metadata: authors: 0: author: Mahul,Olivier
1: author: Seo, John
count: World
docna: 0: docna: The impact of climate change on catastrophe
            risk models : implications for catastrophe risk markets in
            developing countries
docty: Policy Research Working Paper
subtopic: Science of Climate Change,Climate Change and Health,Private Sector Economics,Climate Change and Environment,Private Sector Development Law,Inflation,Marketing,Natural Disasters
teratopic: Environment,Conflict and Development,Macroeconomics and Economic Growth,Urban Development,Finance and Financial Sector Development
abstracts: cdata!: Catastrophe risk models allow insurers,
            reinsurers and governments to assess the risk of loss from
            catastrophic events, such as hurricanes. These models rely
            on computer technology and the latest earth and
            meteorological science information to generate thousands if
            not millions of simulated events. Recently observed
            hurricane activity, particularly in the 2004 and 2005
            hurricane seasons, in conjunction with recently published
            scientific literature has led risk modelers to revisit their
            hurricane models and develop climate conditioned hurricane
            models. This paper discusses these climate conditioned
            hurricane models and compares their risk estimates to those
            of base normal hurricane models. This comparison shows that
            the recent 50 year period of climate change has potentially
            increased North Atlantic hurricane frequency by 30 percent.
            However, such an increase in hurricane frequency would
            result in an increase in risk to human property that is
            equivalent to less than 10 years worth of US coastal
            property growth. Increases in potential extreme losses
            require the reinsurance industry to secure additional risk
            capital for these peak risks, resulting in the short term in
            lower risk capacity for developing countries. However,
            reinsurers and investors in catastrophe securities may still
            have a long-term interest in providing catastrophe coverage
            in middle and low-income countries as this allows reinsurers
            and investors to better diversify their catastrophe risk portfolios.
repnme: repnme: The impact of climate change on catastrophe
            risk models : implications for catastrophe risk markets in
            developing countries
display_title: The impact of climate change on
            catastrophe risk models : implications for catastrophe risk
            markets in developing countries
listing_relative_url: /research/2009/06/10645285/impact-climate-change-catastrophe-risk-models-implications-catastrophe-risk-markets-developing-countries
topicv3: Private Sector Development m1326060 1921,Inflation m1326709 0870F4727ACED1CF8525815C00471347,Climate Change m1326829 567,Earthquake m1503308 3154,Hurricane m1503314 3179
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Environment,Conflict and Development,Macroeconomics and Economic Growth,Urban Development,Finance and Financial Sector Development
no_of_pages: 18
author_keys: 0: author_key: 675198
model_extractions: WPS4959 Policy Research Working Paper 4959 The Impact of Climate Change on Catastrophe Risk Model Implications for Catastrophe Risk Markets in Developing Countries _John Seo Olivier Mahul_ The World Bank Sustainable Development Network Vice Presidency Global Facility for Disaster Reduction and Recovery Unit & Financial and Private Sector Development Vice Presidency Global Capital Markets Development Department June 2009
Policy Research Working Paper 4959

# **Abstract**

Catastrophe risk models allow insurers, reinsurers and governments to assess the risk of loss from catastrophic events, such as hurricanes. These models rely on computer technology and the latest earth and meteorological science information to generate thousands if not millions of simulated events. Recently observed hurricane activity, particularly in the 2004 and 2005 hurricane seasons, in conjunction with recently published scientific literature has led risk modelers to revisit their hurricane models and develop climate conditioned hurricane models. This paper discusses these climate conditioned hurricane models and compares their risk estimates to those of base normal hurricane models. This comparison shows that the recent 50 year period of climate change has potentially increased North Atlantic hurricane frequency by 30 percent. However, such an increase in hurricane frequency would result in an increase in risk to human property that is equivalent to less than 10 years’ worth of US coastal property growth. Increases in potential extreme losses require the reinsurance industry to secure additional risk capital for these peak risks, resulting in the short term in lower risk capacity for developing countries. However, reinsurers and investors in catastrophe securities may still have a long-term interest in providing catastrophe coverage in middle and low-income countries as this allows reinsurers and investors to better diversify their catastrophe risk portfolios.

