Cat Bond and Traditional Insurance

Catastrophes: Traditional and AlterativeInsurances

Giorgio A. Spedicato, Ph.D C.Stat FCAS FSA

20th May 2016

Intro

I Insurance coverages are available for typical catastrophicalperils affecting property insurances like: Hurricanes,EarthQuake, Flood, Hail, Tornadoes, etc. . .

I Italian S2 SF mandates capital charges for EarthQuake, Floodand Hail.

I CAT models have been developed since 80s to overcomeshortcoming of traditional ratemaking.

Figure 1: cat bond issuances per year

I Traditional (re) insurance is often not available to fully meetcoverage demands.

I CAT bonds increase availability since they take capacity fromthe capital markets more easily than traditional reinsurance.

I CAT bonds issues exponentially grew in last decades.Alternative forms of coverages besides CAT Bonds also exists.

Non - Proportional Reinsurance and CAT Risks

I Coverage for property catastrophe risks is usually sold in nonproportional basis. That is, coverage is sold in layered forms.

I For example, a 90% 300Mln xs 500 Mln loss occurring contractmeans that 90% of losses for occurrencies in the layer between500 and 800 Mln are paid. A reinsurance program is usuallymade by many layers in which different reinsurers participate.

I Reinstatement clauses are also common. A three reinstatementprovision says that the primary insurer can reinstate the initialprotection up to three times (repaying a premium recalculatedaccording a proper formula).

I Traditional reinsurance pricing methods are: experience ratingand exposure rating. After loading, they lead to a rate on lineor on premium.

I Experience rating uses historical loss data (properly adjustedand trended) to estimate average losses in layer. Exposurerating uses exposure curve (% pure premium for % ofdestruction rate) to estimate ceded losses.

I Despite their drawbacks, catastrophe losses are too complex,too vary, too extreme to be priced using only historica data.

CAT models

Figure 2: cat models

I A CAT model is comprised by four parts: hazard, inventory,vulnerability and loss.

I The Hazard module the losses: frequency, severity and spatio -temporal location. The inventory one stores the insuredproperties characteristics: location (lat & long), value,occupancy, use. The vulnerability simulated gross losses oninventory from simulated events. loss applies insurancecontract provisions (deductibles, limits, existing reinsurance) togenerate individual and portfolio - level gross and net losses.

I CAT models requires multiple highly specialized skills, some ofwhich are not familiar to actuaries. Teams of engineers, naturalscientists, gis experts and statisticians are needed to build thesemodels.

Figure 3: Italy EarthQuake

I The figure above diplays the AAL by ZIP code for EarthQuakelosses.

I CAT models are often a black box. The three main firmsproducting CAT modeling tools are: AIR, RMS and EQECAT.Modeling results can differ significantly for the same portfoliodue to epistemik risk due to epistemic uncertainty.

I Typical risk metrics are: Average Annual Losses, PML,Excedance Probabilities.

I Excedance probability curves allows to assess ProbableMaximum Loss (amount of loss that will occur one out of n-thperiods on average).

Figure 4: Sample Exceedance Probability

I CAT models allow to figure out loss distribution for a givenportfolio.

I They may be used by: underwriters (which, where, how muchunderwrite), actuaries (price covergare for direct and assumedbusiness), risk managers (risk retention and cession, capitalallocation).

I Portfolio’s CAT modeling is often performed by reinsurancebrokers that assist primary insurers to seek and placescoverages.

Reinsuring CAT Risk: CAT Bonds

I Traditional reinsurers offers coverage for CAT risks.I Alternative have been seek due to traditional reinsurance

drawbacks: difficult to reinsure high layers (low capacity oftraditional market, RoL markups swiflty increases byattachment point), reinsurers’ credit risk, volatility of yearlyprices.

I CAT bonds represent the most used alternatives. Other areCAT-Eputs, Catastrophe Swaps.

Figure 5: Property RoL PnG

I Usually, a CAT bond is ussued by a Special Purpose Vehicle(SPV). The SPV is a reinsurer company that has been createdjust to issue and serve the CAT Bond stuff.

I Typical duration is 3Y. The bond-holders will receive floatingrate (es. EURIBOR-linked coupon) plus a spread (equivalent ofreinsurance premiu), that compensate them for the losspotential.

I Should an event triggering SVP protection occurr, the principalis eroded.

The figure below displays a typical CAT bond corporatearrangement.

Figure 6: CAT Bond Structure

I CAT bond allows primary insurer to lock for multi - yearprotection.

I They are fully collateralized, so their credit risk charge is muchlower than traditional reinsurance.

I Allow the insurer access to financial capital market, that havealmost unlimited capacity. Also, they are attractive for hedgefunds since their risk is uncorrelated with financial marketsmovements.

I The relationship of spread and Loss on Line appears empiricallylinear for US Wind Losses.

Figure 7: Spread Vs Expected loss

I Information asimmatries issues (moral hazard and adverseselection) exists between the Sponsor and the Bondholders.

I Events triggering SVP proctection could be based on: IdemnityTrigger (actual losses suffered by the Sponsor, high moralhazard); Index Trigger (based on well - known World CATindex); Modeled (applyign actual CAT event on a modeledportfolio); parametric (based on a phisical meausure).

I Regulators require a direct link (idemnity) between SPVprotection and actual losses in order to grant reinsurancebenefits.

Conclusions

I CAT bonds represent a growing alternative risk transfer vehiclefor Property risks.

I The market seems already mature in terms of offers.I Deciding whether using traditional reinsurance or CAT Bonds

requires ad - hoc analysis of business.