Slides of my seminar at Catholic University of Milan

1. Catastrophes: Traditional and Alterative
Insurances
Giorgio A. Spedicato, Ph.D C.Stat FCAS FSA
20th May 2016

2. Intro
Insurance coverages are available for typical catastrophical
perils affecting property insurances like: Hurricanes,
EarthQuake, Flood, Hail, Tornadoes, etc. . .
Italian S2 SF mandates capital charges for EarthQuake, Flood
and Hail.
CAT models have been developed since 80s to overcome
shortcoming of traditional ratemaking.

3. Figure 1: cat bond issuances per year

4. Traditional (re) insurance is often not available to fully meet
coverage demands.
CAT bonds increase availability since they take capacity from
the capital markets more easily than traditional reinsurance.
CAT bonds issues exponentially grew in last decades.
Alternative forms of coverages besides CAT Bonds also exists.

5. Non - Proportional Reinsurance and CAT Risks
Coverage for property catastrophe risks is usually sold in non
proportional basis. That is, coverage is sold in layered forms.
For example, a 90% 300Mln xs 500 Mln loss occurring contract
means that 90% of losses for occurrencies in the layer between
500 and 800 Mln are paid. A reinsurance program is usually
made by many layers in which different reinsurers participate.
Reinstatement clauses are also common. A three reinstatement
provision says that the primary insurer can reinstate the initial
protection up to three times (repaying a premium recalculated
according a proper formula).

6. Traditional reinsurance pricing methods are: experience rating
and exposure rating. After loading, they lead to a rate on line
or on premium.
Experience rating uses historical loss data (properly adjusted
and trended) to estimate average losses in layer. Exposure
rating uses exposure curve (% pure premium for % of
destruction rate) to estimate ceded losses.
Despite their drawbacks, catastrophe losses are too complex,
too vary, too extreme to be priced using only historica data.

7. CAT models
Figure 2: cat models

8. A CAT model is comprised by four parts: hazard, inventory,
vulnerability and loss.
The Hazard module the losses: frequency, severity and spatio -
temporal location. The inventory one stores the insured
properties characteristics: location (lat & long), value,
occupancy, use. The vulnerability simulated gross losses on
inventory from simulated events. loss applies insurance
contract provisions (deductibles, limits, existing reinsurance) to
generate individual and portfolio - level gross and net losses.
CAT models requires multiple highly specialized skills, some of
which are not familiar to actuaries. Teams of engineers, natural
scientists, gis experts and statisticians are needed to build these
models.

9. Figure 3: Italy EarthQuake
The figure above diplays the AAL by ZIP code for EarthQuake

10. CAT models are often a black box. The three main firms
producting CAT modeling tools are: AIR, RMS and EQECAT.
Modeling results can differ significantly for the same portfolio
due to epistemik risk due to epistemic uncertainty.
Typical risk metrics are: Average Annual Losses, PML,
Excedance Probabilities.
Excedance probability curves allows to assess Probable
Maximum Loss (amount of loss that will occur one out of n-th
periods on average).

11. Figure 4: Sample Exceedance Probability

12. CAT models allow to figure out loss distribution for a given
portfolio.
They may be used by: underwriters (which, where, how much
underwrite), actuaries (price covergare for direct and assumed
business), risk managers (risk retention and cession, capital
allocation).
Portfolio’s CAT modeling is often performed by reinsurance
brokers that assist primary insurers to seek and places
coverages.

13. Reinsuring CAT Risk: CAT Bonds
Traditional reinsurers offers coverage for CAT risks.
Alternative have been seek due to traditional reinsurance
drawbacks: difficult to reinsure high layers (low capacity of
traditional market, RoL markups swiflty increases by
attachment point), reinsurers’ credit risk, volatility of yearly
prices.
CAT bonds represent the most used alternatives. Other are
CAT-Eputs, Catastrophe Swaps.

14. Figure 5: Property RoL PnG

15. Usually, a CAT bond is ussued by a Special Purpose Vehicle
(SPV). The SPV is a reinsurer company that has been created
just to issue and serve the CAT Bond stuff.
Typical duration is 3Y. The bond-holders will receive floating
rate (es. EURIBOR-linked coupon) plus a spread (equivalent of
reinsurance premiu), that compensate them for the loss
potential.
Should an event triggering SVP protection occurr, the principal
is eroded.

16. The figure below displays a typical CAT bond corporate
arrangement.
Figure 6: CAT Bond Structure

17. CAT bond allows primary insurer to lock for multi - year
protection.
They are fully collateralized, so their credit risk charge is much
lower than traditional reinsurance.
Allow the insurer access to financial capital market, that have
almost unlimited capacity. Also, they are attractive for hedge
funds since their risk is uncorrelated with financial markets
movements.

18. The relationship of spread and Loss on Line appears empirically
linear for US Wind Losses.
Figure 7: Spread Vs Expected loss

19. Information asimmatries issues (moral hazard and adverse
selection) exists between the Sponsor and the Bondholders.
Events triggering SVP proctection could be based on: Idemnity
Trigger (actual losses suffered by the Sponsor, high moral
hazard); Index Trigger (based on well - known World CAT
index); Modeled (applyign actual CAT event on a modeled
portfolio); parametric (based on a phisical meausure).
Regulators require a direct link (idemnity) between SPV
protection and actual losses in order to grant reinsurance
benefits.

20. Conclusions
CAT bonds represent a growing alternative risk transfer vehicle
for Property risks.
The market seems already mature in terms of offers.
Deciding whether using traditional reinsurance or CAT Bonds
requires ad - hoc analysis of business.