This paper—a joint product of the Global Facility for Disaster Reduction and Recovery Unit, Sustainable Development Network Vice Presidency, and the Global Capital Markets Development Department, Financial and Private Sector Development Vice Presidency—is part of a larger effort in the department to is part of a larger effort to disseminate the emerging findings of the forthcoming joint World Bank-UN Assessment of the Economics of Disaster Risk Reduction. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The authors may be contacted at john@fcm.com and omahul@worldbank.org respectively. We are grateful to Apurva Sanghi and participants of the seminar at the World Bank held on this topic for their suggestions and constructive comments.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
The Impact of Climate Change on Catastrophe Risk Models: Implications for Catastrophe Risk Markets in Developing Countries<sup>1</sup>

# John Seo

_Co-Founder and Managing Principal, Fermat Capital Management LLC_

# Olivier Mahul

_Program Coordinator, Insurance for the Poor, Global Capital Markets Development Department, Financial and Private Sector Development Vice Presidency, The World Bank_

> 1 This paper, a product of the Global Facility for Disaster Reduction and Recovery (GFDRR) Unit, Sustainable Development Network Vice Presidency, is part of a larger effort of the GFDRR to disseminate the emerging findings of the forthcoming joint World Bank-UN Assessment of the Economics of Disaster Risk Reduction. We are grateful to Apurva Sanghi and participants of the seminar at the World Bank held on this topic for their suggestions and constructive comments.
# **1. Introduction**

Catastrophe models are complex and almost completely inaccessible to the non-specialist. Yet, these models tell policymakers what are the economic risks to society and form the basis of rate making for billions of dollars in insurance premiums per year in the United States alone. We summarize two important results from US hurricane catastrophe models: one for base normal (BN) hurricane risk and one for climate conditioned (CC) hurricane risk. Summary results are presented in Loss Exceedance Curve (LEC) form, which is a kind of cumulative distribution function and thus gives considerable summary information about what hurricane catastrophe models are saying about hurricane risk, both in the absence and in the presence of climate conditioning.

This paper presents a simple method for the comparison of catastrophe model outputs based on a so-called intensity profile (IP) and residual intensity profile (RIP). The IP and RIP are used to compare the catastrophe model risk estimates of BN hurricane risk versus CC hurricane risk. CC hurricane models were implemented by catastrophe modeling companies in 2006 after a series of academic papers and the heightened hurricane activity of 2004 and 2005 gave impetus to the notion that tropical cyclones occur more frequently in the current climactic regime. CC catastrophe models offer the darkest view of U.S. hurricane risk that can be justified from historical observations of North Atlantic hurricanes. Therefore, a comparison of BN versus CC catastrophe models offers a glimpse into the assumed causes and costs of climatically driven increases in hurricane activity. Using our simple method of comparison, we show that CC catastrophe models imply that the recent 30 to 50 years’ worth of climate change has increased North Atlantic hurricane frequency to a level approximately 30% greater than normal. While a significant increase, we put this increase in perspective by pointing out that increases in U.S. coastal property density have exhibited a long-term secular trend of 50% real growth per decade. This means that the total impact of up to 50 years’ worth of climate change on U.S. Hurricane risk is worth less than 10 years’ worth of U.S. coastal property growth. The potential impact on non-U.S. reinsurance markets is a decline in coverage capacity.

