Property Catastrophe Bonds and Insurance Risk Part 1
Property Catastrophe Bonds
This article describes property catastrophe bonds, which are probably the
best known type of insurance-linked securities. Standard structural features
of catastrophe bonds are explained and the main analytical approaches
introduced. The chapter explains advantages and disadvantages of these
securities from both an insurance company and an investor perspective.
best known type of insurance-linked securities. Standard structural features
of catastrophe bonds are explained and the main analytical approaches
introduced. The chapter explains advantages and disadvantages of these
securities from both an insurance company and an investor perspective.
SECURITISATION OF PROPERTY INSURANCE RISK
The insurance industry is one of the largest warehouses of risk, incorporating
the roles of both risk underwriter and risk bearer in the way that the
banking industry did three decades ago. Since then, the banking industry
has undergone dramatic changes and now passes much of the risk on to
investors in the form of mortgage-backed and other securities.
the roles of both risk underwriter and risk bearer in the way that the
banking industry did three decades ago. Since then, the banking industry
has undergone dramatic changes and now passes much of the risk on to
investors in the form of mortgage-backed and other securities.
A strong argument could be made that the insurance industry should move in the
same direction by underwriting insurance risk and then passing a sizable
part of it on to investors in the form of standard securities. Many believe that
this is eventually going to happen, in particular for the products that are
more homogeneous and relatively commoditised, such as some types of life
and automobile insurance.
same direction by underwriting insurance risk and then passing a sizable
part of it on to investors in the form of standard securities. Many believe that
this is eventually going to happen, in particular for the products that are
more homogeneous and relatively commoditised, such as some types of life
and automobile insurance.
At this point, however, capital markets� involvement
in the insurance industry is starting not from the standard
homogeneous risk but rather from the most unusual and severe type of risk
� that is, the risk of natural catastrophes.
in the insurance industry is starting not from the standard
homogeneous risk but rather from the most unusual and severe type of risk
� that is, the risk of natural catastrophes.
Insurance and reinsurance industries, while considered to be well capitalised,
do not have the capacity to withstand the financial impact of a
large-scale natural disaster. Individual insurance companies, especially
those with significant exposure in certain geographic locations, face the risk
of large losses or financial ruin even from smaller-scale catastrophic events.
The sheer size of capital markets makes them the natural candidate for
providing the backstop protection to the insurance industry should a
Category 5 hurricane make a landfall in Miami, Florida, or should an earthquake
Category 8 on the Richter scale hit San Francisco, California. Capital markets, whose size exceeds that of the insurance industry by orders of
magnitude, may more easily weather such catastrophic losses.
do not have the capacity to withstand the financial impact of a
large-scale natural disaster. Individual insurance companies, especially
those with significant exposure in certain geographic locations, face the risk
of large losses or financial ruin even from smaller-scale catastrophic events.
The sheer size of capital markets makes them the natural candidate for
providing the backstop protection to the insurance industry should a
Category 5 hurricane make a landfall in Miami, Florida, or should an earthquake
Category 8 on the Richter scale hit San Francisco, California. Capital markets, whose size exceeds that of the insurance industry by orders of
magnitude, may more easily weather such catastrophic losses.
MOTIVATION FOR TRANSFERRING NATURAL CATASTROPHE RISK TO THE CAPITAL MARKETS
The idea behind catastrophe (cat) bonds is to transfer to the capital markets
the risk that extreme catastrophic events would inflict sizable losses on portfolios
of insurance policies held by insurance companies. Cat bonds offer a
new way for insurance companies to manage their risk exposure, a way that
provides benefits to insurance company shareholders by controlling the risk
and, if used appropriately, deploying their capital more effectively. From
the point of view of policyholders and regulators, the advantage is the
decreased likelihood of the company�s inability to pay its claims in the event
of a natural catastrophe.
the risk that extreme catastrophic events would inflict sizable losses on portfolios
of insurance policies held by insurance companies. Cat bonds offer a
new way for insurance companies to manage their risk exposure, a way that
provides benefits to insurance company shareholders by controlling the risk
and, if used appropriately, deploying their capital more effectively. From
the point of view of policyholders and regulators, the advantage is the
decreased likelihood of the company�s inability to pay its claims in the event
of a natural catastrophe.
Insurance company motivation
The primary motivation of an insurance company in securitising its property
catastrophe exposure by entering into a cat bond transaction is risk
transfer. In contrast, in triple-X and most other life insurance securitisations,
the primary motivation is not risk transfer but relieving the capital strain
created by regulatory requirements. As part of the overall capital-management
programme, the transfer of catastrophe risk to the capital markets is
another tool that insurance companies have in their overall arsenal of ways
to find the right balance between risk and return, and to manage capital
more efficiently.
catastrophe exposure by entering into a cat bond transaction is risk
transfer. In contrast, in triple-X and most other life insurance securitisations,
the primary motivation is not risk transfer but relieving the capital strain
created by regulatory requirements. As part of the overall capital-management
programme, the transfer of catastrophe risk to the capital markets is
another tool that insurance companies have in their overall arsenal of ways
to find the right balance between risk and return, and to manage capital
more efficiently.
Cat bonds are used as an alternative to traditional reinsurance for lowprobability
events. In some cases, protection obtained this way is cheaper
than the cost of reinsurance. An additional advantage is the fully collateralised
nature of the cat bond protection. It reduces the credit risk that is
always present in traditional reinsurance.
This risk could be significant since, when a sizable natural disaster strikes, reinsurance companies are
exposed to large losses and some might not be able to make good on their
obligations. Cat bond transactions also allow insurance and reinsurance
companies to lock in the cost of protection for a period longer than the one
year that is standard for reinsurance contracts.
exposed to large losses and some might not be able to make good on their
obligations. Cat bond transactions also allow insurance and reinsurance
companies to lock in the cost of protection for a period longer than the one
year that is standard for reinsurance contracts.
Investor motivation
The motivation of the insurer in hedging risk exposure is clear. What are the
advantages of the transaction to the investor in these securities? In other
words, why would capital markets players be interested in investing in cat
bonds? The first reason is the excess return that has been available on cat bond
transactions. The excess (relative to similarly rated corporate debt) return
has existed from the very first days of insurance risk securitisation and has
been attributed primarily to market inefficiency.
advantages of the transaction to the investor in these securities? In other
words, why would capital markets players be interested in investing in cat
bonds? The first reason is the excess return that has been available on cat bond
transactions. The excess (relative to similarly rated corporate debt) return
has existed from the very first days of insurance risk securitisation and has
been attributed primarily to market inefficiency.
