Capital Market Reinsurance Solutions

July 9, 2001

Philip Kane, ACASTel: +1 212 723 5851

Philippe Joly

Tel: +1 212 723-6461

Page 2

Insurance Derivatives and Reinsurance

• Derivatives are any financial instrument which “derives” its value from some “underlying” asset or another derivative

• The increase in the sophistication of the reinsurance market has paralleled the development of the derivatives market.

• Insurance Derivatives relate to those derivatives which are concerned with insurance risks, placed with insurers, or use insurance techniques and structures.

• Insurance Derivatives are used as an alternative to reinsurance transactions and as a new source of risk taking opportunities. But often they involve the blending of insurance and derivative structures.

• Insurance Derivative groups have been formed at all the major Investment Banks. At Citigroup, we are a 10 year old group with 8 professionals directly attached to insurance derivatives and handling transactions in excess of over $20 billion notional a year.

Page 3

Capital Market Risk Transfer Opportunities for the Reinsurance Market

• Risk Classes:

–Credit Risk

–Future Flows

–Project Finance

–Private Equity

–Basis Risks

–Residual Value

–Sovereign/Political Risk

–Plant Outage

–Volatility Risks

–Correlation Risks

–Weather Risks

Page 4

Risk Transfer Opportunities for the Reinsurance Market

• Reasons for Reinsurance Risk Transfer

–Relationships

–Unique Risk Appetites (Class and level)

–Analytical Expertise

–Flexible Mandates

–RAT (Regulatory, Accounting, Tax)

Page 5

Synthetic CDO Example

• CDO= Collateralized Debt Obligation

• CDO’s represent a class of financial instruments each composed of a portfolio of loans, bonds, or other debt form representing the obligations of underlying third parties to pay.

• These third parties are referred to as “names” and are pooled for diversity: there can be as many as 150 or more in a single CDO

• CDO’s are tranched in layers of risk:

–The first tranche or layer represents the first set of default losses between 0-5% of the notional and therefore is the riskiest. It is often referred to as the equity layer.

–The next tranche is the mezzanine tranche which represents the next losses between 5-10% of the notional.

–The remaining obligations are the last to default, and this layer is considered the least risky, and therefore named the senior tranche.

Page 6

Credit Default Swap

• The Synthetic qualifier represents the use of derivatives transfer the risk of the losses to third parties without the debt notionals changing hands. This is done through Credit Default Swaps.

• Credit Default Swap: Two parties enter into an agreement whereby one party pays the other a fixed periodic coupon (premium) for the specified life of the agreement. The other party makes no payments unless a specified credit event occurs (floating payer). Credit events are typically defined to include a material default, bankruptcy, or debt restructuring for a specified reference asset.

• Upon a credit event the floating payer either pays the market value of the asset (physical settlement) or the difference between par and such market value (cash settlement).

Page 7

CDO: Sample Capital Structure

AAA+

BBB

B/BB

Senior: 90% of notional

Mezzanine: 7% of notional

Equity: 3% of notional

Page 8

Binomial Model of CDO’s

• Moody’s is leading ratings provider for tranches

• Basic Rating model divides names into industry/country groups and reduces the total number of names to an index based on the notional in each group: this index is termed a diversity score

• This diversity score is used as the n for a binomial model

• Given the average rating, and historical defaults, a frequency can be determined for default.

• Assuming a recovery rate under each obligation one can determine the number of defaults necessary to provide losses to a tranche. This can be used to determine the expected loss within a tranche by assigning probability to each number of defaults

• Probability of a specific number (x) of defaults =

n! / [x! (n-x)!] * (p)x(1-p) n-x

Page 9

Default Probabilities: Moody’s

The tables below provide Moody’s estimates of the cumulative and marginal defaultrates, during the period 1970-1996, given a particular initial rating:

MOODY’S CUMULATIVE DEFAULT RATES (%) 1970-1996

Long-Term Rating 1 yr 2 yrs 3 yrs 4 yrs 5 yrs

Aaa 0.00 0.00 0.00 0.04 0.13Aa 0.03 0.05 0.10 0.25 0.40A 0.01 0.07 0.22 0.39 0.57