# **2.  Catastrophe models are not pricing models**

Before going on to discuss catastrophe models, it is important to emphasize that catastrophe models are not pricing models. The results of catastrophe models do not lead directly to insurance and reinsurance prices, mainly because of the cost of the capital which must be put-up against systemic insurance risks.<sup>2</sup> An in-depth discussion of the issues and reasons behind the incomplete linkage between actuarial estimates of risk and market prices for risk transfer is beyond the scope of this report; however, the reader can gain some understanding to the issue through a simplified example of a reinsurance price function. A reinsurance broker might summarize for insurance clients the cost of reinsurance in a given year with something like the following formula:<sup>3</sup> ROL = LOL + 5%, (1)

> 2 Cummins, J.D. and Olivier Mahul (2009): “Catastrophe Risk Financing in Developing Countries: Principles for Public Intervention.” The International Bank for Reconstruction and Development / The World Bank.

> 3 Cummins and Mahul (2009). See in particular Figure 2.2 on p.35.

2
where ROL is “rate on line,” the reinsurance premium divided by the limit of coverage, and LOL is “loss on line,” the average annual loss (AAL) of a reinsurance contract divided by the limit of coverage. The AAL is the expected annual loss averaged over a long period of time. It is typically gotten from a catastrophe model, which performs detailed, stochastic scenario analyses, as will be discussed further in the next section below. Putting aside taxes, overhead, and other transactional costs, if reinsurance premiums were purely determined by actuarial risk, the additional 5% term in (1) would not exist: ROL would equal to LOL in a world with no cost of capital and no transaction costs.

The impact of catastrophe model changes most often has a muted impact on insurance and reinsurance premiums, which is supported well by the form of price functional illustrated by (1). For example, the LOL might vary by up to 30% up or down from model to model (so a 1% LOL in one model might be 1.3% in another, equally valid model<sup>4</sup> ), but the excess premium represented by the 5% term in (1) might range anywhere from 3% to 12% year to year, depending on the cost of insurance and reinsurance capital in a given year.<sup>5</sup> This means, especially for catastrophic risks which have a low probability of occurrence, the majority of the year-to-year volatility in reinsurance prices might be attributed to factors outside of the variation in risk estimates produced by catastrophe models.

All of this is not to say that catastrophe models do not matter. They matter a great deal because they form the basis of a market-driven conversation on prices and availability of insurance and reinsurance. Also, too, catastrophe models potentially form a constructive link between science, engineering, and commerce. By their integration into the global insurance and reinsurance market, catastrophe models subject scientific developments in meteorology and seismology to an intense examination, the results of which are disseminated annually into a market that involves hundreds of billions of dollars in premiums worldwide. When this model-based system of commerce functions as intended, risk is taken more deliberately and with the costs and benefits more clearly in mind.

# **3.  Catastrophe models**

Catastrophe models are specialized computer models6 that use probabilistic scenario analysis to provide estimates of the probability of different size losses occurring in well-defined insurance systems. Catastrophe models first emerged in the late 1980s as affordable computing power 4 The most commonly asked question (what is the characteristic model uncertainty in catastrophe models) is typically unanswered by modeling firms. Generalizations are difficult to come by. Model uncertainty varies according the hazard being modeled. In case of U.S. hurricane risks, a reasonable estimate of model uncertainty is plus or minus 30%. So, for example, if an event is judged to have an annual probability of occurrence of 1% by one modeler, another, equally expert modeler, might estimate the probability of occurrence of the same event at 1.3% and yet another, equally expert modeler, might estimate the probability of occurrence of the same event at .7%. More typically, the variance among expert opinion in U.S. hurricane would be expected to be closer to plus or minus 15%, so the plus or minus 30% range is intended to encompass a wide range of variance in expert opinion.

5 In the Spring of 2009, in the reinsurance market for US hurricane risks, the ROL is anywhere from 8 to 12% for a 1% LOL.

6 Commercial models include those from Applied Insurance Research (AIR), EQECAT, Risk Management Solutions (RMS). Public domain models include the FEMA HAZUS model by Applied Research Associates (ARA) as well as the Florida Office of Insurance Regulation’s Florida Public Hurricane Model.

