The use of parametric structures in ART products.

The successful placement of Munich Re's Prime Capital Hurricane, Prime Capital CalQuake and Eurowind catastrophe bonds has given new life to the catastrophe risk securitisation market and thrown powerful support behind the use of parametric structures for achieving alternative risk transfer (ART). The outcome of the two three-year bonds, initiated on 1 January 2001 with a total value of $300m, is entirely determined by the specifics of parameters reported by US federal agencies. These parameters are in reference to the size and location of earthquakes and hurricanes, along with the values of recorded windspeed observations from meteorological agencies across five European countries.

Prime Capital represents important endorsement of parametric structures, in a market that has seen a ‘Cambrian explosion' (an extravagant proliferation of varied designs and styles emerging to take advantage of a new economic ‘niche') of ART mechanisms. Wherever and whenever such an explosion of alternatives has occurred – from biplanes to dot.coms – this has inevitably been followed by consolidation and rationalisation, as the Darwinian process of natural selection proceeds, and economic efficiency comes to rule over the marketing and ‘first-mover' motivations of many of the earlier transactions.

Will parametric structures become the standards of the ART market?

In the taxonomy of alternative catastrophe risk transfer, securitisation structures can be separated into two fundamental classes:

l indemnification deals that are simple substitutes for reinsurance contracts, whose outcome is entirely determined by the loss to the insured party; and

l parametric structures, based on the value of some independent index, that shadows insured loss, but cannot be classified, either legally, or in accounting standards, as an insurance contract.

Indemnification contracts are often favoured by issuers, but suffer a number of problems with investors that are likely to be penalised by a reluctance to participate or a demand for a higher spread. As the period over which the loss is settled tends to be proportional to the size of the event, investors may not know whether they have preserved their money until some time after the event has happened (although this opens the interesting proposition of a secondary market in distressed cat bonds). More importantly, there are always questions about the quality of the underlying data employed in the risk analysis for an indemnification transaction, and suspicion from the investor about the nature of the risks that are being allocated to the contract by the issuer. Every transaction, by definition, is unique, and therefore cannot be commoditised as part of any secondary trading market.

The parametric structures can themselves be separated into at least three categories:

  • industry loss parametric in which the outcome is determined by industry losses published by some authoritative source;
  • nominal portfolio parametric in which the outcome is determined by applying directly recorded parameters to a fixed, but nominal portfolio, with an assumed vulnerability relation, linking the hazard to the loss; and
  • pure parametric in which the outcome is determined directly from the recorded parameters of the event itself, and generally includes some composite of size and location.

    Industry reporting is only standardised in the US, with the availability of the RMS Cat Index (as employed in the Gold Eagle catastrophe bond for American Re) or in the PCS loss estimates (as used in the Seismic Ltd securitisation for Lehman Brothers). Therefore, outside the US, contracts can only be written on either a nominal or pure parametric basis. It is to the pure parametric category that Munich Re has swung its support and influence in bringing the Prime Capital transactions to the market.

    To work, all parametric structures need to fulfil five key criteria:
    1) parametric reporting has to be provided by an independent and reputable agency;
    2) reporting has to be timely, so that settlement can be conclusive and rapid;
    3) the mechanism to calculate the parametric index has to be transparent, available for scrutiny and verifiable by an external party;
    4) the index has to show a correlation with insured loss, to the degree that the basis risk (the difference between the actual loss and recovered loss) is within bounds that are acceptable to the issuer; and
    5) there has to be an adequate scientific understanding of the phenomenon and depth of historical information on which to found a comprehensive risk analysis.

    The first step in the design of a structure is to identify which parameters are published by the appropriate government monitoring agencies in the immediate aftermath of an event, and to explore how these could be turned into an appropriate index. Some parameters that would be useful for refining the overall loss impact, such as the extent of fault rupture in an earthquake or the diameter of a hurricane, may not be formally published by the specific government agency.

    Much of the actual work in designing the indices then concerns fine-tuning the structure to minimise the basis risk (the difference between the repayment achieved through the bond and that of a matching reinsurance protection). This involves iterating variations of the geography or threshold, each time segregating which stochastic catastrophe events and calculated losses fall inside and outside the parametric structure, and hence how recovered losses compare with an equivalent layer of excess of loss reinsurance.

    The complexity of the proposed structure needs to be weighed against any associated reduction in basis risk. As one bond market veteran put it: “For every extra minute it takes to explain the structure to an investor, add an extra ten basis points (0.1%) to the spread (the additional premium that the investor will demand to accept the risk).” Complexity is itself a form of risk if it opens the potential for disputes over the certainty of the outcome following a borderline catastrophe event. There is credit risk involved in any reinsurance transfer, a risk that becomes exacerbated the larger the size of the loss (and the lower the credit-worthiness of the reinsurer), as the counterparty is more likely to be overwhelmed by the catastrophe claims. With a bond, the risk is less in the availability of the funds than in the potential for litigation if the structure itself is not watertight in its definition and application.