Baa 0.12 0.39 0.76 1.27 1.71Ba 1.36 3.77 6.29 8.88 11.57B 7.27 13.87 19.94 25.03 29.45

MOODYS’ MARGINAL DEFAULT RATES (%) 1970-1996

Long-Term Rating 1 yr 2 yrs 3 yrs 4 yrs 5 yrs

Aaa 0.00 0.00 0.00 0.04 0.09Aa 0.03 0.02 0.05 0.15 0.15A 0.01 0.06 0.15 0.17 0.18

Baa 0.12 0.27 0.37 0.51 0.44Ba 1.36 2.41 2.52 2.59 2.69B 7.27 6.60 6.07 5.09 4.42

Page 10

Historical Recovery Rates

T h e tab le b elo w p r o v id es aver age r eco ver ies o n d efau l ted d eb t g iven th e lega l sta tu so f each ca tego ry o f d eb t.

W h i le th ese fi gu r es w o u ld ap p ea r cr i ti ca l to p r o p er p r i c in g o f cr ed i t r i sk , th ei r u t i l i tyi s d im in i sh ed a g r ea t d ea l w h en acco u n t i s tak en o f th ei r va r iab i l i ty , a s o b ser ved inth e h i sto g r am b elo w ( d er ived fr o m a lead in g stu d y o f b an k lo an s) :

S e n i o r i t y A v e r a g e R e c o v e r y R a t e

S en io r secu r ed 6 4 .5 9 %S en io r u n secu r ed 4 8 .3 8S en io r su b o r d in a ted 3 9 .7 9S u b o r d in a ted 3 0 .0 0J u n io r su b o r d in a ted 1 6 .3 3

R e c o v e r ie s

0 %

5 %

1 0 %

1 5 %

2 0 %

2 5 %

3 0 %

0-2.5

%

2.5%

-12.5

%

12.5%

-22.5

%

22.5%

-32.5

%

32.5%

-42.5

%

42.5%

-52.5

%

52.5%

-62.5

%

62.5%

-72.5

%

72.5%

-82.5

%

82.5%

-92.5

%

92.5%

-100

%

P e r c e n ta g e

Page 11

Synthetic CDO Expected Loss Calculation using Binomial Model

• From previous slides we assume a diversity score of 20, a 5 year average life, and an average Baa rating, producing a default frequency of 1.71%. We also assume a Recovery Rate of 50%.

• We are interested in determining the Expected Loss (and the rating) of Tranche, say, [4% , 8%]

• Using the binomial model we can produce the following distribution of defaults:

Number of Net Loss to Loss toProbability Defaults Default Loss Tranche Tranche (%)70.82502% 0 0% 0% 0% 0% E[Loss to Tranche] (%)24.64356% 1 5% 3% 0% 0% 1.424%4.07299% 2 10% 5% 1% 25%0.42516% 3 15% 8% 4% 88%0.03144% 4 20% 10% 4% 100%0.00175% 5 25% 13% 4% 100%0.00008% 6 30% 15% 4% 100%0.00000% 7 35% 18% 4% 100%0.00000% 8 40% 20% 4% 100%

Page 12

CDOs: Note on Correlation

An intuitive way of understanding the concept of Loss to a tranche is to realize that the E(Loss) to a small tranche dx is equal to the Probability of Attachment at x.

This explains why the E(Loss) to a bottom tranche is essentially determined by the probability of attachment at the portfolio level.

And the E(Loss) to a top tranche is essentially determined by the probability of Exhaustion at the portfolio Level.

0%

100%

a

b

0% 100%a b

Probabilityof Exceedence

E ( L[a,b] )

b

aba dxxLPab

LE )(1

)( ],[

Page 13

Synthetic CDO Market

• Market was originally driven by Bank Regulatory Capital Relief

• Banks’ capital charge of 8% of notional on non-OECD bank debt; but only 1.6% for OECD banks and VAR (economic) charges for trading book. Therefore, banks with trading books can provide capital relief to non-trading book banks, and buy protection in the form of derivatives.

