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Modeling Credit Risk and Pricing Credit Derivatives

©2001 Diplomarbeit 142 Seiten

Zusammenfassung

Inhaltsangabe:Abstract:
Banks are financial intermediaries originating loans and consequently facing credit risk. Credit risk can be defined as the risk of losses caused by the default or by the deterioration in credit quality of a borrower. Default occurs when a borrower cannot meet his key financial obligations to pay principal and interest.
Banks increasingly recognize the need to measure and manage the credit risk of the loans they have originated not only on a loan-by-loan basis but also on a portfolio basis. A precondition for diversification after the origination of the loans is their transferability. But as it is wellknown transferring credit risk of loans is difficult due to severe adverse selection and moral hazard problems. That is why the use of existing tools like loan sales has not been very successful in transferring the credit risk on a broad scale. However, in recent years, the development of markets for credit securitization and credit derivatives has provided new tools for managing credit risk.
Credit derivatives are often described as „synthetic loans“ which reflects only too narrowly their common use and enormous potential. More broadly defined credit derivatives are sophisticated financial instruments that enable the unbundling and intermediation of credit.
A risk seller, which is the party seeking credit risk protection, may want to reduce exposures while maintaining relationships that may be endangered by selling their loans, reduce or diversify illiquid exposures, or reduce exposures while avoiding adverse tax or accounting treatment. A risk buyer, the party assuming credit risk, may want to diversify credit exposures, get access to credit markets which are otherwise restricted by corporate statute or off-limits by regulation, or simply exploit arbitrage pricing discrepancies, for example resulting from perceived mispricing between bank loans and subordinated debt of the same issuer.
The pricing and management of credit derivatives requires more sophisticated credit risk models. With the advent of the market-based models the mathematical modeling of the pure interest-rate risk in the bond market is coming closer to a generally accepted benchmark. Of the remaining risk components in the bond market, credit risk is the largest unresolved modeling problem.
The valuation of credit derivatives changed the focus of many credit risk models. Instead of developing a pricing framework which yields the fair prices for defaultable […]

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ID 4783
Wolf, Martin: Modeling Credit Risk and Pricing Credit Derivatives / Martin Wolf - Hamburg:
Diplomica GmbH, 2001
Zugl.: Innsbruck, Universität, Diplom, 2001
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Credit Derivatives
Table of Contents
Table of Contents
1
INTRODUCTION
4
2
CREDIT RISK MANAGEMENT
6
2.1
Credit Risk versus Market Risk
6
2.2
Methods of Credit Risk Management
7
2.2.1
Risk Transfer in the Cash Market
8
2.2.2
Risk Transfer with Credit Derivatives
8
2.2.3
Regulatory Treatment of Credit Derivatives
8
3
CREDIT DERIVATIVES ­ STRUCTURES AND APPLICATIONS
10
3.1
Definition
10
3.2
Classification
10
3.2.1
The Transfer of Default Risk
11
3.2.2
The Transfer of Credit Spread Risk
15
3.2.3
Exotic and Hybrid Instruments
17
3.3
Contract Elements
19
3.3.1
Reference Asset
19
3.3.2
Credit Event
19
3.3.3
Compensation
20
3.3.4
Premium
20
3.3.5
Notional Amount
20
3.3.6
Term of the Contract
20
3.4
Standardized Documentation
21
3.5
The Application of Credit Derivatives
21
3.5.1
Portfolio Diversification
21
3.5.2
Limits
22
3.5.3
Concentration Risk
22
3.5.4
Hedging
23
3.5.5
Achieving Target Profiles
23
3.5.6
Arbitrage
24

