Videos marked with an (*) contain discussion of new content in ICRFS-Plus 10.6.
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The training videos should be used for hands on training. We suggest you run the videos on a separate computer using a data projector, and train as a group.
The only way you will learn all the new concepts and be able to exploit all the immense benefits is by using the system. Experiential learning is imperative.
It is important that you study the videos in sequential order as set out below.
- 12.1 Common drivers and Process Correlation: TG GrossVsNet
- 12.2 Design of a composite model for Company B and allocation of risk capital
- 12.3 VaR, T-VaR, Risk Capital Allocation, and Underwriting risk charge versus Reserve risk charge
- 12.4 Company B LOB ReA versus the aggregate of all LOBs and simulation of a composite dataset from the composite model
- 12.5 Excel based Report for Company B for all LOBs (Company Wide Report)
12. Capital Management of long-tail liabilities
12.1 Common drivers and Process Correlation: TG GrossVsNet
How do we know if two LOBs have common drivers?
Gross and net of reinsurance data have very much the same trend structure and high process correlation because they have common drivers (especially in the calendar year direction). This is illustrated with a real life example.
However, it is very rare to see two LOBs with similar trend structure or significant process correlation. That is, in general, LOBs do not have common drivers.
The video illustrating common drivers and process correlation is viewable here (12 minutes).
12.2 Design of a composite model for Company B and allocation of risk capital
A composite model is designed for all the long tail LOBs of Company B. The starting point is the optimal model designed (identified) for each LOB in the (PTF) modelling framework and the associated forecast scenarios.
Clusters are identified based on process correlations between the LOBs.
We find that most LOBs do not have significant process correlation. Moreover, LOBs do not share the same trend structure and process variance. Accordingly they do not have common drivers.
Forecast summaries include:
- Reserve distribution correlations
- Risk capital allocation (percentages) by LOB
- Payment streams by calendar year for each LOB and the aggregate
- Risk capital allocation (percentages) by calendar year for each LOB and the aggregate
Risk Capital allocation by LOB and calendar year is based on a variance/covariance formula.
Calendar year payment streams are critical for the cost of capital calculations. These payment streams are inseparably related to the interaction between of the development period and calendar period parameters. (An accurate projection of the calendar year streams cannot be obtained in any other way).
The volatility of ReA is examined. The process volatility in the past is high. We expect to see the same volatility when we project into the future.
The video analysing the Case Study is available here (19 minutes).
12.3 VaR, T-VaR, Risk Capital Allocation, and Underwriting risk charge versus Reserve risk charge (*)
Forecast scenarios going forward are adjusted so that estimates of the means of the reserve distributions correspond to reserves held. For most LOBs they are quite conservative. The CV of the aggregate is smaller than the CVs for most of the individual lines.
Since there is no analytical form for the sum of log normals, we simulate from the projected correlated log normals in each cell for each LOB to find the distribution of aggregates.
Graphs of risk capital allocation for selected VaRs and T-VaRs are discussed.
It is shown that the combined risk charge for reserve and underwriting risk is less than the sum of the individual risk charges.
The video illustrating VaR, T-VaR and comparing underwriting and reserve risk charges is available here (13 minutes).
12.4 Company B LOB ReA versus the aggregate of all LOBs and simulation of a composite dataset from the composite model
The LOB ReA has the largest CV and if this were the only line written by Company B it would require a large amount of risk capital. Company B affords substantial risk diversification credit as a result of the reserve distributions exhibiting essentially zero correlation.
A composite dataset is simulated from the composite model for all the long tail LOBs. It is shown to have the same risk characteristics as the real data.
The video comparing Company B LOB ReA versus the here (13 minutes).
12.5 Excel based Report for Company B for all LOBs (Company Wide Report)
A report is generated in Excel for Company B using a report template that exhibits reserve summaries for the aggregate across all LOBs and each LOB by accident year and calendar year. Capital allocation tables and graphs are also given for specific VaR.
One great benefit of an ICRFS-Plus database is that all reports are linked to the corresponding triangle groups and accordingly a report can be found with just a few mouse clicks.
To view this video, click here. This video is approximately 8 minutes long.