Visiting a couple of industry conferences and seminars in the last few months, including Swiss Re's 1st Catastrophe Knowledge Exchange, has prompted me to look more into the linkages between product evolution, market conditions, and systemic shocks and the parallels between financial and (re)insurance product design.
Financial product engineers tend to turn to complexity, aggregation and multi-tiered riskiness to provide vehicles of higher returns. Let us take a collateralised debt obligation (CDO).
The aggregation concept in product design comes into play with the idea that pulling together independent, uncorrelated loans, i.e. loans from independent industry sectors, into a combined securitised loan product will produce a likelihood of default of the combined product that is not greater than the cumulative defaults of the individual loans. Simply said the combined product is not riskier than the sum of risks of two or more individual loans.
Because the likelihood of default of the combined product is smaller than any of the contributors, it is thought safer, less likely to be triggered, and hence of higher credit rating. Again to put it simply, holding the combined product is not riskier than holding all the individual loans, but the portfolio manager can demand a higher premium i.e. return for the combined product.
This is counter-intuitive perhaps, because higher returns are associated with higher risks, but the argument is that a portfolio manager will not hold such a volume of credit risk unless in a combined basket product. The idea of multi-tiered riskiness is expressed in assigning expected losses into tranches, or layers in CAT modeling speak, with highest credit rated contributing loans and bearing least expected loss, being part of the top rated tranches - layers.
To properly model and price such combined collateralised product one needs a few mathematical tools. Firstly a methodology is needed to understand both the likelihood of very large losses even to the best rated individual loans and higher frequency and more likely smaller losses to the bottom tranches. This is a very similar concept to exceedance probability modeling of natural catastrophe losses.
Next an understanding of the dependencies and correlations between the contributing risks is required to put together the joint risk profile of the combined product – in statistical terms, we need critical knowledge of the joint multivariate statistical distribution and its correlation matrix.
Now we look in parallel to a similarly structured reinsurance product. The reinsurance treaty underwriter employs very similar business logic to address the market motivations of the cedents. Aggregation in reinsurance product design has at least two aspects. Multiple ceded risks, in our case at least two insurance policies, are combined together and their joint losses are expected to trigger a joint retention and exhaust a combined reinsured limit.
Retentions and limits are exhausted in chronological order, after a first CAT event the remainder of the retention and limit is applied to a second event. Aggregation by and large is advantageous to the reinsurer in terms of administrative and management cost. Some practitioners comment that it also allows for lapses in underwriting discipline. Per-risk treaties are advantageous to the reinsured. They require more underwriting due diligence and more accurate modeling, but they are inevitably more expensive. In simplest calc. the joint probability of triggering a combined retention is always less than the probability of triggering a single per-risk retention. Hence premiums should be sub-additive, but they are not always so.
This we will have to address in a separate note. Multi-tiered riskiness is expressed in the concept of layers on joint losses. Lower working layers are triggered by both high and low exceedance probability events. Expectation of loss is high, hence the naming convention – a working layer’ – i.e. almost certain to be triggered, to get to work, and so reinsurance premiums are higher.
While ‘top layers’ are triggered only by low exceedance probability rare events - lower expectation of loss demands lower premium. Exactly the same statistical mechanics are needed – understanding the probability scenarios of losses triggering and subject to a layer; and secondly a model for loss aggregation with components for measuring dependencies and correlations.
A critical difference needs to be noted: natural catastrophe dependencies and correlations have a geo-spatial component derived from distances and physical properties of the geography of the (re)insured risks, while credit default dependencies are typically indifferent to distances of where the securitized loans are issued, and where the actual physical assets underlying the loan reside.
In a later blog entry I will look at how market conditions stimulate product design, and then how rare and extreme events test the resilience of complex products.
Category: Climate/natural disasters: Climate change, Disaster risk, Floods/storms
Location: Rüschlikon, Switzerland