Spread = (EL)^ (1/p)
Here, EL is the Expected Loss as a percentage and p is greater than or equal to 1, is a Risk Aversion Level (RAL).
In the absence of systematic risk, as is the case with these particular Insurance Linked Securities (ILS), the risk costs under the comprehensive framework correspond to the values calculated by the Wang PH Transform. This simplifies the analysis and facilitates both the derivation of the formula as well as the subsequent analysis.
The p's implicit in over 70 of these ILS are then identified and the majority found to be in the range 1.65 ± 0.15. A rationale for identifying appropriate values for this ñ is then developed by considering the role of the related frictional cost index in the comprehensive risk framework. This approach is demonstrated using data on US Hurricane losses.
The analysis indicates that current ILS spreads appear consistent with the assumption that the catastrophe model loss estimates are around the 1st or 2nd percentile of the 'true' loss distribution. This is both an extremely cautious approach for pricing these securities as well as a damning indictment on the work of the specialist catastrophe modelling companies.
A more realistic choice of the implicit pricing percentile, say to around the 10th percentile level (around 1.3), would result in reductions of over 50% in current spreads. These new spreads should still provide fair returns to investors, whilst also becoming very attractive to issuers. A market that makes sense to buyers and sellers will prosper rather than decline.
KEYWORDS: Insurance Linked Securities, Catastrophe Bonds, Securitization, Reinsurance, Risk Premium, Systematic Risk, Non-Systematic Risk, Dynamic Financial Analysis, Frictional Costs, Proportional Hazards (PH) Transform, Unbundled PH Transform, Risk Aversion Index, Cobb-Douglas Production function, Generalised Pareto Distribution.
