12.8 Additional Analysis

Test the quality of our result

Sensitivity Testing:
Varying the different CoV and correlations

Scenario Testing:
Consider what assumptions need to change in our mid point to eat up the risk margin (similar to back testing)

Internal Benchmarking:
Compare CoVs within between OCL and PL and also with other valuation groups to look for consistency

Independent risk:

  • Large liability will have smaller CoV due to law of large numbers

  • Short tail line will have a small CoV as well due to less volatility

Therefore:

  • Outstanding Claims Liability:

    \(\phi_{short \: tail} < \phi_{long \: tail} < \phi_{long \: tail, \: small \: book}\)

  • Premium Liability - Long Tail:

    OCL > PL \(\Rightarrow\) \(\phi_{OCL} < \phi_{PL}\)

    • Because there are many AYs of claims in the reserves

  • Premium Liability - Short Tail:

    OCL < PL \(\Rightarrow\) \(\phi_{OCL} > \phi_{PL}\)

    • Because OCL is small

    • LoB with significant event risk will have different risk profiles for the PL and OCL

Internal Systemic:

  • If the methods to estimate liabilities is similar across valuation groups, we would expect the CoV to be similar for classes that have similar claim payment patterns

External Systemic:

  • Main sources of external systemic risk are higher for long tail lines; Event risk is higher for property; Liability for HO can also be significant

External Benchmarking:
Compare selected CoV with external sources

  • Such as APRA 2008

  • Use just as a sanity check, not appropriate to simply take the risk margins from benchmarks

  • Independent risk CoV depend on the size of liabilities

    \(\Rightarrow\) Similar sized liability today would represent a small book due to inflation

    \(\Rightarrow\) Adjust CoV upward

  • Estimate PL with a scale up factor from OCL

Hindsight Analysis:

  • Compare the actual results with expected over multiple periods

  • Blend of all 3 risks (independent, internal/external systemic), at least the actual episodes of those risk

  • Useful as a guide if the CoVs are reasonable

  • Works well for short-tailed LoB where the AY’s liabilities don’t move together too much

    • Where for long tail lines you can change your mind significantly about the liabilities for multiple AYs in one reserve study

Mechanical Hindsight:

  • Value the liabilities today using a mechanical method and repeat with information at older evaluation date

  • Measure independent risk over stable periods

  • By using multiple methods you can measure the internal systemic risk

  • By measuring over long periods of time, you can measure risk from all sources