3
became available to those in the insurance industry who wanted to overlay hazard estimates on current estimates of property exposure<sup>7</sup> . Complex, largely non-transparent, and often subject to commercial non-disclosure agreements, catastrophe models nonetheless provide the support for public and private rate setting on billions of dollars of insurance in the United States each year— consider, for example, the Florida Hurricane Catastrophe Fund<sup>8</sup> and the California Earthquake Authority<sup>9</sup> ; public statements regarding their necessity and capital adequacy involve the use of catastrophe models.

Catastrophe risk models are well developed for developed economies where there is a demand for such models, for example from insurance and reinsurance companies that offer catastrophe coverage to their clients. In developing countries, where the property insurance market is usually under development (such as most middle income countries) or undeveloped (such as most lowincome countries), the demand for catastrophe insurance is almost non-existent and, consequently, catastrophe risk models are scarce. The donor community has been recently sponsoring the development or the enhancement of catastrophe risk models. Hurricane and earthquake risk models have been developed for the Caribbean region under the sponsorship of the Caribbean Catastrophe Risk Insurance Facility. Likewise, donors have financed the development of country-specific catastrophe risk models for the South Pacific Islands. In addition, there have recently been attempts to develop catastrophe risk models on open platform. For example, the Central American Probability Risk Assessment (CAPRA) initiative, supported by the World Bank and other development agencies, is based on an open and modifiable platform which allows governments and institutions to supplement the model with previous and ongoing initiatives (Cummins and Mahul, 2009). Such models are not only useful for insurance purpose, but also they offer policy makers new tools for their country management and mitigation programs. Such models are expensive to develop and the private sector may be reluctant to invest due to uncertainty about generating sufficient business to recover development costs. There is clearly a role for donors to finance such models to help countries better assess their economic and fiscal exposure to natural disasters, and ultimately, help reduce the physical and financial vulnerability of developing countries to natural disasters.

For those unfamiliar with catastrophe models, we describe here a highly simplified hurricane model. To calculate the Average Annual Loss (AAL) from US hurricanes, consider the following landfall model specification, outlined here only for illustration purposes: where _i_ is a coastal segment (CS) index;

> 7 Karen Clark (1986): “A Formal Approach to Catastrophe Risk Assessment and Management,” _Proceedings of the Casualty Actuarial Society_ , vol. LXXIII, no. 139. http://www.casact.org/pubs/proceed/proceed86/86069.pdf

> 8 Florida Hurricane Catastrophe Fund (FHCF) website. See in particular the annual reports under the “FHCF Reports” section. http://www.sbafla.com/fhcf/

9 California Earthquake Authority (CEA) website. See in particular the history of the CEA reports under the “About the CEA” section. http://www.earthquakeauthority.com/ 4
_n_ is the total number of CSs; _j_ is hurricane intensity given as Saffir-Simpson category 1 to 5.

W _i_ is the property value in the _i_<sup>th</sup> CS; H _i,j_ is the annual probability of occurrence of a hurricane of intensity _j_ in the _i_<sup>th</sup> CS; and D _j_ is the portion of property value lost to hurricane of intensity _j_ .

W _i_ can be described as an _exposure distribution_ ; H _i,j_ a _hazard distribution_ , and D _j_ a _damage function_ . These three elements of a catastrophe model determine annual probability of losses to property. The model underlying (2) above is highly simplified in many respects—for one, it assumes one hurricane, no more and no less, per year. The details of full blown catastrophe model are difficult to summarize into a simple model like this, but to give the reader a general feel for rough numbers, for major hurricanes (j=3,4,5), D _j_ is roughly 10 percent for insured losses. In a major coastal segment of property, such as around Miami, Florida, total property value, W _i_ (where i is suitably chosen to select the coastal segment that encompasses the greater Miami area), is effectively around 1 trillion USD<sup>1011</sup> . Therefore, given these simplified numbers, a major hurricane striking a major urban coastal segment of property is expected to cause an insured loss of property of about 100 billion USD. Such an event (major hurricane striking a major urban coastal segment of property) is expected to occur with annual probability of about 1 percent, or once every 100 years.<sup>12</sup> Therefore, as of 2009 we would say that a 1-in-100 year hurricane insured loss is 100 billion USD. The hazard distribution is considered relatively stable and biased toward higher intensity storms in warmer, southern waters<sup>13</sup> . In an unfortunate, partial coincidence, the US East Coast exposure distribution is sometimes, though not always, peaked where the coastline juts out into the ocean as well<sup>14</sup> . The damage function is relatively stable over time, so the main factor affecting changes in hurricane risk is changes in the exposure distribution. For US hurricane, AAL is currently estimated at about 10 billion USD<sup>15</sup> .