Credit Derivatives
Table of Contents
3.5.7
Remaining problems
24
3.5.8
Credit Derivatives and Regional Banks
24
3.6
The Market for Credit Derivatives
25
4
PRICING CREDIT RISKY INSTRUMENTS: AN OVERVIEW
28
4.1
Classification of Valuation Models
28
4.2
Firm's Value Models
29
4.2.1
Valuation Approach
29
4.2.2
Advantages and Disadvantages
30
4.3
Credit Rating Transition Models
30
4.3.1
Valuation Approach
31
4.3.2
Advantages and Disadvantages
34
5
THE DUFFIE-SINGLETON FRAMEWORK FOR MODELING CREDIT RISK
AND PRICING CREDIT DERIVATIVES
35
5.1
Term Structure Models
35
5.2
Valuation Approach
36
5.3
Discrete-Time Valuation
38
5.4
Continuous-Time Valuation
39
6
SIMULATION APPROACH FOR CREDIT-RISKY INSTRUMENTS
43
6.1
Simulations with Affine-Term-Structure Models
43
6.1.1
Limited Approaches in Simulation Short Rates and Spreads
43
6.1.2
Models with More Flexible Correlation Structures for (r
t
, s
t
)
45
6.2
Implementation of the Duffie-Singleton Framework
48
6.2.1
Parameters influencing Factor Volatility
52
6.2.2
Negative Correlation between r and s
56
6.2.3
Parameterization with Initial Drift
58
6.2.4
Diffusions of Simulation Results
62
6.2.5
Conclusion
63
6.3
Practical Aspects of Pricing Credit-Risky Debt
64
6.3.1
The Identification Problem of separate h and L
64

Credit Derivatives
Table of Contents
6.3.2
One Solution to the Separation Problem
65
6.3.3
Empirical Evidence
66
6.3.4
Non-Exogenous Hazard Rate and Fractional Recovery
68
6.3.5
Other Issues
68
7
PRICING CREDIT-RISKY INSTRUMENTS
70
7.1
Differentiation between Valuation Models
70
7.2
Valuation of Corporate Bonds
72
7.2.1
Zero Coupon Bonds
72
7.2.2
Coupon Bonds
77
7.3
Valuation of Default Digital Puts
79
7.3.1
Default Digital Puts with Payoff at Maturity
79
7.3.2
Default Digital Puts with Payoff at Default
80
7.3.3
Implementation of the Pricing Approach
81
7.4
Valuation of Default Digital Swaps
83
7.5
Valuation of Default Puts and Default Swaps
85
7.5.1
Difference to Par
86
7.5.2
Difference to Default-free Bond
88
7.6
Valuation of Credit Spread Forwards
90
7.7
Valuation of Credit Spread Puts
93
7.8
Valuation of Puts on Defaultable Bonds
96
8
CONCLUSION
99
APPENDIX
43
LIST OF REFERENCES
133

Credit Derivatives
4
Introduction
1 Introduction
Banks are financial intermediaries originating loans and consequently facing credit risk.
Credit risk can be defined as the risk of losses caused by the default or by the deterioration
in credit quality of a borrower. Default occurs when a borrower cannot meet his key
financial obligations to pay principal and interest.
Banks increasingly recognize the need to measure and manage the credit risk of the loans
they have originated not only on a loan-by-loan basis but also on a portfolio basis. A
precondition for diversification after the origination of the loans is their transferability. But
as it is wellknown transferring credit risk of loans is difficult due to severe adverse
selection and moral hazard problems. That is why the use of existing tools like loan sales
has not been very successful in transferring the credit risk on a broad scale. However, in
recent years, the development of markets for credit securitization and credit derivatives has
provided new tools for managing credit risk.
Credit derivatives are often described as "synthetic loans" which reflects only too narrowly
their common use and enormous potential. More broadly defined credit derivatives are
sophisticated financial instruments that enable the unbundling and intermediation of credit.
A risk seller, which is the party seeking credit risk protection, may want to reduce
exposures while maintaining relationships that may be endangered by selling their loans,
reduce or diversify illiquid exposures, or reduce exposures while avoiding adverse tax or
accounting treatment. A risk buyer, the party assuming credit risk, may want to diversify
credit exposures, get access to credit markets which are otherwise restricted by corporate
statute or off-limits by regulation, or simply exploit arbitrage pricing discrepancies, for
example resulting from perceived mispricing between bank loans and subordinated debt of
the same issuer.
The pricing and management of credit derivatives requires more sophisticated credit risk
models. With the advent of the market-based models the mathematical modeling of the
pure interest-rate risk in the bond market is coming closer to a generally accepted
benchmark (see Sandmann and Sondermann (1997), p.119). Of the remaining risk
components in the bond market, credit risk is the largest unresolved modeling problem.

