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May 7, 2007. CAS Seminar on Reinsurance 2007 Hidden Risks in (Re)Insurance Systemic Risks and Accumulation:. Spencer M. Gluck, FCAS New York. Outline. Section 1: Systemic Risks and Accumulation A: Introduction - Model Structure B: Systemic Risks C: Accumulation Section 2: Examples

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may 7 2007
May 7, 2007

CAS Seminar on Reinsurance 2007Hidden Risks in (Re)InsuranceSystemic Risks and Accumulation:

Spencer M. Gluck, FCAS

New York

outline
Outline
  • Section 1: Systemic Risks and Accumulation

A: Introduction - Model Structure

B: Systemic Risks

C: Accumulation

  • Section 2: Examples

Impact of Systemic Risks and Accumulation

introduction
Introduction
  • A modeling framework that captures important risks that we may have been missing.
  • Important applications:
    • Impact of reinsurance, especially casualty
    • Cross-lines correlation and whole company models:
      • Capital adequacy and allocation
      • ERM
reasons for us p c insurer impairments 1969 2005
Reasons for US P/C Insurer Impairments 1969-2005

2003-2005

1969-2005

*Includes overstatement of assets.

Source: A.M. Best: P/C Impairments Hit Near-Term Lows Despite Surging Hurricane Activity, Special Report,Nov. 2005;

getting the structure right
Getting the Structure Right
  • Catastrophe models “understand” the risk that’s being modeled.
    • The most dangerous risks are those that act in a correlated way on accumulated exposure.
  • We require a model structure for other types of underwriting risk that reflect the impact of correlation and accumulation.
some historical casualty killers
Some Historical Casualty Killers
  • Runaway Trends
    • WC: 1970 through 1990 (California, Texas, etc.)
    • Med Mal: Late 1960’s through early 1980’s (e.g. NY) and then again in the 1990’s.
    • All casualty 1970’s through early 1980’s.
  • Extended Downcycles
    • E.g., early 1980’s, late 1990’s
  • Latent Losses
    • E.g. asbestos, environmental, construction defects

For the risk model to be meaningful, these types of risk must be captured.

systemic risks are crucial
Systemic Risks Are Crucial
  • Systemic Risks:
    • Difficult to Measure
    • Affect all LOB’s -- but
    • Greatest Impact in Casualty
  • Systemic Risks Accumulate
elements of systemic risk
Elements of Systemic Risk
  • Time Related Risk
    • Trend and Development Parameters.
    • Changing Trends
    • Simultaneously impact new business and accumulated reserves.
  • Market Related Risk

Also: Casualty catastrophes

    • But we’re not yet modeling these.
casualty markets are more volatile
Casualty Markets are More Volatile
  • Price is driven by the lowest estimated costs.
  • Long tails increase:
    • Risk of misestimated costs.
    • Positive cash flows.

Therefore:

Long tail casualty market cycles are the most severe.

components of risk other than diversifying process risk
Components of RiskOther than diversifying process risk
  • Limitations of the sample
  • Uncertainty in other analysis parameters
    • Trend factors
    • Loss development factors
    • Payment patterns
  • Market Risks (pricing / underwriting)
    • Imperfect exposure data / on-level process
    • Actual prices achieved differ from targets
    • Risk quality changes (underwriting selection)
  • External Conditions
    • Changes in inflation
    • Changes in insurance loss trends / social inflation
    • Other economic conditions (line specific)
  • Differences in exposure between the data and the future period
summarized elements of systemic risk
Summarized Elements of Systemic Risk
  • Time Related Risk (i.e. the tail)
    • Trend and Development Parameters.
    • Changing Trends
    • Simultaneously impact new business and accumulated reserves.
  • Market Related Risk (i.e. the cycle)

Also: Casualty catastrophes

the risk factor model model structure one lob one ay
The Risk Factor Model Model Structure (one LOB, one AY)
  • Nominal Incremental Paid for accident year i =AYifor a single simulation.
  • Each RV is sampled once per simulation.
  • RV’s are mutually independent