It has always been expected that with the growth of the cat bond issuance and the increase in the number and sophistication level of the market participants, the excess return would
become very small. However, this has not happened in the decade since the
first cat bond was issued even as we witnessed wide fluctuations in pricing.
On the contrary, in the aftermath of the huge insurance losses in the 2004
and 2005 hurricane seasons, the excess return widened. This �Katrina effect�
has led to investors� being able to obtain high yields on securities that have
relatively high credit ratings. The ubiquitous search for alpha has led some
investors to this asset class.
become very small. However, this has not happened in the decade since the
first cat bond was issued even as we witnessed wide fluctuations in pricing.
On the contrary, in the aftermath of the huge insurance losses in the 2004
and 2005 hurricane seasons, the excess return widened. This �Katrina effect�
has led to investors� being able to obtain high yields on securities that have
relatively high credit ratings. The ubiquitous search for alpha has led some
investors to this asset class.
The second and probably more important reason is the fact that cat bonds
are often seen as almost �zero-beta� securities that provide a diversification
benefit. The rationale behind this view is that cat bonds are weakly correlated
with the other securities, leading to the comparison with Kipling�s �Cat That
Walked by Himself�. For cat bonds that are properly structured, where all
risks besides that of natural catastrophes are minimised,default rates are only
slightly affected by movements in the financial markets.
are often seen as almost �zero-beta� securities that provide a diversification
benefit. The rationale behind this view is that cat bonds are weakly correlated
with the other securities, leading to the comparison with Kipling�s �Cat That
Walked by Himself�. For cat bonds that are properly structured, where all
risks besides that of natural catastrophes are minimised,default rates are only
slightly affected by movements in the financial markets.
If the stock market crashes or the economy enters a recession, the effect on such cat bonds should
be minimal. (In the past,most cat bonds included significantly greater credit
risk than was intended by the structurers or appreciated by the investors. The
bankruptcy of Lehman Brothers revealed this weakness in a painful way for
some investors. The �new� cat bonds, issued since the beginning of 2009,
have structural features than minimise the credit risk.)
be minimal. (In the past,most cat bonds included significantly greater credit
risk than was intended by the structurers or appreciated by the investors. The
bankruptcy of Lehman Brothers revealed this weakness in a painful way for
some investors. The �new� cat bonds, issued since the beginning of 2009,
have structural features than minimise the credit risk.)
HISTORICAL PERSPECTIVE
The idea of securitising insurance risk had been floating around for a long
time before the first insurance-linked securities saw the light of day. Some of
the first securities intended to transfer the insurance risk of natural catastrophes
directly to investors were catastrophe options. Traded on the Chicago
Board of Trade (CBOT) in the 1990s, they were met with lukewarm reception
by both insurers and investors and were ultimately withdrawn.
time before the first insurance-linked securities saw the light of day. Some of
the first securities intended to transfer the insurance risk of natural catastrophes
directly to investors were catastrophe options. Traded on the Chicago
Board of Trade (CBOT) in the 1990s, they were met with lukewarm reception
by both insurers and investors and were ultimately withdrawn.
Exchange-traded catastrophe derivatives have recently reappeared and are
now traded, in slightly different forms, on exchanges that include the
Chicago Climate Futures Exchange, CME and Eurex. We will discuss this further by providing
more in-depth treatment of these securities.
now traded, in slightly different forms, on exchanges that include the
Chicago Climate Futures Exchange, CME and Eurex. We will discuss this further by providing
more in-depth treatment of these securities.
Cat bonds have enjoyed greater success. One of the first cat bonds was issued on behalf of USAA, a large insurance company, in 1997. It transferred
to investors the risk that a hurricane in the Eastern US and the Gulf Coast
would result in catastrophic insured losses to the company. The size of the
bond was US$395 million, which was the maximum protection size
provided to USAA by the transaction.
to investors the risk that a hurricane in the Eastern US and the Gulf Coast
would result in catastrophic insured losses to the company. The size of the
bond was US$395 million, which was the maximum protection size
provided to USAA by the transaction.
Since that pioneering transaction, the volume of property catastrophe
insurance securitisations has steadily grown, primarily in the form of catastrophe
bonds. Insurance and reinsurance companies as well as corporate
entities have turned to the capital markets for protection against catastrophe
risk. The type of risk transferred to investors has ranged from hurricanes to
earthquakes to typhoons, in geographic areas spanning the globe from the
US to Europe to Japan.
Until recently, the growth was not as fast as observers had anticipated.
However, in the aftermath of Hurricane Katrina in 2005, the interest in
securitising property catastrophe insurance risk has exploded, and there
has been dramatic growth in the total amount of capital invested in securitised
risk in the forms of cat bonds, industry loss warranties and reinsurance
sidecars. The last two are described in greater detail in Chapter 6. The
temporary pause in issuance in the second half of 2008 had to do with
the above-mentioned credit risk issues, which have now been largely
resolved.
distribution (the bell curve). They are referred to as fat-tailed distributions
because of the high probability of extreme diversion from the mean. (More
precisely, these are leptokurtic distributions.
Their excess kurtosis leads to the higher probability of outliers in a sample relative to samples drawn from a Gaussian distribution.) Insurance losses resulting from natural catastrophe
events lie at the far-right tail of the aggregate loss distribution, the �cat�s
tail�. These events and their financial impact are difficult to model but are
important for insurance companies to protect against.
Insurance companies often find themselves unable or unwilling to retain
all of the risk inherent in their portfolios of insurance policies. In dealing
with catastrophe risk, the two main mechanisms for risk transfer are reinsurance
and, more recently, cat bonds or similar capital markets solutions.
Reinsurance plays a very important role by providing a somewhat efficient
risk exchange mechanism for the insurance industry. In dealing with large scale
catastrophic events, however, even reinsurance fails to provide adequate protection due to the limited capital in the reinsurance and insurance industry relative to the magnitude of potential losses.
describing reinsurance, the main mechanism for risk transfer in the insurance
industry. Simply put, reinsurance is insurance for insurance
companies. In the case of catastrophe risk transfer, an insurance company
can buy reinsurance protection against losses exceeding a certain level.