Credit Derivatives
5
Introduction
The valuation of credit derivatives changed the focus of many credit risk models. Instead
of developing a pricing framework which yields the fair prices for defaultable bonds, now
these bonds are to be taken as input to derive prices for more exotic derivative instruments.
Therefore, models had to be developed that had this degree of flexibility. (see Schönbucher
(2000), p.3)
The thesis for diploma (in the rest of this paper simply called thesis) starts with a short
description of the credit derivatives' place in the credit risk management. Then it proceeds
by outlining the basic forms of credit derivatives, their applications, and their contract
elements. Chapter 4 gives a first impression of the two common pricing frameworks,
whereas chapter 5 describes the Duffie-Singleton approach in more detail. Chapter 6
applies this framework and examines the importance of the different parameters on the
outcomes of the simulation. Finally, chapter 7 gives examples for the valuation of credit-
risky securities.

Credit Derivatives
6
Credit Risk Management
2 Credit Risk Management
Over the years, the importance of understanding credit risk has slowly spread from loan
departments of various financial institutions to a broad array of capital market participants.
Credit risk is the risk of loss on a financial or non-financial contract due to the
counterparty's failure to perform on that contract. Credit risk's two components are default
risk and recovery risk. Default risk is the possibility that a counterparty will fail to meet its
obligation, and recovery risk is the possibility that the recovery value of the defaulted
contract may be less than its promised value (see Skora (1998a), p.1).
Banks are not the only entities affected by credit risk. Investors who purchase corporate,
municipal, or sovereign bonds also face credit risk. Even if the likelihood of default of a
given bond issuer is small, an investor can still face the possibility of a bond being
downgraded by a rating agency. Rating downgrades often result in an immediate drop in
value of the bond. Note that this not only hurts the bondholders, it also increases the cost of
financing for the issuer who has been downgraded. Given these risks, one might expect
formal models of credit risk valuation to be prevalent in the various bond markets.
However, this is not the case.
2.1 Credit Risk versus Market Risk
Credit risk has both similarities and differences to other risks such as interest rate risk or
equity risk. These latter risks are usually referred to as market risk. Credit risk can be
traded just as interest rate risk may be traded. A corporate bond or emerging market bond
is an excellent mechanism for taking credit exposure to a particular issuer. The price of the
bond is affected by changes in the credit risk or perceived credit risk of the issuer. Of
course, a bond is not a perfect instrument for trading credit risk: its price is also affected by
changes in the general level of interest rates.
On the other hand, credit risk has many properties that make it different from market risk ­
especially for modeling purposes. A US treasury bond is the quintessential example of a
security that has interest rate risk, but no credit risk. The treasury bond markets are liquid,
so the Treasury rate is set through the trading activities of thousands market-makers and