• Additional volume provided by non-bank Credit Derivative Trading volume

• Synthetic CDO Market has traded in excess of $400,000,000,000 of notional.

• Reinsurance Market has been attracted to the risk and structure of synthetic CDO’s due to actuarial pricing methodology and regulatory needs of end-buyers

• Credit-Default Swaps are also be treated as insurance policies for insurance regulatory purposes in certain jurisdictions (eg, Bermuda), allowing insurance entities to be providers of protection and the booking of insurance premiums

Page 14

CDO: Actual Deal

PaymentThreshold

2.00%

ReliefSeekingBank

OTC Market

CorporateLoan &Bonds

OECD BANK

OECD BANK

CITIBANK

CIT

IBA

NK

OEC

D B

AN

K

JuniorDefault Swap

MezzanineDefault Swap

SeniorDefault Swap

Super SeniorDefault Swap

Credit LinkedNote

OTC MarketCredit Default

Swap

Page 15

Synthetic CDO Market

Capital Relief

Seeking Bank

Counterparty Bank’s

Trading Book

Premium

Losses

Credit Default Swap Market

Premium

Losses

Reinsurance and Bank Market

Page 16

Synthetic CDO Accounting

• Market traded risks, even if in insurance form, should be marked to market based on US GAAP

• If blended with insurance or other risks, bifurcation should take place

• Insurance, weather, and other natural risks are specifically excluded from FASB 133

• Credit risk is marked to market as a derivative but not as insurance.

• Insurers who choose to take credit risk in insurance form do not have to mark portfolio if the form meets GAAP criteria as a financial guarantee (identifiable failure to pay) but default swap providers do, regardless of jurisdiction .

• Currently, banks haven’t accepted insurance policies in trading books.

• The use of Transformers has been common to address this problem.

Page 17

In order to qualify for the scope exception in paragraph 10(d), a

financial guarantee contract must require, as a precondition for

payment of a claim, that the guaranteed party be exposed to a loss

on the referenced asset due to the debtor's failure to pay when

payment is due both at inception of the contract and over its life. If the

terms of a financial guarantee contract require payment to the

guaranteed party when the debtor fails to pay when payment is due,

irrespective of whether the guaranteed party is exposed to a loss on

the referenced asset, the contract does not qualify for the scope

exception in paragraph 10(d). Even if, at the inception of the contract,

the guaranteed party actually owns the referenced asset, the scope

exception in paragraph 10(d) does not apply if the contract does not

require exposure to and incurrence of a loss as a precondition for

payment. Furthermore, to qualify for the scope exception in paragraph

10(d), the compensation paid under the contract cannot exceed the

amount of the loss incurred by the guaranteed party.

Accounting: Statement 133 Implementation Issue No. C7

Page 18

The guaranteed party's exposure to and incurrence of a loss on the

referenced asset can arise from owning the referenced asset or from

other contractual commitments, such as in a back-to-back guarantee

arrangement. The application of the scope exception to financial

guarantee contracts under which the guaranteed party incurs a loss

resulting from the debtor's failure to pay either because it owns the

referenced asset or because of other contractual commitments is

consistent with the reasoning for Statement 133's scope exception for

certain insurance contracts. Paragraph 281, which relates to the

exclusion of certain insurance contracts from the scope of Statement

133, indicates that those contracts are excluded from the scope

because they entitle the holder to compensation only if, as a result of

an identifiable insurable event (other than a change in price), the

holder incurs a liability or there is an adverse change in the value of a

specific asset or liability for which the holder is at risk.

Accounting: Statement 133 Implementation Issue No. C7(Continued)

Page 19

Capital Market Alternatives to Reinsurance

• Reinsurance Transactions often address financial issues that can also be addressed by the capital markets

–Property Catastrophe risk linked notes

–Life Reinsurance may transfer interest rate risks which can be addressed by the interest rate swap market

–Life and P/C Surplus Relief could be structured with an SPV supported by a securitization of the profits

–Contingent Capital can be securitized in form of a note with different spreads pre- and post- contingency/exercise.