The insurance company, or �cedent� of risk in the reinsurance parlance,
pays premiums to a reinsurer for the protection, and is reimbursed for
claims in the scope of the reinsurance contract.
Depending on jurisdiction, reinsurer�s rating and other considerations,
the reinsurance company might be required to post collateral. Reinsurance
companies could in turn reinsure some of their risk. This type of reinsurance
is called retrocession.
In the above presented in diagram, if the company decides that it is
too risky to retain the exposure between US$500 million and US$630 million,
it has two main options. One of them is to reinsure this exposure. Another
is to go to the capital markets and obtain protection in the form of a catastrophe
bond or a similar instrument. In addition, there is always an option
to reduce the insurance risk exposure by either writing less insurance business
or by changing the concentrations, policy limits or policy conditions of
the insurance portfolio.
There are also options of raising additional capital in
the form of equity, debt or hybrid securities, as well as obtaining contingent
capital. From the point of view of the efficient use of capital, these options
are usually less effective than reinsurance or catastrophe bonds. Advantages
and disadvantages of using cat options and futures to protect against catastrophic
events are discussed in earlier articles.
Effectively, securitising insurance risk amounts to securitising a liability
rather than an asset.
Unlike the case of corporate bonds, the insurance or reinsurance company
transferring catastrophe risk to the capital markets is not issuing the bond
directly. Instead, the bond is issued by a special purpose reinsurance
company, which is generally located offshore. Thus, the entity that transfers
the risk to the capital markets is referred to as the sponsor rather than the
issuer of the catastrophe bond.
An entity that wants to transfer catastrophe risk to the capital markets
would enter into a catastrophe reinsurance contract with a special purpose
vehicle (SPV), a reinsurance company. The SPV will issue a bond with the
payment of principal and interest contingent on there not occurring a catastrophe
causing specified damage. The term of the reinsurance contract is
the same as the term of the bond.
If during this term no such catastrophe has
happened, investors get back the principal and interest in full. Should there
be a natural catastrophe triggering the reinsurance contract, the SPV will
pay the claims. The remainder of the funds, if any, will go towards the
payment of principal and interest to investors.
The simplified structure of a catastrophe bond is shown in the diagram below
If no covered catastrophe has occurred during the term of the bond,
investors receive back their principal at the end of the term.
by a certain natural catastrophe. The second transaction is the issuance of a
fixed-income security, a cat bond, to investors. The cat bond provides for
payment of interest and repayment of principal unless a default is triggered
by a natural catastrophe leading to a high level of insured losses.
Proceeds from the sale of the cat bond are deposited into a trust account
that serves as collateral.
The trust account would contain very secure, highly
rated short-term instruments. While in many cases a cat bond sponsor could
legally own the SPV without affecting its bankruptcy-remote status, in practice
the SPV would usually be established by a third party such as an
investment bank structuring the transaction.
Returns from the collateral account are swapped for a Libor-based rate
with a highly rated counterparty. The total-return swap feature has become
common in cat bond structures. Thus, interest rate-risk is minimised and the
cat bonds become floating-rate instruments.
The interest payments received by investors are composed of the Liborbased
returns on the funds in the collateral account; they can also include all
or part of the reinsurance premiums received by the SPV from the sponsor.
Several ways to minimise credit risk related to the swap counterparty and
to the assets in the collateral account have emerged post-2008.
No credit enhancement or credit wrapping has been used in property
catastrophe bond securities. This has to do, in part, with the relatively low
ratings of most catastrophe bonds, which makes them too risky for monoline
financial guarantee companies to add a credit wrap. (Credit
enhancement used to be a common feature of extreme-mortality catastrophe
bonds and other life-insurance-linked securities.
Credit enhancement of this type is no longer available from financial guarantors.
proposed and used in cat bond transactions. In general, the triggers fall into
one of two categories: indemnity and index. Indemnity triggers
Indemnity triggers provide for cat bond payout based on the actual insurance
losses suffered by the bond sponsor. This makes the cat bond a very
effective hedge against the risk of losses from the natural catastrophe since
the basis risk is minimised.
It largely avoids the unfortunate situation of a
natural catastrophe occurring, an insurance company suffering significant
losses, but finding itself unable to collect from the cat bond it sponsored.
The negative side of indemnity triggers, from the point of view of the
sponsor, is the need for information disclosure about its book of insurance
business and underwriting practices. Many insurance companies prefer to
keep this data confidential. Some of them are also hesitant to undergo the
data quality review needed to present the information to investors in an
offering circular.
Many investors see only negatives in the use of indemnity triggers. By its
very nature, an indemnity trigger is less objective since it is based on actual
insured losses rather than on parameters of a physical event. Investors are
justifiably wary of the asymmetric information, with the insurance company
sponsoring the bond having a significant information advantage in better
knowing the types of risks it underwrites, risk aggregation, its underwriting
standards and claim-settlement practices.
The investors also assume the risk that, as the company implements its strategy or responds to market conditions during the term of the bond, its insurance portfolio might change and increase the risk of bond default. The very fact that the bond sponsor has
obtained protection via a cat bond could lead to a morale hazard, demonstrating
itself in less care being taken in insurance underwriting and claim
settlement.
In addition to the morale hazard, there is always a potential for
moral hazard, with the insurer intentionally (but without violating the bond
covenants) making changes to its portfolio to the detriment of the cat bond
investors. While indemnity-based bonds historically were the first issued and are
still common, the general trend has been away from the indemnity-type triggers
and towards index triggers.
losses. Rather, they depend on parameters that are outside of the
control of the sponsor, thus providing more comfort to investors by eliminating
the information asymmetry inherent in indemnity-based triggers.
Index triggers usually fall into one of the following four categories: simple
index, parametric, model portfolio loss and industry loss.
physical event happens. A simple example would be a Category 5 hurricane
making a landfall in Florida. If such an event happens, a cat bond with this
trigger will suffer a default and make a payment to the benefit of the
sponsor. It could, but does not have to, be structured like a binary option,
providing either no payment to the sponsor if not triggered or the full
payment (full default) if triggered.
From the point of view of an investor, this structure is very attractive.
Investors have access to full information, and the dependence on sponsor�s
underwriting and other practices is eliminated.
On the other hand, the insurance company sponsoring the bond faces
significant basis risk.
