16.8 Key Elements of Enterprise Risk Model
Underwriting Risk
Reserving Risk
Asset Risk
Dependencies (Correlation)
16.8.1 Underwriting Risk
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Estimation risk
Projection risk
Event risk
Systematic risk
16.8.1.1 Loss Frequency and Severity Distribution
Use statistical methods to:
Estimate parameters
Test quality of fit
Understand uncertainties that remain
Common distributions for insurance loss are available in many papers
Transformed Beta and Gamma Distributions and Aggregate Losses - Venter
Continuous Distributions - Kreps
16.8.1.2 Pricing Risk
Instability from variations in the premiums as well as losses
Misestimation of projected losses as well as competitive market pressures
Deficiency may exist for many years for long tailed lines \(\Rightarrow\) Accumulation of reserve deficiency
Model should include u/w cycle as it contributes significantly to pricing risk
- See additional details in ERA 5.2
16.8.1.3 Parameter Risk
Misestimated parameters, imperfect form and risk not modeled (Likely largest risk net of reinsurance (larger than cat exposure))
Estimation Risk
Error in estimations the form and parameters
- Depends on available data (i.e. more and better data reduces this risk)
Projection Risk
Error on forecast of future value even if we fit the historical data accurately
Examples:
Freq/Sev trend from the time of the data to the current and future underwriting periods
Development of ultimate losses
Affected by macro factors (e.g. inflation) and the corresponding dependencies should be reflected in the model
Unexpected change in external risk conditions also add to projection risk, e.g.
Lower fuel price \(\Rightarrow\) Increased driving
Long term shift to more extreme weather
Event Risk:
Causal link between a large unpredictable event and losses to an insurer
Example:
Court ruling that favors a large group of policyholders (e.g. class action)
Exposure that existed, unknown, for many years comes to light (e.g. asbestos)
New cause of loss emerges that was previously regarded as not covered (e.g. environmental, CD)
Regulator or court expands coverage by barring important exclusions
New entrant into market reduces rates to grab market share
Systematic Risk:
Operates simultaneously on a large number of policies
Undiversifiable, i.e. do not improve with added volume
e.g. macro factors such as inflation
See additional detail in ERA 3.2
16.8.1.4 Catastrophe Modeling Uncertainty
Exposure to natural and man-made cat
Likely largest risk after parameter risk, special case of parameter risk
Based on proprietary cat models, further source of uncertainty
Differences between commercial models and different versions of the same model
Considerable amount of uncertainty in the probabilities of various events and the amount of insured damage
Additional uncertainty from data quality
- Mismatches of company data fields and cat model assumptions
Can quantified by the use of more than one model for each peril
Cat distributions are subject to the same considerations of parameter risk and correlation as other risk distributions
16.8.2 Reserving Risk
Adverse development can be significant for long tailed lines
\(\uparrow\) reserve uncertainty \(\Rightarrow\) \(\uparrow\) capital requirement & \(\uparrow\) time holding the capital
Model needs to capture both process variance and parameter risk
Key aspects of risk modeling process
Specifying the reserve runoff model
Testing it with quality of fit measures
Unearned premium reserve should be modeled in underwriting risk
16.8.3 Asset Risk
Need to focus on issues of the specific markets that the company operates
Main asset classes: equities, fixed income, real estate
Different types of fixed income are important in different regions
FX and inflation are closely related to asset modeling as well
Asset Modeling: Probabilistic Reality
Modeling scenarios consistent with historical patterns
Generate a large variety of scenarios against which to test the insurer’s strategy
Scenarios are weighted by probability
Scenarios should be reasonable when compared to historical patterns
Asset liability matching
Offset between insurance risk and investment risk
P&C companies can opt for longer duration assets and not match the liabilities to increase investment return while still maintain reasonable ALM risk
Need to consider that P&C liabilities are inflation sensitive as well
Or if liabilities are carried at PV marked to current interest rate
Efficient Frontier: \(\sigma\) vs \(\operatorname{E}[Return]\)
See how it changes by modifying reinsurance structure or asset mix
More details in ERA 2.4
Modeling Considerations
Bonds:
Model with arbitrage free models
Should capture historical features of bond markets
(high auto-correlations and distribution of yield spreads)
Equities:
Incorporate correlations with bonds
Geometric Brownian motion model with additional volatility is more realistic
(Allow for more extreme motion or even discontinuities)
FX:
First model interest rates of the currencies then model the FX rates
Changes in actual and anticipated interest rates in two countries lead to changes in the FX rates
Interest rate movements across different economies are correlated as well
16.8.4 Dependencies
Important to capture dependencies or else the model will be unrealistically stable
Sources of Dependencies:
Simultaneous impact of macro economic conditions on many risks
A good ESG should capture the dependence between inflation, interest rates, equity values, etc
This will impact asset values
Inflation will impact underwriting losses, loss reserve development
Interest rates may influence the underwriting cycle
U/w cycle, loss trends and reserve development can be correlated across LoB and with each other
Cat and other event losses can impact across lines
Large man made cat (e.g. 9/11) can have impact on both insurance and market risk
Difficult to quantify
May reference studies of multiple insurers, public insurance industry information and macroeconomic data
Still require professional judgement
Modeling Dependencies:
Avoid using just the correlation coefficient to describe and oversimplify dependency
We are most interested in the tail dependency
- e.g. High inflation or large cat that impacts multiple LoB that would typically be uncorrelated
Use copulas to capture different forms of dependency
- See ERA 3.3 for more details