–Dual Risk Covers: Cat Protection contingent on equity index move

–Aggregate Stop Losses can include financial risks such as interest rate risks

Page 20

Combined Aggregate Stop Loss Example

• Stop Loss which combines both losses on asset and liability side

• By converting asset risk into a formula using duration, notional, and interest rates, can generate losses on asset side derived from interest rate movements

• Covered losses under reinsurance would include indexed interest rate losses as above

• When these losses and insurance losses exceeded attachment point, reinsurer pays, up to limit.

• Usual duration is one year, covering all lines of insurance business as well.

• Catastrophe losses are usually capped as well.

Page 21

Combined Aggregate Stop Loss Pricing

• Aggregate Loss Models are available for insurance risks and are usually based on stochastic models of losses

• Insurance risks are generally modeled with statistical models and insurance risk only stop losses are generally priced using Monte Carlo simulation

• Issues are generally correlations, event losses (catastrophe), trended and untrended expected loss ratios, growth rates, etc….

• Transaction models combining asset risk with insurance risks have generally added these risks as another stochastic variable.

• For liquid risks such as short interest rates there can be great divergence between insurance pricing and Capital Markets pricing.

• For illiquid risks, the pricing results tend to converge due to the lack of liquid markets for these risks. These risks get treated as event risks in the capital markets much like insurance pricing rather than continuous risks.

Page 22

Insurance Pricing vs. Derivatives Pricing

Typical Insurance Pricing: ‘Call Contract’

S=100

S=110

S=90Option Value = 0

Option Value = 10Probability: p = 55%

Probability: 1-p = 45%

Interest Rate: r = 5%

Option Price: S= [ p.10 + (1-p).0 ] / (1+r) = 10p / (1+r) = 5.24

Page 23

Insurance Pricing vs. Derivatives Pricing

Derivatives Pricing: Call Option

S=100

S=110

S=90Option Value = 0

Option Value = 10Probability: p = 55%

Probability: 1-p = 45%

Interest Rate: r = 5%

Pricing is determined by the construction of a replicating portfolio, not by actual probabilities

Page 24

Insurance Pricing vs. Derivatives Pricing

Derivatives Pricing: Building a Replicating Portfoliomade of x bonds and y underlying securities

S=100

S=110

S=90Option Value = 0

Option Value = 10Probability: p = 55%

Probability: 1-p = 45%

Interest Rate: r = 5%

Portfolio = ( -0.42 Bonds , 0.5 securities)Portfolio Value = -0.42*105 + 0.5 * 110

= 110

Portfolio = ( -0.42 Bonds , 0.5 securities)Portfolio Value = -0.42*105 + 0.5 * 90

= 0

The option and the Porfolio have the same final value in all cases, therefore they should have the same price at time 0

Option Price = -0.42 * 100 + 0.5 * 100 = 7.14

Page 25

Insurance Pricing vs. Derivatives Pricing

Derivatives Pricing: Using Risk-Neutral Probabilities

If we calculate the probability p* satisfying

100 * (1.05) = 110 p* + 90 (1- p*)

p* = 0.75,

then we can check that

[ 10 p* + 0 (1- p*) ] / (1+r) = 7.14 = Call Price

S=100

S=110

S=90Option Value = 0

Option Value = 10Probability: p = 55%

Probability: 1-p = 45%

Interest Rate: r = 5%

Page 26

Combined Aggregate Stop Loss Pricing

• We will assume for each .005% change in interest rates, the bond portfolio moves a value equal to 1% of premium.

• We will also assume no correlation between a move in interest rates during the year and the resulting accident year loss ratio.