Catastrophe models use Monte Carlo techniques to generate 10 thousand years or more of simulated losses. Using the simple model above, a catastrophe model would generate random occurrence of hurricanes in simulated year via H _i,j_ , then overlays those random hurricanes on the fixed property distribution, W _i_ . The damage function D _j_ then translates the incidence of 10 FHCF website.

11 These figures are very high in absolute terms, and represent about 7 percent of the 2008 US GDP. Hurricanes hitting small islands can losses that are several times larger than their GDP. For example, a major hurricane hitting Jamaica could cause losses of more than 200% of GDP.

12 Note again that these numbers are rough and not consistently defined from researcher to researcher. For example, depending on how strictly one defines a hurricane strike on a particular location (from landfall within 5 miles to bypassing within 90 miles), the probability of a strike on a particular location can vary by a factor of 10 from model to model. Here, an emphasis was placed on giving round numbers that bear a reasonable resemblance to the kinds of numbers used in detailed commercial catastrophe models.

13National Hurricane Center website. See in particular the Climatology section. http://www.nhc.noaa.gov/HAW2/english/basics.shtml

> 14 Pielke, Jr., R. A., Gratz, J., Landsea, C. W., Collins, D., Saunders, M. A., and R. Musulin (2008): “Normalized Hurricane Damages in the United States: 1900-2005,” _Natural Hazards Review_ , vol. 9, no. 1, pp. 29-42.

http://sciencepolicy.colorado.edu/publications/special/normalized_hurricane_damages.html 15 Karen Clark & Company (2008): “Near Term Hurricane Models: How Have They Performed?” http://www.karenclarkandco.com/pdf/KCC_NearTermHurricanes.pdf 5
<!-- Start of picture text --> Loss =<br>(USD bin’s)<br>200 “<br>150<br>100 “<br>50<br>l 2 3 4<br>z, log return period<br><!-- End of picture text -->
<!-- Start of picture text --> 00<br>Loss<br>(USD bln’s) <9<br>200 ’<br>150<br>100) *<br>30<br>| 2 3 5<br>z, log return period<br><!-- End of picture text -->
<!-- Start of picture text --> Loss 300<br>(USD bln’s)<br>20 .<br>10<br>loc<br>50<br>I 2 3 4<br>z, log return period<br><!-- End of picture text -->
hinted at in previous section, we call these near-term models _climate conditioned_ . It is necessary to use such general terminology because there is disagreement among scientists about the ultimate causes of elevated hurricane activity in climate conditioned catastrophe models (CC catastrophe models). More specifically, there is disagreement among scientists about the significance of the observed approximate 0.5<sup>o</sup> C rise in SST over the last 30 years. One group of scientists believes that this rise in SST is part of a multidecadal cycle that is signaled by variations in de-trended SST records<sup>21</sup> . Another group of scientists believes that this rise in SST directly drives increases in hurricane activity<sup>22,23</sup> . Since the IPCC has concluded that SST has risen approximately 0.5<sup>o</sup> C over the last 30 to 50 years<sup>24</sup> , we might take CC models to reflect the maximum potential increase in hurricane activity that might occur from the last 30 to 50 years’ worth of climate change (CC)<sup>25</sup> .