Credit Derivatives
7
Credit Risk Management
end-users. As a result one may take both long and short positions in the treasury bond
market of almost any tenor while incurring small transaction costs.
In contrast to the treasury bond market, markets for credit risky debt are illiquid. The
illiquidity is due in part to the size of the credit market. The market of credit risky debt is
segmented ­ each corporation issues its own debt which trades at prices representing the
investors' perceptions for that particular corporation. As a result, instruments that would
allow one to assume the credit risk of a particular corporation at a particular tenor may
simply not exist; sometimes those that do exist either do not trade or trade for large
transaction costs.
A second difference between market risk and credit risk is that changes in credit risk often
cause the price of the associated debt instrument to "jump". Moreover, that jump can be
very large, particularly when it is caused by default. At default the recovery value can be a
small fraction of the face value of the debt instrument; furthermore, the recovery value is
highly uncertain and may only be determined after a negotiation process (see Skora
(1998a), p.3).
2.2 Methods of Credit Risk Management
In years past, the intuition of the participants in the corporate bond market provided an
informal model of credit risk which dictated the spread over treasuries that bonds of
differing credit ratings were traded at. Historically, banks have dealt with credit risk by
requiring borrowers to meet certain underwriting standards. This is done so that the bank
can acquire debt that has a low probability of default. In addition, banks slowly learned
that they could diversify their credit risk exposure by making different types of loans in
different geographic regions.

Credit Derivatives
8
Credit Risk Management
2.2.1 Risk Transfer in the Cash Market
Many types of credit risks cannot be sold in the cash market. Also when diversifying
concentrations in a credit portfolio, suitable assets may not be readily available. Reasons
why unacceptable credit risks cannot be discarded or diversified include the following (see
Lloyd (1998), p.3):
·
Lack of liquidity: Instruments such as private placements and receivables cannot
easily be traded in the market.
·
Relationship concerns: Selling exposures may be harmful to client relationships.
·
Lack of availability of credit assets for all maturities.
·
Inability to obtain the exact return and risk profile sought.
·
High financing costs or risk of short squeeze associated with short sale of assets.
·
Tax, accounting and regulatory issues.
2.2.2 Risk Transfer with Credit Derivatives
Managing credit risk with credit derivatives has the advantage that they can be held off
balance sheet and do not require funding. Due to their high flexibility credit derivatives can
be structured according to the endusers' needs. Furthermore, since derivatives are over-the-
counter contracts, transactions are confidential. Finally speed of settlement and liquidity
are reasons why credit derivatives are a better alternative to the reinsurance market (see
Lloyd (1998), p.4). Chapter 3 gives a more detailed description of these instruments.
2.2.3 Regulatory Treatment of Credit Derivatives
In reviewing credit derivatives, examiners are considering the credit risk associated with
the reference asset as the primary risk, as they do for loan participations or guarantees. A
banking organization providing credit protection through a credit derivative can become as
exposed to the credit risk of the reference asset as it would if the asset was on its own
balance sheet. Because of that, banking organizations providing credit protection through a
credit derivative should hold capital and reserves against their exposure to the reference
asset. This broad principle holds for all credit derivatives, except for credit derivative
contracts that incorporate periodic payments for depreciation or appreciation, including
most total rate of return swaps. Here the guarantor can deduct the amount of depreciation

Credit Derivatives
9
Credit Risk Management
from the notional amount (see Board of Governors of the Federal Reserve System (1996),
p.2).
Furthermore, examiners must ascertain whether the amount of credit protection a
beneficiary receives by entering into a credit derivative is sufficient to warrant treatment of
the derivative as a guarantee for regulatory capital and other supervisory purposes. Those
arrangements that provide virtually complete credit protection to the underlying asset are
considered effective guarantees for purposes of asset classification and risk-based capital
calculations. If the reference asset is not identical to the asset actually owned by the
beneficiary this incomplete protection has to be considered in the risk-based capital
calculations. In addition, the banking organization offsetting the credit exposure is
obligated to demonstrate to examiners that there is a high degree of correlation between the
two instruments; the reference instrument is a reasonable and sufficiently liquid proxy for
the underlying asset so that the instruments can be reasonably expected to behave in a
similar manner in the event of default; and, at a minimum, the reference asset and
underlying asset are subject to a mutual cross-default provisions amount (see Board of
Governors of the Federal Reserve System, p.6).