• The cover will be 20% in excess of 70%, with a sublimit of 10% on asset losses due to interest rate moves

Interest Rate Move

Effective Pure Loss Ratio Attachment

Effective Pure Loss Limit

Required Reinsurance Premium on Pure Losses

Interest Rate Option Payoff

0.00% 0.7 20.00% 4.00% 0.00%0.50% 0.69 20.00% 4.99% 0.99%1.00% 0.68 20.00% 6.01% 2.01%1.50% 0.67 20.00% 7.06% 3.06%2.00% 0.66 20.00% 8.16% 4.16%2.50% 0.65 20.00% 9.31% 5.31%3.00% 0.64 20.00% 10.52% 6.52%3.50% 0.63 20.00% 11.80% 7.80%4.00% 0.62 20.00% 13.16% 9.16%4.50% 0.61 20.00% 14.59% 10.59%5.00% 0.6 20.00% 16.10% 12.10%

Page 27

Combined Aggregate Stop Loss Pricing

Interest Rate Option Payoff

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

14.00%

Interest Rate Movements

Inte

res

t R

ate

Op

tio

n P

ay

off

Page 28

Combined Aggregate Stop Loss Pricing

• The interest rate option payoff is based on the cumulative change in the required premium from the pure loss (no interest rate moves) premium.

• The Premium changes as the effective loss ratio attachment drops due to interest rate losses.

• Assuming this option cost 1.5% and the pure stop loss cost 4%, the total upfront premium would be 5.5%.

• With this payoff we can arrange an interest rate only option for a reinsurer to be able to bind a combined aggregate stop loss delivering the necessary premium to underwrite the loss risk.

• This could also be done for “finite” stop loss covers and multi-year stop loss covers.

Page 29

Combined Aggregate Stop Loss Accounting

• There is no explicit accounting pronouncements on Combined Aggregate Stop Loss Covers.

• There have been FAS clarifications of combined insurance and financial risks.

• There would be merit to NOT bifurcating the interest rate option embedded in the trade.

• This is because a pure loss ratio in excess of 60% is required for any interest rate losses to be covered, and this is not certain.

• The insured must also actually experience the interest rate losses, much like the actual loss requirement of industry loss covers.

Page 30

Only those contracts for which payment of a claim is triggered only by a

bona fide insurable exposure (that is, contracts comprising either solely

insurance or both an insurance component and a derivative instrument)

may qualify for the exception under paragraph 10(c). In order to qualify,

the contract must provide for a legitimate transfer of risk, not simply

constitute a deposit or form of self-insurance. A property and casualty

contract that provides for the payment of benefits/claims as a result of

both an identifiable insurable event and changes in a variable would in its

entirety qualify for the insurance exclusion in paragraph 10(c)(2) of

Statement 133 (and thus not contain an embedded derivative instrument

that is required to be separately accounted for as a derivative instrument)

provided all of the following conditions are met:

1.Benefits/claims are paid only if an identifiable insurable event

occurs (for example, theft or fire) pursuant to the requirements of

paragraph 10(c)(2) of Statement 133.

Accounting: Statement 133 Implementation Issue No. B26

Page 31

Accounting: Statement 133 Implementation Issue No. B26 (Continued)

2.The amount of the payment is limited to the amount of the

policyholder’s incurred insured loss.

3.The contract does not involve essentially assured amounts of

cash flows (regardless of the timing of those cash flows) based on

insurable events highly probable of occurrence because the

insured would nearly always receive the benefits (or suffer the

detriment) of changes in the variable. If there is an actuarially

determined minimum amount of expected claim payments (and

those cash flows are indexed to or altered by changes in a

variable) that are the result of insurable events that are highly

probable of occurring under the contract and those minimum

payment amounts are expected to be paid each policy year (or on

another predictable basis), that "portion" of the contract does not

qualify for the insurance exception.

Page 32

Conclusions

• Convergence is here!!

• Capital Markets are sourcing risks for the Reinsurance market as well providing solutions to insurance problems

• Be cautious when underwriting liquid risks, but look for structural exploitations.

• In illiquid risk markets there are many opportunities for savvy players and Reinsurers are a major player.

• Re/insurance has unique regulatory, accounting, and tax implications that can work to the advantage or disadvantage of transactions.