A trigger so crudely defined could have poor correlation
with actual insurance losses, reducing the effectiveness of the cat bond
as a hedge. In other words, there is a significant chance that the cat bond
would provide little or no protection against actual insurance losses suffered
by the sponsor. There is also a chance that the bond will be triggered when
the sponsor has not suffered sizable losses. In this case, the sponsor has paid
for unneeded protection.
The basis risk is present in all non-indemnity trigger types, but is greatest
when the trigger is based on a basic index.
combination of defined physical parameters. More than one type of catastrophic
event (hazard) could be involved, and the amount of the payout is
a function of the physical parameters of the cat events. A predefined formula
is used to determine whether the bond is triggered and what the payout
amount is.
The formula could be quite complex. It is structured in a way that
reduces the basis risk by identifying physical parameters of cat events (such
as wind speeds at several locations) that would lead to insurance losses of
the magnitude that the sponsor wants to transfer to capital markets.
Identification of such parameters and the construction of the formula (the
overall index), if done properly, involve a significant modelling exercise on
the part of the sponsor.
The investor, on the other hand, is not concerned
with the sponsor�s insurance losses and hedge effectiveness. Since the probability
of default and the loss given default are independent of actual
insured losses, investor analysis is focused on the probabilities of the physical
events and their severities included in the parametric trigger formula.
portfolio of insurance policies or the portfolio that the sponsor expects to
hold during the term of the bond. The portfolio is held �in escrow� together
with the modelling software used to calculate losses to the portfolio. If a
natural catastrophe happens, its actual physical parameters are input into
the modelling software and losses to the model portfolio are generated.
The bond payout depends on whether and by how much the modelled losses
exceed a predetermined level. To further reduce basis risk, the sponsor could use its actual current insurance portfolio instead of the representative model portfolio.
The negatives of this approach have to do with the unwillingness of insurance companies to
reveal detailed information about their insurance portfolios and the fact that
such detailed policy-level disclosure could sometimes be unlawful.
Investors not possessing specialised expertise and knowledge of cat
modelling software sometimes feel uncomfortable with the use of this
trigger type.
as a whole as a result of a natural catastrophe. While not based directly on physical parameters of a catastrophic event, this index could be modelled
much better than indemnity losses. Given that a specific catastrophic event
has occurred, insurance losses for the whole industry are more predictable
than losses for an individual insurance company.
They also are not subject to manipulation by the sponsor through claim settlement or another mechanism. Insurance loss-reporting organisations provide information to
determine the overall loss level for the industry from a specific catastrophic
event. The sponsor bears the basis risk, which depends on how its actual loss
distribution differs from the rest of the insurance industry.
and simplicity on the one side, and the minimisation of basis risk on
the other. It is also worth noting that trigger choice to some degree affects structuring
costs, with indemnity-based transactions being the most expensive to
structure.
Indemnity-based cat bonds also take longer to generate a payout
since the sponsor might have to settle its claims first to determine the loss
size. Basic index, parametric and model portfolio triggers provide for fast
payout, while cat bonds based on industry-loss triggers have a payment
delay due to the need to calculate the estimates of industry losses.
While in general all default triggers fall into one of the described categories,
modifications of these triggers could be and have been used too.
Some investors, especially in the aftermath of 2005 Hurricane Katrina, have expressed a strong aversion to indemnity-based transactions, and
prefer bonds with parametric and similar triggers.
achieve the best protection for the insurance company while satisfying
investor concerns. Sometimes an insurance company is not afraid of
suffering one catastrophic loss, but wants to get protection in case one catastrophe
is followed by another in the same or the following year.
A second-event trigger could provide the required protection to the company,
with the bond providing no payout (but being �activated�) after the first
catastrophic event and paying only if the second event occurs as well.
as a hurricane, typhoon or earthquake. It could also be based on a number of perils, with losses from any one of them or a combination of perils triggering
the payout.
While the first cat bonds were generally designed to provide protection
against one type of peril, we have now seen a strong trend towards incorporating
multiple perils in a bond. The same bond could have a number of
peril/geographic location combinations.
Larger insurance or reinsurance companies with portfolios of insurance policies on more than one continent are interested in this aggregate protection. When it comes to multiple perils,
investors fall into two categories. Some are happy to see various types of
uncorrelated risk in the same security. Effectively, diversification is
provided for them in such a bond. Others prefer to buy cat bonds tied to a
single peril and to achieve diversification on their own.
The latter category tends to include investors with better understanding of the insurance-linked
securities, including the funds focused exclusively on these financial instruments.
The table, overleaf, shows a sample of catastrophe bonds issued
based on various default triggers and types of catastrophe peril. Some cat
bonds have included a number of tranches, each of which corresponds to a
specific type of insurance risk and has its own trigger.
The securitisation of insurance risk has moved beyond property catastrophe
and has included some liability insurance cat bonds, as well as
securitisation of property-casualty insurance risk that is not truly catastrophic
in nature.
but has now stabilised with the average being three years. This term
is long enough for the sponsor to lock into a multi-year protection at a
predetermined price and to avoid paying the fixed cost of issuing a cat bond
every year. At the same time, it is short enough for the sponsor to predict the
composition of its future insurance portfolio with a reasonable degree of
confidence.
losses, that is, the probability distribution of cat bond payouts. This
probability distribution is in turn based on probabilities of the cat bond
being triggered, and the payout amounts given that the bond has been
triggered.
risk analysis is included in the investor prospectus. For catastrophe
bonds the analysis, performed by one of the firms specialising in modelling
catastrophe events and their financial impact on portfolios of insurance policies,
is usually presented in the form of a probability exceedance curve (EC).
The exceedance curve shows probabilities of insurance losses of various
magnitudes.
If the annual exceedance probability is 1%, then the probability of
exceedance during a three-year period is 3%. (More precisely, the probability
of exceedance over a three-year period is equal to 1�(1�0.01)3 = 2.97%.
The approximation works well for only very small annual exceedance probabilities
and short time periods. For example, if the annual exceedance probability is 2% and the term is eight years, we might think that the probability of exceedance over the term equals 16%. In reality, it is 14.92%, which is calculated as 1�0.988.) The following figure shows an example of an exceedance
probability curve for a portfolio of insurance risk.
In this example, losses above US$500 million might have a catastrophic
effect on the insurance company�s financial position. The company has
several options to protect itself against this possibility. Some of them have to
do with raising additional capital or reducing or rearranging the company�s
portfolio of insurance policies. The most common solution is purchasing
reinsurance � that is, insurance protection for this insurance risk portfolio.