Credit Derivatives
10
Structures and Applications
3 Credit Derivatives ­ Structures and Applications
3.1 Definition
Credit derivatives are off-balance sheet arrangements that allow one party (the beneficiary)
to transfer the credit risk of a reference asset, which it often actually owns, to another party
(the guarantor). This arrangement allows the guarantor to assume the credit risk associated
with the reference asset without directly purchasing it. In exchange the guarantor receives a
premium. The credit derivative's payoff depends on:
·
the value of the reference asset or
·
the entry of the credit event or
·
the size of a predefined credit spread or
·
a change in credit rating.
Credit derivatives can be based on a single or a number of borrowers or even a broad based
index. In the case of the credit event, it can be agreed upon in the contract, if the payment
is made in cash or in form of physical settlement of the underlying instrument (see
Hüttemann (1998), p.55).
A more general description is given by Frank Iacono (1996): "A credit derivative is based
on the credit performance of some credit sensitive asset or assets. Credit performance
typically is measured
·
by yield or price spreads relative to benchmarks,
·
by credit ratings or
·
by default status."
3.2 Classification
For each type of credit risk, both option-based and forward-based (swap) products exist.
One structural dimension unique to credit derivatives is the trigger or payoff variable, the
other dimension is the type of the product (swap, forward or option contract) which is used
to manage credit risk. The following table gives an overview classified by credit event and
the structural dimension:

Credit Derivatives
11
Structures and Applications
BASIC
FORMS
Structural Dimension
Credit Event
Options
Swaps
Forwards
Structured
Notes
Changes in
Credit Spread
Credit Spread
Option
Credit Spread Swap/
Total Return Swap
Credit Spread
Forward
Credit-
Linked
Note
Change in
Market Value /
Rating
Credit Event
Option
Credit Event Swap/
Total Return Swap
Credit Event
Forward
Credit-
Linked
Note
Default
Credit Default
Option
Credit Default Swap
Credit-
Linked
Note
Table 1: Classification of Credit Derivatives
1
3.2.1 The Transfer of Default Risk
Credit Default Option
Through a credit option, a bank or investor can take over the risk of a single company
without having a credit relationship. It will receive an option premium in exchange.
Depending on the compensation three types of put options can be distinguished:
2
a default
digital put pays a lump sum in case of default, the default put pays the difference of the
value of a defaulted asset to the reference asset, and the credit put enables the holder to sell
a defaultable asset to a specified price also if no default took place.
3
The option is
exercised by the referring party and pays a certain compensation. The following
representation shows the structure of credit default options:
1
Own illustration on basis of Kässbohrer (1998), p.14
2
See chapters 7.3, 7.5, and 7.8 for a description of the valuation of these instruments.
3
Therefore, the credit put option is also suitable to lay off both, credit spread risk and interest rate risk.

Credit Derivatives
12
Structures and Applications
Illustration 1: Credit Default Option
4
The payment profile of a plain credit put option can be plotted as follows:
Illustration 2: Payment Profile of a Credit Put Option
5
Credit Default Swap
The credit default swap is the most straightforward type of a credit derivative. It is an
agreement between two counterparties that allows one counterparty to be long a third-party
credit risk, and the other counterparty to be short the credit risk. Explained another way, it
is a transaction where one party makes periodic payments in exchange for receiving a
specified payment if a predetermined credit event occurs (see Lloyd (1998), p.3). In the
4
Own illustration on basis of Bank of England (1996), p.6 and Kässbohrer (1998), p.15
5
Own illustration on basis of Kässbohrer (1998), p.15
Bond -
Market Value
Exercise Price
Premium
Protection Buyer,
Beneficiary
Credit Default Put
0
Compensation
Risk Buyer,
Guarantor
Option Premium
Credit Relationship
Synthetic Risk Position
Profit
Loss
Credit Put Option (long)
Debtor

