PROPERTY CASUALTY REINSURANCE
Property Casualty Coverages
- General Liability (GL) - Premises and Operations, Products
- Commercial Auto (CA) - Liability (AL) and Physical Damage (PD, trucking,
busses, taxis, etc.)
- Commercial Property (CP) - fire, wind, explosion, business interruption
- Workers Compensation (WC)
- Professional Liability - E&O, D&O, Medical Malpratice
- Specialist - ocean marine, satellite, airplane hull, kidnap and ransom
Personal Lines Coverages
- Homeowners - Fire, theft, liability, hurricane, tornado, earthquake
- Auto - liability and physical damage
- Miscellaneous personal property, boats
A reinsurance company insures risks assumed by a primary insurance
company. The reinsurer assumes the risk, the reinsured company, or cedent,
cedes the risk. The primary company retains the part of the risk
it does not cede.
The reinsurer has a contract with the cedent but not the cedent's clients.
Reinsurance on reinsurance is called a retrocession.
Why do primary companies purchase reinsurance?
- Balance and Diversification
- Stability of Earnings
- Solvency Protection, Catastrophe Protection
- Financial Results Management
- Tap Expertise of Reinsurer
Treaty vs. Facultative Reinsurance
Treaty reinsurance covers a set of subject policies
for a given period of time. Subject policies are often defined in terms of lines
of business, e.g. "all commerical auto liability policies" or "all
Facultative reinsurance covers a single underlying
insured. Unlike a treaty, facultative ("fac") reinsurance is underwritten
by the reinsurer one account at a time.
Quota Share vs Excess of Loss
Under a Quota Share reinsurance contract, a fixed percentage
of the premiums and a fixed percentage of the losses are ceded to the reinsurer.
For this reason, quota shares are called proportional reinsurance. The
reinsurer typically allows a ceding commission to
the cedent to cover costs of producing the business. The level of the ceding
commission ("cede") is essentially the only pricing variable in a
simple quota share deal.
Under an Excess of Loss reinsurance contract the reinsurer
covers losses in excess of an attachment, so the recovery is not directly proportional
to the cedent's loss. Thus Excess of Loss contracts are non-proportional.
Excess of Loss ("XOL") contracts can cover losses in many different
- Per Risk Excess of Loss: losses excess of an attachment
on a per location or per policy basis. Primarily used in property covers.
- Per Occurrence: losses excess of an attachment on a
per occurrence basis. An earthquake or hurricane would generally be a single
- Aggregate XOL: losses in an excess layer which are in
excess of an attachment point.
- Stop Loss: covers the cedents total losses on a book of business over a
period of time. Attachment is generally expressed as a percentage of coveraed
A typical reinsurance program for a small insurance company, or independently
run department of a larger company, may look something like:
- AL, GL, WC and commerical property only
- AL, GL policies have $1M limits or $5M limits, mostly $1M
- Properties generally in $10-25M range, but some upto $100M
- Fac on all property policies to bring retention down to $1M. E.g. on a $25M
property the company would buy a per risk XOL cover of $24M excess a $1M retention.
- Fac on all AL and GL policies to bring retention down to $250,000. E.g.
on a $1M policy the company would buy a $750,000 excess $250,000 per occurrence
- Fac $9.75M excess $250,000 on all WC policies. (WC is written without policy
limits, though claims in excess of $5M are very rare.)
- A per occurence property catastrophe treaty covering $45M excess $5M.
- A 50% quota share on the retained liability lines with a 30% ceding commission.
Pricing: the Actuary's Role
||Highly regulated by State
+ schedule credits/debits
|+ experience credits/debits
||Large commerical, unusual risks, reinsurance
Manual rating creates rates for statistical classes and uses very objective
criteria to determine rates. Actuarial involvement is in setting the rates (for
all insureds). No involvement in individual account pricing.
Experience and schedule credits/debits give the underwriters more flexibility
in determining a rate. Actuarial involvements tends to be in setting underlying
manual rates and designing procedures for experience rating.
Loss Rating: scope for actuarial involvement in individual account pricing
(each treaty or certificate for reinsurance).
Reinsurance Pricing: Treaty Quota Share
What is the loss ratio? What are reinsurer's expenses? What is the ceding commission?
Reinsurance Pricing: Fac XOL
See Exhibit 1.
Reinsurance Pricing: Treaty XOL
Two key differences with Fac XOL:
- Do all the underlying risks expose the treaty? For example, primary
company writes $500,000, $1M and $2M policy limits. A treaty $1M excess of
$1M would only be exposed by the $2M policy limits---which may account for
a relatively small proportion of the premium. Problem is more pronounced for
- Rate is determined as a percentage of the underlying premium. On most of
the risks covered, the reinsurer doesn't actually know what the ceding company
will charge! Introduces a big pricing risk for reinsurers (see last night's
Treaties often contain complicated policy terms which
make pricing difficult. The following give an example of some of the more common
- A sliding scale commission: the ceding commission paid to the ceded
varies inversely with the loss ratio on the ceded business. The lower the
loss ratio the more commission is paid to the cedent, as a reward for producing
- A swing rated treaty charges a premium equal to some multiple of
losses, but with a minimum and a maximum premium due. This provides needed
protection to the cedent while keeping the "out-the-door" price
as low as possible.
- With an aggregate annual deductible on an XOL cover, the cedent agrees
to pay losses in the excess layer upto a certain threshold. Again, this lowers
the upfront cost to the cedent.
To price all of these special features requires knowing the probability distribution
of aggregate losses or aggregate loss distribution. Determining aggregate
distributions is a central question in actuarial science and is usually addressed
in a couse on Risk Theory. For an excellent survey of computing aggregate loss
distributions see Wang.
Connection to Options
The payments on an excess of loss reinsurance contract or a primary insurance
policy with a deductible are similar to the payoff from a call option (the right
to buy). For these reasons option pricing techniques are sometimes mentioned as
applicable to reinsurance pricing. However, there are some very important differences
between insurance and reinsurance on the one hand and options pricing on the other.
See my paper Mildenhall
for a more in-depth discussion.