For example, the reinsurance coverage could take the form of the reinsurance
company reimbursing the insurance company for all losses above the
level of US$500 million, limited to the total payout of US$250 million. In this
case, the insurance company would still be unprotected if the total losses
exceed US$750 million, but would probably be willing to take this risk if
losses above US$750 million were considered to be exceptionally unlikely.
The company might wish to protect itself from losses in excess of US$500
million even if the effect of such losses would not have a truly catastrophic
effect on its financial position.
The reasons for it could be the desire to
decrease earnings volatility or to reduce capital requirements.
In property insurance, unique terminology has been developed. Probable
maximumloss, or PML, is the loss level thatwould be reached only extremely
rarely. There are many opinions of how rare is �rare�, leading to multiple
definitions of PML. If a company wants to define PML as the aggregate loss
level thatwould be reached only once in 100 years, then in the example above
the PML will be US$500 million.
With the increased emphasis on risk management and themore stringent capital-adequacy requirements promulgated by the rating agencies, there is growing shift of focus to property
catastrophe events that happen on average less often than once in 250 years,
leadingmany to define PML as the 1-in-250-year event.
While the concept of PML is often used in relation to losses from individual policies, here we
discuss the aggregate PML of an insurance portfolio. We also avoid nonquantitative
definitions of PML still common in the insurance industry. In insurance, probability of exceedance is usually expressed on an annual basis, that is, as a probability that insured losses will exceed a certain level over a period of 12 months. In the context of cat bonds, exceedance probability
could also be expressed as the probability of losses exceeding a certain
level, such as the bond trigger level, over the term of the bond.
Modelling catastrophe risk presents numerous challenges, but, even when it is accomplished,
the results by themselves do not tell the investors what price is
appropriate or fair for the cat bond being modelled. Several pricing models
have been proposed. Often, they use as an input the observed prices for
other cat bonds.
As �neat� mathematically as the Wang transform is, its practical application
is very difficult. It has also been pointed out (Pelsser 2008) that its use
in pricing financial and insurance risks is consistent with arbitrage-free
pricing, only under rather restrictive assumptions (this statement, however,
has been disputed).
Other pricing approaches have been proposed, such as the application of
extreme-value theory to cat bond pricing. This approach requires making
assumptions not fully appropriate for cat bond analysis, and it does not
produce results resembling observed cat bond prices. A simple rule-ofthumb
approach to pricing includes the use of �multiples� of expected
annual loss (average annual loss, or AAE) to determine the required spread over Libor or risk-free rate. Different multiples correspond to different levels
of expected loss.
While this approach has a questionable mathematical foundation,
it is easy to use and there are some investors that utilise it. Another
simple approach that has been proposed calculates prices based on the
expected frequency and severity of the losses. The parameters are estimated
based on the observed cat bond prices. This approach has the appeal of
simplicity, but it lacks any theoretical foundation.
Finally, some still use approaches that calculate prices based on the mean plus a multiple of standard
deviation. Many of these relatively simple approaches are borrowed
from reinsurance pricing, where they have been used for many years, but
even there they are being replaced by the more sophisticated methods.
In addition to the shaky theoretical foundations of some of the pricing
approaches, their common weakness is the dependence � either for parameter
fitting or for results validation � on the actual observed cat bond
prices. The cat bond market and the ILS markets in general are far from
2004; Pelsser 2008) with the goal of linking actuarial pricing and modern
finance theories. It has been used for both pricing cat bonds and excess-ofloss
reinsurance. While the full explanation of this method is outside the
scope of this chapter, the basics of the approach are explained below.
Based on the underlying loss variable X, the loss to the excess-of-loss
layer attaching at a with the limit of h, which is equivalent to the loss to a
cat bond, is defined as
being efficient, and the observed prices, even relative to each other, do not
necessarily follow the logic evident in more efficient markets.
The supply�demand dynamics play a very important role in pricing cat
bonds and catastrophe risk in general. When reinsurance markets �harden�,
the spread over Libor is likely to increase. This effect does not necessarily
correlate with the behaviour of the financial markets.
Even more importantly, the �peak peril� effect results in prices that are difficult to predict
based on the assumption that markets are efficient. Two cat bonds, one
linked to hurricane losses in Florida and the other to typhoon losses in
Australia, might have exactly the same exceedance probability distributions,
but the yield on the Florida hurricane bond is likely to be dramatically
greater than on the Australia typhoon one.
While the proposed pricing approaches often fail in the analysis of individual
bonds, relative-value analysis is still possible and helpful. More
importantly, the existing modelling tools allow us to manage cat risks on a
portfolio basis, and � instead of trying to come up with a theoretically
correct price for an individual bond � to see what incremental impact its
addition to the portfolio is going to have relative to the available alternatives.
This topic is further discussed in Property Catastrophy Bonds Part 2.
However, in the aftermath of Hurricane Katrina in 2005, the interest in
securitising property catastrophe insurance risk has exploded, and there
has been dramatic growth in the total amount of capital invested in securitised
risk in the forms of cat bonds, industry loss warranties and reinsurance
sidecars. The last two are described in greater detail in Chapter 6. The
temporary pause in issuance in the second half of 2008 had to do with
the above-mentioned credit risk issues, which have now been largely
resolved.
RISK TRANSFER IN INSURANCE
Insurance loss distributions tend to differ significantly from the normaldistribution (the bell curve). They are referred to as fat-tailed distributions
because of the high probability of extreme diversion from the mean. (More
precisely, these are leptokurtic distributions.
Their excess kurtosis leads to the higher probability of outliers in a sample relative to samples drawn from a Gaussian distribution.) Insurance losses resulting from natural catastrophe
events lie at the far-right tail of the aggregate loss distribution, the �cat�s
tail�. These events and their financial impact are difficult to model but are
important for insurance companies to protect against.
Insurance companies often find themselves unable or unwilling to retain
all of the risk inherent in their portfolios of insurance policies. In dealing
with catastrophe risk, the two main mechanisms for risk transfer are reinsurance
and, more recently, cat bonds or similar capital markets solutions.
Reinsurance plays a very important role by providing a somewhat efficient
risk exchange mechanism for the insurance industry. In dealing with large scale
catastrophic events, however, even reinsurance fails to provide adequate protection due to the limited capital in the reinsurance and insurance industry relative to the magnitude of potential losses.