Credit Derivatives
13
Structures and Applications
event of the specified credit default, the hedger delivers to the swap counterparty a pre-
specified reference asset (for example a bond issued by the defaulted borrower though it
can also be loans, swaps, trade receivables, ...) and the counterparty pays the hedger par.
While there is no default event, the hedger pays the swap counterparty a spread derived
from the Libor spread received by an investor in the underlying obligation in the cash or
asset-swap market. The construction of a credit default swap looks similar to an option
with the difference that the risk seller has to pay the premium periodically.
6
Illustration 3: Credit Default Swap
7
Strongly related to this instrument are the letter of credit (LC) and the bond insurance.
Under a LC, the issuer pays the bank an annual fee in exchange for the bank's promise to
make debt payments on behalf of the issuer, should the issuer fail to do so. Since a bond
insurance is also undertaken by the issuer of a bond, again the issuer pays the insurer the
premium, who guarantees performance on the bond.
6
This is also true for the valuation as it can be seen in sections 7.4 and 7.5.
7
Own illustration
Risk Seller,
Beneficiary
0
Compensation
Risk Buyer,
Guarantor
Periodic Premium
Credit Relationship
Synthetic Risk Position
Debtor
Credit Default
Swap

Credit Derivatives
14
Structures and Applications
Illustration 4: Letter of Credit and Bond Insurance
8
Credit Linked Note
A credit linked note is a structured note with an embedded credit derivative. Unlike a credit
derivative, a credit linked note is an on-balance sheet transaction. An investor holding a
bond can purchase a credit linked note in which the coupon payments and the amount of
principal paid at the note's maturity are linked to default events. The buyer of the credit
linked note holds a short put option on the defaultable debt. For this additional risk the
investor receives Libor plus a premium. With this credit linked note, the investor takes
over the synthetic risk position of the reference credit. However, he is also subject to the
credit risk of the issuer of the credit linked note.
The advantage for the seller of the risk in this contract is, that she has no exposure to the
institution that assumes the default risk. The buyer of the notes simply gets less principal
back or a lower coupon. The risk seller holds a long put on the defaultable bond when
selling the credit linked note.
Because of the higher risk of the risk buyer a company with its own capital equipment
which distributes the credit linked notes can be set up, which then is called special purpose
vehicle. In this case issuer and risk seller do not have to be identical persons.
8
Own illustration
Promised
Payments
minus
Default
Losses
Risk Seller,
Beneficiary
0
Compensation
Insurance,
Guarantor
Insurance Contract
LC or
Bond Insurance
Premium
Debtor
Risk
Seller has
Claim

Credit Derivatives
15
Structures and Applications
Illustration 5: Credit Linked Note and Special Purpose Vehicle
9
3.2.2 The Transfer of Credit Spread Risk
Credit Spread Options
Credit spread options, also called differential options, protect the insuring party against an
unfavorable development of the credit spread of two assets with same maturity but
different credit risk. In a spread put option, one party pays a premium for the right to sell a
bond to a counterparty at a certain spread at a certain time in the future. The credit spread
is the yield differential between the reference credit and a predetermined benchmark rate
(see Lloyd (1998), p.12). Thus, in a credit spread derivative, the payment is based on the
movement of the value of one reference credit against another.
The buyer of a credit spread put makes a profit if the credit spread increases as a result of a
decline in credit quality.
10
The buyer of a credit spread call believes in a future
improvement in credit quality. If the credit spread contracts he will make a profit.
9
Own illustration on basis of Kässbohrer (1998), p.19
10
Equation (88) on page 93 describes the payoff function of a credit spread put option.
Special Purpose
Vehicle
Interest +
Repayment
- Compensation
Risk Buyer,
Guarantor
Interest +
Repayment
Synthetic
Risk Position
Debtor
Credit Linked Note
Face Value
Credit Relationship
Protection Buyer,
Beneficiary
Premium
Compen-
sation

