9.5 Variations on the ODP Bootstrap

Reason to use paid data:

  • For insurance risk it is best to focus on the claim payment stream:

    It measures the variability of the actual cash flows that directly affect the bottom line

  • Case reserves temper the volatility

    Changes in case reserves and IBNR reserves will also impact the bottom line, but to a considerable extent the changes in IBNR are intended to counter the impact of the changes in case reserves

    To some degree, then, the total reserve movements can act to mask the underlying changes due to cash flows

Reason to include case reserves:

  • Case reserves contain valuable information about potential future payments

9.5.1 Bootstrapping the Incurred Loss Triangle

2 approaches to model the unpaid loss distribution using incurred loss triangle

Method 1: Modeling the incurred data and convert the ultimate values to a payment pattern

  1. Run the paid and incurred data model in parallel

  2. For each iteration and each AY individually:

    Use the payment pattern (from paid model) to convert the ultimate values (from incurred model) to a payment stream

Method 1 Advantages:

  • We improve the ultimate estimates by incorporating the case reserves while still focusing on the payment stream for measuring risk

  • Which effectively allows a distribution of IBNR to become a distribution of IBNR and case reserves

  • Can make it more sophisticated by correlating some part of the paid and incurred models (e.g. the residual sampling and/or process variance portions)

    So that if we have large payment @ an older age, the incurred should be large as well

Method 2: Applying the ODP bootstrap to the Munich chain ladder model

  • See Liu and Verrall (2010)

Method 2 Advantages:

  • Don’t have to model the paid loss twice

  • Explicitly measuring and imposing a framework around the correlation of the paid and outstanding losses

9.5.2 Bootstrapping the BF and Cape Cod Method

ODP issue: Distribution for the most recent AYs can produce results with more variance than you would expect when compared to earlier AYs in the actual data

  • Due More LDFs are used to extrapolate the sampled values for the most recent accident years and the random samples of incremental values

  • Similar to the leverage effect of the deterministic chainladder

Solution: Incorporate BF or Cape Cod

  • Have the a-priori be stochastic e.g. draw the BF a-priori from a distribution or apply Cape Cod to each simulated triangle

  • More complicated approach is to modify the underlying assumptions of the GLM framework which would results in a completely different set of residuals (this is beyond scope)