Reinsurance risk transfer
Discussion of risk transfer and catastrophe bonds is impossible withoutdescribing reinsurance, the main mechanism for risk transfer in the insurance
industry. Simply put, reinsurance is insurance for insurance
companies. In the case of catastrophe risk transfer, an insurance company
can buy reinsurance protection against losses exceeding a certain level.
The insurance company, or �cedent� of risk in the reinsurance parlance,
pays premiums to a reinsurer for the protection, and is reimbursed for
claims in the scope of the reinsurance contract.
Depending on jurisdiction, reinsurer�s rating and other considerations,
the reinsurance company might be required to post collateral. Reinsurance
companies could in turn reinsure some of their risk. This type of reinsurance
is called retrocession.
too risky to retain the exposure between US$500 million and US$630 million,
it has two main options. One of them is to reinsure this exposure. Another
is to go to the capital markets and obtain protection in the form of a catastrophe
bond or a similar instrument. In addition, there is always an option
to reduce the insurance risk exposure by either writing less insurance business
or by changing the concentrations, policy limits or policy conditions of
the insurance portfolio.
There are also options of raising additional capital in
the form of equity, debt or hybrid securities, as well as obtaining contingent
capital. From the point of view of the efficient use of capital, these options
are usually less effective than reinsurance or catastrophe bonds. Advantages
and disadvantages of using cat options and futures to protect against catastrophic
events are discussed in earlier articles.
CATASTROPHE bONd STRUCTURE
The structure of a cat bond is different from that of asset-backed securities.Effectively, securitising insurance risk amounts to securitising a liability
rather than an asset.
Unlike the case of corporate bonds, the insurance or reinsurance company
transferring catastrophe risk to the capital markets is not issuing the bond
directly. Instead, the bond is issued by a special purpose reinsurance
company, which is generally located offshore. Thus, the entity that transfers
the risk to the capital markets is referred to as the sponsor rather than the
issuer of the catastrophe bond.
An entity that wants to transfer catastrophe risk to the capital markets
would enter into a catastrophe reinsurance contract with a special purpose
vehicle (SPV), a reinsurance company. The SPV will issue a bond with the
payment of principal and interest contingent on there not occurring a catastrophe
causing specified damage. The term of the reinsurance contract is
the same as the term of the bond.
If during this term no such catastrophe has
happened, investors get back the principal and interest in full. Should there
be a natural catastrophe triggering the reinsurance contract, the SPV will
pay the claims. The remainder of the funds, if any, will go towards the
payment of principal and interest to investors.
The simplified structure of a catastrophe bond is shown in the diagram below
If no covered catastrophe has occurred during the term of the bond,
investors receive back their principal at the end of the term.
fixed-income security, a cat bond, to investors. The cat bond provides for
payment of interest and repayment of principal unless a default is triggered
by a natural catastrophe leading to a high level of insured losses.
Proceeds from the sale of the cat bond are deposited into a trust account
that serves as collateral.
The trust account would contain very secure, highly
rated short-term instruments. While in many cases a cat bond sponsor could
legally own the SPV without affecting its bankruptcy-remote status, in practice
the SPV would usually be established by a third party such as an
investment bank structuring the transaction.
Returns from the collateral account are swapped for a Libor-based rate
with a highly rated counterparty. The total-return swap feature has become
common in cat bond structures. Thus, interest rate-risk is minimised and the
cat bonds become floating-rate instruments.
The interest payments received by investors are composed of the Liborbased
returns on the funds in the collateral account; they can also include all
or part of the reinsurance premiums received by the SPV from the sponsor.
Several ways to minimise credit risk related to the swap counterparty and
to the assets in the collateral account have emerged post-2008.
No credit enhancement or credit wrapping has been used in property
catastrophe bond securities. This has to do, in part, with the relatively low
ratings of most catastrophe bonds, which makes them too risky for monoline
financial guarantee companies to add a credit wrap. (Credit
enhancement used to be a common feature of extreme-mortality catastrophe
bonds and other life-insurance-linked securities.
Credit enhancement of this type is no longer available from financial guarantors.
DEFAULT TRIGGERS
A number of payout triggers � triggers of the cat bond default � have beenproposed and used in cat bond transactions. In general, the triggers fall into
one of two categories: indemnity and index. Indemnity triggers
Indemnity triggers provide for cat bond payout based on the actual insurance
losses suffered by the bond sponsor. This makes the cat bond a very
effective hedge against the risk of losses from the natural catastrophe since
the basis risk is minimised.
It largely avoids the unfortunate situation of a
natural catastrophe occurring, an insurance company suffering significant
losses, but finding itself unable to collect from the cat bond it sponsored.
The negative side of indemnity triggers, from the point of view of the
sponsor, is the need for information disclosure about its book of insurance
business and underwriting practices. Many insurance companies prefer to
keep this data confidential. Some of them are also hesitant to undergo the
data quality review needed to present the information to investors in an
offering circular.
Many investors see only negatives in the use of indemnity triggers. By its
very nature, an indemnity trigger is less objective since it is based on actual
insured losses rather than on parameters of a physical event. Investors are
justifiably wary of the asymmetric information, with the insurance company
sponsoring the bond having a significant information advantage in better
knowing the types of risks it underwrites, risk aggregation, its underwriting
standards and claim-settlement practices.
The investors also assume the risk that, as the company implements its strategy or responds to market conditions during the term of the bond, its insurance portfolio might change and increase the risk of bond default. The very fact that the bond sponsor has
obtained protection via a cat bond could lead to a morale hazard, demonstrating
itself in less care being taken in insurance underwriting and claim
settlement.
In addition to the morale hazard, there is always a potential for
moral hazard, with the insurer intentionally (but without violating the bond
covenants) making changes to its portfolio to the detriment of the cat bond
investors. While indemnity-based bonds historically were the first issued and are
still common, the general trend has been away from the indemnity-type triggers
and towards index triggers.
Index triggers
Index triggers do not directly depend on the bond sponsor�s actual insurancelosses. Rather, they depend on parameters that are outside of the
control of the sponsor, thus providing more comfort to investors by eliminating
the information asymmetry inherent in indemnity-based triggers.
Index triggers usually fall into one of the following four categories: simple
index, parametric, model portfolio loss and industry loss.