AYi = A x B x C(Fi-E) x Di

E : Average date of payment in historical data

Fi : Average date of payment for period i

risk factor model components process risk
Risk Factor Model Components: “Process+” Risk

AYi =Ax B x C(Fi-E) x Di

  • Input Loss Distribution
  • Reflects both process risk and sample-size related parameter risk
    • The data “sample” in this case is usually claims at estimated ultimate values, trended to the appropriate prospective level.
    • Reflects risks that typically do not correlate across lines of business
  • Alternatively, A can be a placeholder for output from another model.
risk factor model components accident year deviation
Risk Factor Model Components: Accident Year Deviation

AYi =Ax B x C(Fi-E) x Di

  • Structured as an independent random variable multiplied by the overall aggregate losses
  • Multiply B by expected frequency in a frequency/severity model.
  • Parametric distribution
    • Usually mean 1.0
  • May be considered to reflect:
    • Market risk (pricing / underwriting)
    • Non-diversifying frequency risk (contagion)
    • Differences between past and future exposures
risk factor model components trend development parameter risk
Risk Factor Model Components: Trend/Development Parameter Risk

AYi = A x B x C(Fi-E) x D

  • Structured as an annualized error
  • Annual error is compounded from the average date of payment in the experience data to each future payment
    • The period includes both the “development” and “trend” periods
    • The structure is appropriate for both trend parameter error and development parameter error
  • C~ N(1,σ) or C~ L-N(0,σ) are reasonable choices.
  • Compounded error factor for each payment is multiplied by the payment
trend and development parameter risk
Trend and Development Parameter Risk

Long-Tail LOB

Historical

Data

Development

Trend

Short-Tail LOB

Ultimate

Future Accident Year

risk factor model components future trend process risk
Risk Factor Model Components: Future Trend Process Risk

AYi =Ax B x C(Fi-E) x Di

  • The result of a time series model
  • The dynamic risk component -- reflects unpredictable changes in future trends / external conditions
  • Can also be considered as a reflection of specification error
  • Future trend deviation is modeled as a time series:
    • First order auto-regressive (AR(1))
    • The simplest mean-reverting time series (reverts to mean of zero)
future trend process risk the ar 1 process
Future Trend Process Risk The AR(1) Process
  • Xi (i = 1, 2, …, n) are independent mean zero Normal random variables drawn from the same distribution.
  • Then define:
  • is the autocorrelation coefficient.
  • Annual trend error =
  • Cumulative trend error for year k = Dk=
changing trends
Changing Trends

Historical

Data

Future Accident Year

Expected Future

Trend

some pictures from the erm book
Some Pictures from the ERM Book
  • The estimated trends may be wrong:
  • Plus the trends may change:
accumulated risk
Accumulated Risk
  • Trend and development risks accumulate over many years of underwriting.
  • Extended down cycles accumulate losses over several years of underwriting.
  • This appears as reserve risk.
  • Risk decisions you make now affect reserves for years to come.
  • The business you write this year absorbs capital for years to come.
drawing capital for years to come
Drawing Capital for Years to Come

Calendar YearExposure Drawing Capital

1 The new AY (Premium)

2 Reserves for one year old AY

3 Reserves for two year old AY

4 Reserves for three year old AY

5 Reserves for four year old AY

6 Reserves for five year old AY

• •

• •

• •

etc.

as if reserves an approach to accumulated risk
“As-If” Reserves: An Approach to Accumulated Risk
  • Reserves “As If” the company had been writing the business consistently over time.
  • Equivalent to capital to be allocated in the future.
  • Can reflect the correlated risks on accumulated exposure.
  • Can measure the impact of reinsurance over time.
accumulation of systemic risks
Accumulation of Systemic Risks
  • Trend and development parameter risk is identical (100% correlated) between the new AY and the reserves.
  • Risk of changing trends is identical (100% correlated) between the new AY and the reserves.
  • The model for changing trend risk can also be a surrogate for latent losses and emerging exposures.
  • Market risk is partially correlated between successive AY’s.