Credit Derivatives
16
Structures and Applications
Illustration 6: Credit Spread Put Option
11
A ratings downgrade option is sometimes embedded in bond structures. If a specified
company's rating is downgraded the option pays out a specific amount. However, the
relationship between spread and rating is unstable and does not guarantee enough
compensation for the reduction in bond price.
Credit Spread Swaps and Forwards
In a credit spread forward contract, one party agrees to buy an asset from another party at a
certain spread on a given date in the future. Whereas, an option needs not to be exercised, a
swap or forward is a binding contract. The difference between a credit spread option and
swap is how the premium is paid. Options on the one hand require an up-front payment,
the premium of the swaps on the other hand consists of periodic payments.
Total Return Swap
The total return swap is an agreement in which the coupon and any capital appreciation on
an instrument such as a bond are exchanged for a Libor-linked payment plus any
depreciation in the capital value of the underlying asset. Hence, a total return swap
periodically marks to market the underlying loan or bond. There is no exchange of
principal or ownership and funding of the underlying asset is unchanged. This is also the
difference to a repro which involves initial and final exchange of securities. If the swap
maturity matches that of the reference asset it is simply a synthetic version of the asset that
11
Own illustration on basis of Kässbohrer (1998), p.15
Credit Spread (BP)
Basis Spread
Premium
Profit
Loss
Credit Spread Put (long)

Credit Derivatives
17
Structures and Applications
allows the holder to go long or short easily and without funding. If it is not, then the swap
is a synthetic asset (see Parseley (1997), p.83).
For example, any positive change in value is paid by the premium payer (the bank) to the
default risk holder (the swap counterparty). Any negative change is paid by the default risk
holder to the premium payer. The bank paying the premium in this kind of swap is
effectively warehousing a loan, renting out its balance sheet while transferring the
economic value of the loan to a third party. The motivation behind this type of transaction
is a need to get rid of an asset without entering a physical transaction that might upset the
borrower (see Parseley (1996), p.31).
Illustration 7: Total Return Swap
12
3.2.3 Exotic and Hybrid Instruments
Basket Credit Swap and Note
In addition to the standard credit derivative products, such as credit default swaps and total
return swaps based upon a single underlying credit risk, many new products are now
associated with a portfolio of credit risks. A typical example is the product with payment
contingent upon the time and identity of the first or second-to-default in a given credit risk
12
Own illustration on basis of Kässbohrer (1998), p.16
Protection Buyer,
Beneficiary
Risk Buyer,
Guarantor
Synthetic Risk Position
Total Return Swap
Yield of the Bond
Bond Issuer
Yield of Bond
Libor + Margin

Credit Derivatives
18
Structures and Applications
portfolio. Variations include the instruments with payment dependent upon the cumulative
loss before a given time in the future.
Basket Credit Derivatives can be classified into three broad categories (see Li, p.1):
a) Payment associated with the total loss over a fixed period of time:
This product has a contingent payment based upon the total loss of a given credit
portfolio over a fixed time horizon, such as one year. Suppose L
t
is the cumulative
total loss of a given credit portfolio at a prefixed time t in the future, such as 1 year,
and D is the deductible. The payoff function for this instrument at time t is
-
=
,
,
0
D
L
P
t
if
if
.
,
D
L
D
L
t
t
b) Payment is associated with the cumulative loss across time:
Here the payment starts if the cumulative loss becomes larger than a lower limit L, and
the payment continues after this point whenever new loss occurs until the cumulative
loss reaches an upper limit H. Here an example for a basket derivative over five years
with a lower limit of L = $15m and H = $30:
Year 1
Year 2
Year 3
Year 4
Year 5
Loss
$10m
$13m
$8m
$0m
$19m
Cumulative loss
$10m
$23m
$31m
$31m
$50m
Payment
$0m
$8m
$8m
$0m
$14m
Table 2: Basket Credit Derivative with Cumulative Loss across time
c) Payment is associated with the time and identity of the default:
The payment of this product depends upon the time and identity of the first or the first
few defaults of a given credit portfolio, i.e. a Portfolio manager chooses a portfolio of
three credit risks of face values $100, $150 and $200 million, respectively, and buys
credit protection against the first-to-default of the portfolio. If one of the credit
defaults, she receives the face amount of the defaulted asset, delivers the defaulted
asset to the first-to-default protection seller, and the credit default swap terminates.