Basic index trigger
Basic index trigger provides for cat bond payout in case a predeterminedphysical event happens. A simple example would be a Category 5 hurricane
making a landfall in Florida. If such an event happens, a cat bond with this
trigger will suffer a default and make a payment to the benefit of the
sponsor. It could, but does not have to, be structured like a binary option,
providing either no payment to the sponsor if not triggered or the full
payment (full default) if triggered.
From the point of view of an investor, this structure is very attractive.
Investors have access to full information, and the dependence on sponsor�s
underwriting and other practices is eliminated.
On the other hand, the insurance company sponsoring the bond faces
significant basis risk.
A trigger so crudely defined could have poor correlation
with actual insurance losses, reducing the effectiveness of the cat bond
as a hedge. In other words, there is a significant chance that the cat bond
would provide little or no protection against actual insurance losses suffered
by the sponsor. There is also a chance that the bond will be triggered when
the sponsor has not suffered sizable losses. In this case, the sponsor has paid
for unneeded protection.
The basis risk is present in all non-indemnity trigger types, but is greatest
when the trigger is based on a basic index.
Parametric trigger
Parametric trigger is based on the occurrence of catastrophic events with acombination of defined physical parameters. More than one type of catastrophic
event (hazard) could be involved, and the amount of the payout is
a function of the physical parameters of the cat events. A predefined formula
is used to determine whether the bond is triggered and what the payout
amount is.
The formula could be quite complex. It is structured in a way that
reduces the basis risk by identifying physical parameters of cat events (such
as wind speeds at several locations) that would lead to insurance losses of
the magnitude that the sponsor wants to transfer to capital markets.
Identification of such parameters and the construction of the formula (the
overall index), if done properly, involve a significant modelling exercise on
the part of the sponsor.
The investor, on the other hand, is not concerned
with the sponsor�s insurance losses and hedge effectiveness. Since the probability
of default and the loss given default are independent of actual
insured losses, investor analysis is focused on the probabilities of the physical
events and their severities included in the parametric trigger formula.
Model portfolio loss
In this case, a sponsor creates a model portfolio that closely mirrors its actualportfolio of insurance policies or the portfolio that the sponsor expects to
hold during the term of the bond. The portfolio is held �in escrow� together
with the modelling software used to calculate losses to the portfolio. If a
natural catastrophe happens, its actual physical parameters are input into
the modelling software and losses to the model portfolio are generated.
The bond payout depends on whether and by how much the modelled losses
exceed a predetermined level. To further reduce basis risk, the sponsor could use its actual current insurance portfolio instead of the representative model portfolio.
The negatives of this approach have to do with the unwillingness of insurance companies to
reveal detailed information about their insurance portfolios and the fact that
such detailed policy-level disclosure could sometimes be unlawful.
Investors not possessing specialised expertise and knowledge of cat
modelling software sometimes feel uncomfortable with the use of this
trigger type.
Industry loss trigger
This trigger is tied to an index of losses suffered by the insurance industryas a whole as a result of a natural catastrophe. While not based directly on physical parameters of a catastrophic event, this index could be modelled
much better than indemnity losses. Given that a specific catastrophic event
has occurred, insurance losses for the whole industry are more predictable
than losses for an individual insurance company.
They also are not subject to manipulation by the sponsor through claim settlement or another mechanism. Insurance loss-reporting organisations provide information to
determine the overall loss level for the industry from a specific catastrophic
event. The sponsor bears the basis risk, which depends on how its actual loss
distribution differs from the rest of the insurance industry.
Trigger choice
In choosing a trigger, there is always a balance to be struck between transparencyand simplicity on the one side, and the minimisation of basis risk on
the other. It is also worth noting that trigger choice to some degree affects structuring
costs, with indemnity-based transactions being the most expensive to
structure.
Indemnity-based cat bonds also take longer to generate a payout
since the sponsor might have to settle its claims first to determine the loss
size. Basic index, parametric and model portfolio triggers provide for fast
payout, while cat bonds based on industry-loss triggers have a payment
delay due to the need to calculate the estimates of industry losses.
While in general all default triggers fall into one of the described categories,
modifications of these triggers could be and have been used too.
Some investors, especially in the aftermath of 2005 Hurricane Katrina, have expressed a strong aversion to indemnity-based transactions, and
prefer bonds with parametric and similar triggers.
Second- or third-event trigger
Structuring a cat bond provides a lot of room for creativity in trying toachieve the best protection for the insurance company while satisfying
investor concerns. Sometimes an insurance company is not afraid of
suffering one catastrophic loss, but wants to get protection in case one catastrophe
is followed by another in the same or the following year.
A second-event trigger could provide the required protection to the company,
with the bond providing no payout (but being �activated�) after the first
catastrophic event and paying only if the second event occurs as well.
NUMBER ANd TYPES OF PERILS
A catastrophe bond trigger could be based on one specific type of peril suchas a hurricane, typhoon or earthquake. It could also be based on a number of perils, with losses from any one of them or a combination of perils triggering
the payout.
While the first cat bonds were generally designed to provide protection
against one type of peril, we have now seen a strong trend towards incorporating
multiple perils in a bond. The same bond could have a number of
peril/geographic location combinations.
Larger insurance or reinsurance companies with portfolios of insurance policies on more than one continent are interested in this aggregate protection. When it comes to multiple perils,
investors fall into two categories. Some are happy to see various types of
uncorrelated risk in the same security. Effectively, diversification is
provided for them in such a bond. Others prefer to buy cat bonds tied to a
single peril and to achieve diversification on their own.
The latter category tends to include investors with better understanding of the insurance-linked
securities, including the funds focused exclusively on these financial instruments.
The table, overleaf, shows a sample of catastrophe bonds issued
based on various default triggers and types of catastrophe peril. Some cat
bonds have included a number of tranches, each of which corresponds to a
specific type of insurance risk and has its own trigger.
The securitisation of insurance risk has moved beyond property catastrophe
and has included some liability insurance cat bonds, as well as
securitisation of property-casualty insurance risk that is not truly catastrophic
in nature.
TERM
The cat bond tenor varied widely in the early days of insurance securitisations,but has now stabilised with the average being three years. This term
is long enough for the sponsor to lock into a multi-year protection at a
predetermined price and to avoid paying the fixed cost of issuing a cat bond
every year. At the same time, it is short enough for the sponsor to predict the
composition of its future insurance portfolio with a reasonable degree of
confidence.
