of living 15 years.

  • Losses paid if the claimant lives 5 years = 530k = 150k+(26k+50k)*5

  • Losses paid if the claimant lives 15 years =1,290k = 150k+(26k+50k)*15

  • With 50% probability, the 1Mx1M reinsurer will see 290k development


Example of tail development for 1mx1m layer

Example of “Tail” Development for 1Mx1M layer


Wc exposure rating

WC Exposure Rating

Moshe D. Goldberg, FCAS

CAS Reinsurance Pricing

July 29, 2005


Exposure rating

Exposure Rating

  • Conceptually, exposure rating WC is no different than other lines

    • Compute overall expected losses

    • Allocate these losses to the layer being priced by a size-of-loss curve.

  • Practically, WC exposure rating is very different than other lines

    • Overall expected loss computation is relatively similar

    • However, the allocation to layer is handled vey differently.

Moshe D. Goldberg, FCAS

CAS Reinsurance Pricing

July 29, 2005


Exposure rating1

Exposure Rating

  • For lines with policy limits, like GL, the rating bureaus publish ILFs, which are based on size-of-loss curves

  • But WC doesn’t have policy limits. So NOW what do we do?

  • Retrospective Rating’s Excess Loss Factors (ELFs) to the rescue!

Moshe D. Goldberg, FCAS

CAS Reinsurance Pricing

July 29, 2005


Terminology of wc size of loss curves

Terminology of WC Size-of-loss curves

  • “Injury Type” : Description of the seriousness of a WC injury

  • “Average Cost per Case” : Average severity

  • “Entry Ratio” : Ratio of a number to the ACPC

  • “Hazard Group” : Set of classes with similar severity distributions. Currently there are four HGs, but the NCCI is looking at adding more.

  • “Excess Loss Factor” : Ratio of expected losses in excess of an entry ratio to the overall losses

Moshe D. Goldberg, FCAS

CAS Reinsurance Pricing

July 29, 2005


Injury types

Injury Types

  • Lost-Time Claim Injury Types

    • Fatal

    • Permanent Total (PT)

    • Major Permanent Partial (PP)

    • Minor Permanent Partial

    • Temporary Total (TT)

  • Non-Lost-Time Injury Type

    • Medical Only

Moshe D. Goldberg, FCAS

CAS Reinsurance Pricing

July 29, 2005


Average cost per case

Average Cost per Case

  • These are the average severities by:

    • State

    • Hazard Group

    • Injury Type

  • They are used in computing entry ratios.

Moshe D. Goldberg, FCAS

CAS Reinsurance Pricing

July 29, 2005


Excess loss factors elfs

Excess Loss Factors (ELFs)

ELF(x) = 1 – [LEV(x)/E(X)]

= 1 – Loss Elimination Ratio at x

The “x” is an entry ratio, so E(X) is, by definition, unity.


Entry ratio elf example

Entry Ratio/ELF Example


Example

Example

  • Suppose we’re pricing the $1M xs $1M layer

  • Expected Loss Ratio = 75%

  • ELF(1M) = 0.13; ELF(2M) = 0.06

  • Losses in the layer = ELF(1M) – ELF(2M) = 7.0%

  • 7.0% of the total losses are in this 1M xs 1M layer

  • Exposure Loss Cost Rate = 75% * 7.0% = 5.25%

  • This still needs to be discounted and loaded

Moshe D. Goldberg, FCAS

CAS Reinsurance Pricing

July 29, 2005


Wc trends

WC Trends

Moshe D. Goldberg, FCAS

CAS Reinsurance Pricing

July 29, 2005


Wc trends1

WC Trends

  • The long tail and unlimited medical benefits add to the difficulty in estimating trends for Workers Compensation.

  • In addition, states can – and do – change the WC benefits, adding to the uncertainty.

Moshe D. Goldberg, FCAS

CAS Reinsurance Pricing

July 29, 2005


Workers compensation excess of loss pricing

Source: NCCI, Inc

Used with permission


Impact of non uniform frequency trend on excess of loss pricing

Impact of Non-uniform Frequency Trend onExcess of Loss Pricing

  • Exposure Rating

    • Shape of the distribution changes, with more of the losses coming from larger claims

  • Experience Rating

    • Measured ground-up severity trend will increase from the reduced frequency of the smaller claims

    • Assuming uniform trend by size of loss, the measured large loss trend will be lower than the measured ground-up trend

    • This impact is mitigated by the less-negative frequency trend

Moshe D. Goldberg, FCAS

CAS Reinsurance Pricing

July 29, 2005


Example1

Example

  • Two types of claims, small and large.

  • In year 1, small claims have average severity of 100k, while large claims have average severity of 500k.

  • In year 1, there are an equal number of small and large claims, say 50 of each claim

  • Average Severity in year 1 is 300k

    = (50*100k + 50*500k)/(50+50)

Moshe D. Goldberg, FCAS

CAS Reinsurance Pricing

July 29, 2005


Example continued

Example, continued

  • In year 2, there are now 40 small claims (frequency trend = -20%), while there are still 50 large claims (0% frequency trend). Total frequency trend = -10%

  • The average severity for each claim type increases 10%

    • Small claim severity = 110k

    • Large Claim Severity = 550k

  • But, the measured overall severity is now 354k

    = (40*110k+50*550k)/(40+50)

    This is an 18% increase!

Moshe D. Goldberg, FCAS

CAS Reinsurance Pricing

July 29, 2005


Workers compensation excess of loss pricing

Source: NCCI, Inc.

Used with permission


Workers compensation excess of loss pricing

Source: NCCI, Inc.

Used with permission


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