    Hurricane, earthquake and windstorm modellers in the RMS Global Risk Modelling group worked in collaboration with the Natural Perils Research Group at Munich Re to devise the structure of the parametric triggers involved in the Prime Capital transaction. For the earthquake modelling team led by Don Windeler and Guy Morrow from the RMS California office, the chief challenge was to work with the information that is provided from the US Geological Survey reports, comprising the location of the epicentre and the magnitude. The epicentre – the point on the earth's surface immediately above where the fault that generated the earthquake started to break – is not an ideal way to characterise the source of an earthquake. Where the fault breaks in only one direction the epicentre may be located right at the end of the fault-zone from which the vibrational energy was radiated. Fault area correlates with the size of the earthquake, and while a magnitude 5 earthquake may be only one kilometre in length and can be characterised as ‘a point', a magnitude 7.5 earthquake will involve a fault rupture 100km or more in length. For a circular trigger area, basis risk increases with the magnitude threshold because of the increasing difference in loss outcome between an epicentre on a fault lying tangential or radial to the central point. For this reason, simple single box or circle triggers are only really effective where the level of seismicity (and hence expected magnitudes) are fairly low.

    To get round this problem for California, a series of four trigger boxes were established providing coverage for Greater Los Angeles and another four covering the San Francisco Bay area. For each region, a central box was drawn that covered the principal concentration of exposed risk and then outer boxes were defined that followed the grain of the principal faults. Trigger threshold magnitudes rise away from the central box, as it is only the largest of all earthquakes that would have the potential to rupture all the way into the central box.

    East Coast hurricane
    The challenge for US East Coast hurricane triggers is again to work with the information that is guaranteed to be provided by the National Hurricane Centre (NHC) in Miami. The density of windspeed recorders is too sparse and the potential for equipment failure in a hurricane too great to build a parametric structure on the windspeed observations themselves. However, central pressure, as published by the NHC, provides a good first order descriptor of the overall impact of a hurricane. After testing numerous alternative configurations of boxes and gates protecting the principal sources of hurricane-affected exposure around Greater New York and MetroMiami, a set of gates were defined. One gate runs from halfway down Long Island to the central New Jersey shoreline ‘protecting' New York, while two shorter gates were drawn along the coast adjacent to Miami. The trigger points were established as central pressure thresholds at landfall, for hurricanes crossing from sea to land, for each of these gates.

    Unlike hurricanes, the impact of extra-tropical cyclone (ETC) windstorms in Europe cannot be characterised from central pressure and track-landfall alone because there is a poor correlation between the central pressure and the flanking dynamic pressure gradient that drives the windfield. However, in Europe there is a high density of windspeed recording stations, and at the windspeeds experienced in ETC storms, a low risk of recorders failing.

    For Prime Capital, the windspeed data was transformed into a simple European Windstorm Index that mimics industry insurance loss. This index is a kind of hybrid ‘nominal portfolio' and ‘pure parametric' structure. First, in MapInfo, a surface was fitted to the windspeed observations from 600 first-order synoptic recorders across five territories (UK, France, Germany, Belgium and the Netherlands). The windspeed is then output from this surface at the centroid of each two-figure postcode or Cresta zone. This enables the index to be sustained consistently for multi-year contracts, even while there are changes in the locations of the recorders themselves.

    These Cresta zone windspeeds are then plugged into a formula designed to mimic industry losses. First, an empirically determined ‘loss threshold' of 27m/s is deducted from each windspeed. Each residual windspeed is then entered into a weighted ‘cube root mean cube' function: the cubing reflects the simplification that, over the range of windspeeds encountered in European storms, loss can be represented as a third order function of windspeed. The weighting factor is a combination of the variations in exposure value and relative vulnerability from one Cresta zone to another. By this means, the value of the index is tuned to industry insured loss. At the same time, the index value can be rapidly calculated following a windstorm event simply by inputting all the original windspeed observations. A key part of the calibration procedure was to relate industry losses and index values calculated from the original windspeed observations for all the principal windstorms of the past 40 years: 1999 windstorm Lothar has an index value of 6.68; 1990 windstorm Daria, 7.33.

    Risk Management Solutions has established a catastrophe risk consultancy practice focused on the development and promotion of parametric and index-based risk transfer mechanisms. The team includes some of the global specialists in this area including Dr Fouad Bendimerad who led the Gold Eagle securitisation for American Re, Dr Tibor Winkler, the lead modeller on Namazu Re for Gerling (a parametric structure based on the outputs of earthquake strong-motion recorders across Japan applied to a nominal portfolio), and Dr Gordon Woo, the parametric architect of the recent Mediterranean Re cat bond for AGF. Mediterranean Re involved two parametric structures, the first based on windspeeds recorded across France applied to a nominal portfolio and the second based on the size and distance of an earthquake epicentre away from the centre of Monaco.

    Of course, the process of evolution is not always easy to predict. Whether parametric structures become the market standards will chiefly depend on the investor appetite. In theory, increased standardisation of simple parametric structures should force the current market spreads for cat bonds to become more competitive. A clear price differential with indemnity deals will inspire more parametric issuers. The World Bank has even been trying to inspire parametric catastrophe structures to be issued for currently uninsured areas of the developing world. However, in the catastrophe securitisation marketplace, the chief competitor in the risk transfer space remains old economy reinsurance, still aggressively pricing itself to keep out the new arrivals.

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