QUANTITATIVE ANALYSIS
Both investors and the sponsor require a good understanding of potentiallosses, that is, the probability distribution of cat bond payouts. This
probability distribution is in turn based on probabilities of the cat bond
being triggered, and the payout amounts given that the bond has been
triggered.
Exceedance curve
Insurance-linked securities might be the only asset type for which probabilisticrisk analysis is included in the investor prospectus. For catastrophe
bonds the analysis, performed by one of the firms specialising in modelling
catastrophe events and their financial impact on portfolios of insurance policies,
is usually presented in the form of a probability exceedance curve (EC).
The exceedance curve shows probabilities of insurance losses of various
magnitudes.
If the annual exceedance probability is 1%, then the probability of
exceedance during a three-year period is 3%. (More precisely, the probability
of exceedance over a three-year period is equal to 1�(1�0.01)3 = 2.97%.
The approximation works well for only very small annual exceedance probabilities
and short time periods. For example, if the annual exceedance probability is 2% and the term is eight years, we might think that the probability of exceedance over the term equals 16%. In reality, it is 14.92%, which is calculated as 1�0.988.) The following figure shows an example of an exceedance
probability curve for a portfolio of insurance risk.
In this example, losses above US$500 million might have a catastrophic
effect on the insurance company�s financial position. The company has
several options to protect itself against this possibility. Some of them have to
do with raising additional capital or reducing or rearranging the company�s
portfolio of insurance policies. The most common solution is purchasing
reinsurance � that is, insurance protection for this insurance risk portfolio.
For example, the reinsurance coverage could take the form of the reinsurance
company reimbursing the insurance company for all losses above the
level of US$500 million, limited to the total payout of US$250 million. In this
case, the insurance company would still be unprotected if the total losses
exceed US$750 million, but would probably be willing to take this risk if
losses above US$750 million were considered to be exceptionally unlikely.
The company might wish to protect itself from losses in excess of US$500
million even if the effect of such losses would not have a truly catastrophic
effect on its financial position.
The reasons for it could be the desire to
decrease earnings volatility or to reduce capital requirements.
In property insurance, unique terminology has been developed. Probable
maximumloss, or PML, is the loss level thatwould be reached only extremely
rarely. There are many opinions of how rare is �rare�, leading to multiple
definitions of PML. If a company wants to define PML as the aggregate loss
level thatwould be reached only once in 100 years, then in the example above
the PML will be US$500 million.
With the increased emphasis on risk management and themore stringent capital-adequacy requirements promulgated by the rating agencies, there is growing shift of focus to property
catastrophe events that happen on average less often than once in 250 years,
leadingmany to define PML as the 1-in-250-year event.
While the concept of PML is often used in relation to losses from individual policies, here we
discuss the aggregate PML of an insurance portfolio. We also avoid nonquantitative
definitions of PML still common in the insurance industry. In insurance, probability of exceedance is usually expressed on an annual basis, that is, as a probability that insured losses will exceed a certain level over a period of 12 months. In the context of cat bonds, exceedance probability
could also be expressed as the probability of losses exceeding a certain
level, such as the bond trigger level, over the term of the bond.
Modelling catastrophe risk presents numerous challenges, but, even when it is accomplished,
the results by themselves do not tell the investors what price is
appropriate or fair for the cat bond being modelled. Several pricing models
have been proposed. Often, they use as an input the observed prices for
other cat bonds.
As �neat� mathematically as the Wang transform is, its practical application
is very difficult. It has also been pointed out (Pelsser 2008) that its use
in pricing financial and insurance risks is consistent with arbitrage-free
pricing, only under rather restrictive assumptions (this statement, however,
has been disputed).
Other pricing approaches have been proposed, such as the application of
extreme-value theory to cat bond pricing. This approach requires making
assumptions not fully appropriate for cat bond analysis, and it does not
produce results resembling observed cat bond prices. A simple rule-ofthumb
approach to pricing includes the use of �multiples� of expected
annual loss (average annual loss, or AAE) to determine the required spread over Libor or risk-free rate. Different multiples correspond to different levels
of expected loss.
While this approach has a questionable mathematical foundation,
it is easy to use and there are some investors that utilise it. Another
simple approach that has been proposed calculates prices based on the
expected frequency and severity of the losses. The parameters are estimated
based on the observed cat bond prices. This approach has the appeal of
simplicity, but it lacks any theoretical foundation.
Finally, some still use approaches that calculate prices based on the mean plus a multiple of standard
deviation. Many of these relatively simple approaches are borrowed
from reinsurance pricing, where they have been used for many years, but
even there they are being replaced by the more sophisticated methods.
In addition to the shaky theoretical foundations of some of the pricing
approaches, their common weakness is the dependence � either for parameter
fitting or for results validation � on the actual observed cat bond
prices. The cat bond market and the ILS markets in general are far from
WANG TRANSFORM AND PRICING OF CAT BONDS
The Wang transform was developed by Shaun Wang (Wang 2000; Wang2004; Pelsser 2008) with the goal of linking actuarial pricing and modern
finance theories. It has been used for both pricing cat bonds and excess-ofloss
reinsurance. While the full explanation of this method is outside the
scope of this chapter, the basics of the approach are explained below.
Based on the underlying loss variable X, the loss to the excess-of-loss
layer attaching at a with the limit of h, which is equivalent to the loss to a
cat bond, is defined as
necessarily follow the logic evident in more efficient markets.
The supply�demand dynamics play a very important role in pricing cat
bonds and catastrophe risk in general. When reinsurance markets �harden�,
the spread over Libor is likely to increase. This effect does not necessarily
correlate with the behaviour of the financial markets.
Even more importantly, the �peak peril� effect results in prices that are difficult to predict
based on the assumption that markets are efficient. Two cat bonds, one
linked to hurricane losses in Florida and the other to typhoon losses in
Australia, might have exactly the same exceedance probability distributions,
but the yield on the Florida hurricane bond is likely to be dramatically
greater than on the Australia typhoon one.
While the proposed pricing approaches often fail in the analysis of individual
bonds, relative-value analysis is still possible and helpful. More
importantly, the existing modelling tools allow us to manage cat risks on a
portfolio basis, and � instead of trying to come up with a theoretically
correct price for an individual bond � to see what incremental impact its
addition to the portfolio is going to have relative to the available alternatives.
This topic is further discussed in Property Catastrophy Bonds Part 2.
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