In the case of two out of the three major catastrophe modeling firms, both non-climate conditioned and climate conditioned models are available, which allows for a convenient non-CC versus CC study to be made26. We already laid the groundwork for this comparative study by giving the LECs _BN_ and _CC_ at the end of the previous section above. In the following section, we present a simple method for comparing these two different LECs and show how this method is a useful way to understand the differences among LECs in general.

21 Goldenberg, S. B., Landsea, C. W., Mestas-Nunez, A. M., and W.M. Gray (2001): “The Recent Increase in Atlantic Hurricane Activity: Causes and Implications,” _Science_ , 293, pp. 474-479. http://www.sciencemag.org/cgi/reprint/293/5529/474.pdf

> 22 Emanuel, K. (2005): “Increasing destructiveness of tropical cyclones over the past 30 years,” _Nature_ , 436, pp. 686-688.

http://www.nature.com/nature/journal/v436/n7051/pdf/nature03906.pdf 23 Webster, P. J., Holland, G. J. , Curry, J. A., and H.-R. Chang (2005): “Changes in Tropical Cyclone Number, Duration, and Intensity in a Warming Environment,” _Science_ , 309, pp. 1844-1846. http://www.sciencemag.org/cgi/reprint/309/5742/1844.pdf 24 IPCC (2007): “Summary for Policymakers. In: Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change,” Solomon, S., D. Qin, M. Manning, Z. Chen, M. Marquis, K.B. Averyt, M.Tignor and H.L. Miller (editors), Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA.

http://www.ipcc.ch/pdf/assessment-report/ar4/wg1/ar4-wg1-spm.pdf 25 In this report, depending on the context, CC stands for both climate conditioned and climate change. The apparent double meaning is tolerable as the underlying intention is the same. Climate change, according to the IPCC’s usage (see footnote 1 in [6]), refers to any change in climate over time, whether due to human activity or natural variability. Climate conditioned here means essentially the same thing: CC catastrophe models only gauge potential increase in hurricane activity correlated with past increases or variations in SST. Whether these SST increases or variations are ultimately driven by human-driven changes in SST or natural variability is not decided by CC catastrophe models 26 Karen Clark & Company (2008).

9
<!-- Start of picture text --> 30<br>Intensity Profile (IP)<br>of 2oF!<br>BN and CC<br>15 .<br>1o<br>0 i] 2 3 4<br>z, log return period<br><!-- End of picture text -->
<!-- Start of picture text --> 12<br>10 --————~ a<br>Residual Intensity Profile (RIP)<br>of<br>BN and CC _<br>06<br>0 i 2 3 4<br>z, log return period<br><!-- End of picture text -->
<!-- Start of picture text --> Loss .<br>(USD bin’s) 1g<br>100<br>, z log return period = =<br><!-- End of picture text -->
<!-- Start of picture text --> 500<br>Loss 400<br>(USD bln’s)<br>wo<br>200<br>100<br>0 1 2 3 4<br>z, log return period<br><!-- End of picture text -->
establish<sup>33</sup> . Although beyond the scope of this paper, it is worthwhile to mention a possible strategy to prove or disprove the APH using some of the techniques of this paper. If one were to compare the LECs for US hurricane across all modeling companies and across all years going back to, say, 1999, it might be possible to see eventually, perhaps by 2016 (ten years after CC models were introduced) that property density growth alone will explain most model changes and that CC models eventually become indistinguishable from a BN model from 1999 trended up every year for property density growth. This would provide a hint that the APH is true. Depending on the actual LEC development versus the property density increase trend, CC models in 2006 might in retrospect be seen as either (i) a convenient way either to catch up on property density growth revealed by the active 2004 and 2005 US hurricane seasons or (ii) a way to get ahead of property density growth increases in the near future.

# **8.  US reinsurance markets and the potential effect on developing countries**

What happens in the US reinsurance market (USRM) often affects reinsurance markets abroad, so here we will discuss the USRM. The USRM, like the US insurance market, is the largest in the world34; it is estimated that North America (and mainly the USA) absorb 75% of the worldwide catastrophe reinsurance capacity (Cummins and Mahul 2009). Currently, the USRM is experiencing important challenges. Demand for reinsurance coverage is going up, while the ability of the USRM to provide coverage is going down. Models have some part in this. If modeled risk increases, as they have with the transition to CC models, both the insurer and reinsurer need to raise more capital or shed risk. Loss events often harm insurer and reinsurer differently, but model change events affect both in the same way. This year, this awkward dynamic is exacerbated by a potential change in the way rating agencies view the capital adequacy of insures and reinsurers. As of this year, the Florida Hurricane Catastrophe Fund (FHCF), the largest provider of hurricane reinsurance in the world, is considered substantially hampered in its ability to meet its potential obligations. This is because coming into this year the FHCF has relied upon tens of billions of USD in contingent, post-disaster financing to cover losses to the FHCF should the Big One occur. The recent impairment of the credit markets makes such a massive, post-event financing of losses unfeasible. This has caused a 10 to 30 billion USD gap in hurricane reinsurance, which cannot be easily filled. Furthermore, similar to the state of Florida, the rest of the reinsurance and insurance industry had been relying, at least in part, on post-event financing. Before the credit crisis, rating agencies expected that even substantial shortfalls in capital caused by a loss event could be healed over by the rapid mobilization of capital into the reinsurance and insurance markets after a large loss event—as had been the case in the past after Hurricane Andrew, the Northridge Earthquake, the terrorists attacks on 9/11, and Hurricane Katrina. Now, the outlook on post-event capital mobility and formation is uncertain.

We are still watching the situation unfold, but it appears inevitable that USRM premiums are set to dramatically increase in 2009-2010. Unlike increases driven by a loss event, these premium increases are likely to be slower to wash out of the system becuase they are driven by underlying structural trends and not by a single, rare event of loss.

> 33 Transcripts of private conversations are sometimes used to establish that a transaction has been manipulated, but even this form of evidence is not without its issues. One of the authors (JS) has observed that traders will sometimes confess to rigging a price when they in fact did not. Ultimately, expressing only the desire, not the true ability, to gain an edge in a highly competitive market, a trader’s confession is often a lie about a lie.

> 34 Swiss Re website. See in particular the research and publications of Swiss Re’s sigma group. www.swissre.com

14
In the catastrophe bond market, we are seeing almost a doubling in premiums for 1-in-100 year hurricane risks, which are now approaching 10 to 11 times actuarial levels, versus 4 to 7 times actuarial levels in years past. The expected result is that reinsurance capacity is likely to dry up over the next 2 years for any market abroad that is not a major source of risk and premium. This could manifest itself not so much in rate increases for non-US reinsurance markets, but in nonrenewals of coverage or dramatic reductions in coverage in reinsurance coverage for developing countries.

The hardening catastrophe reinsurance market, due to major insurance and reinsurance losses in 2008, and the increased demand for capacity in some developed countries (particularly the US) may reduce the capacity available for middle and low-income countries, particularly in the short term. However, this impact may be limited in the medium term, given the growing interest of investors and reinsurers for non-peak risks, that is, risks that are not correlated with the peak risks (such as US hurricanes and earthquakes), particularly for middle and low-income countries, which contribute to their portfolio diversification.

15
# **Appendix: How to calculate the AAL of an LEC**

It can be shown that the AAL, which is just an expected loss, can be calculated with the following expression: where zmax is the upper bound of the valid range of the argument of LEC. As a reminder, in this report, we used zmax = 4 throughout.

Because LEC(z) has polynomial form, the integral in (A.1) is solvable in closed form with the following result: Substituting into (A.2) the respective parameters of (4) and (5) in the main text, we get AAL( _BN_ )=11.4 and AAL( _CC_ )=14.6, where AAL is in billions of USD.

16