Credit Derivatives
19
Structures and Applications
Sovereign Risk Option
These options allow investors to hedge all types of risks involving country or sovereign
risks, such as currency restrictions, confiscation, civil war or expropriation. Banks function
as intermediaries between companies seeking protection from these risks and investors,
which want to invest off-balance in emerging markets. They can be modeled similar to
credit default options (see Thym (1998), p.10).
Convertibility Risk Option
A convertibility risk option is generally based on emerging market currencies. This option
gives the buyer the right to exchange a particular currency for dollars or some other hard
currency, if events such as foreign exchange controls lead to inconvertibility of the local
currency.
3.3 Contract Elements
3.3.1 Reference Asset
The contract has to include a reference asset, which is the criterion for the entry of a credit
event as well as the measure for the amount of the compensation. A reference asset is only
required when the deliverable obligations are limited to one asset and if there is cash
settlement or materiality. In this case the asset must be liquid and widely traded. If the
purpose of the credit derivative is mainly hedging of credit risk, the correlation between
the actual loss of the beneficiary and the devaluation of the reference asset should be high
i.e. a bank can reinsure the risk of default by buying puts on the borrowers bonds with a
similar ranking.
3.3.2 Credit Event
The claim for a compensation emerges, if the specified credit event occurs within the term
of the credit derivative. Credit events can be a failure to pay, waiver, restructuring,
bankruptcy, cross-default, or a delayed payment. However, also a less significant decrease
in credit quality can lead to the entry of the credit event, i.e. a rating downgrade or an

Credit Derivatives
20
Structures and Applications
increase of the credit spread can be used as suitable measures. In this case a strike level for
credit spreads that has to be exceeded may apply.
3.3.3 Compensation
On entry of the credit event, the compensation can be made in form of a cash or a physical
settlement. The credit event payment in cash may be:
·
payment of par value in exchange for delivering the reference asset
·
payment of a pre-determined fixed amount
·
payment of par less the recovery value.
If the contract parties agree on a physical settlement, the compensation in case of a credit
event is made in the form of a delivery of a specified other asset in exchange of the
defaulted asset.
3.3.4 Premium
In exchange for the guarantee a premium is paid by the beneficiary. In case of an option
the payment is made at the beginning of the contract term, in case of a swap the premium
is paid periodically until the time of the credit event or the maturity date of the credit swap,
whichever is first (see Board of Governors of the Federal Reserve System (1996), p.2).
3.3.5 Notional Amount
The nominal value is determined by the amount of risk that is being transferred and thus,
the nominal value is a result of the protection seeked by the one party and the risk exposure
accepted by the other.
3.3.6 Term of the Contract
The term of many credit derivative transactions is shorter than the maturity of the
underlying asset and, thus, provides only temporary credit protection to the beneficiary
(see Board of Governors of the Federal Reserve System (1996), p.3). If the credit event

Credit Derivatives
21
Structures and Applications
enters before the end of the term, depending on the contract, the positions can be settled
immediately or can be kept up until maturity and finally settled.
3.4 Standardized Documentation
Until 1999, in Europe, only in Germany, France and the UK have regulators taken the
trouble to lay down a framework for credit derivatives transactions. One major problem is
the issue of documentation. Standardized and generally accepted documentation is useful
and important in various ways: it can reduce legal risk, especially in cross-border
transactions, i.e., by providing clear and precise terminology and definitions and reducing
risk of incompatibility of laws of different jurisdictions, and it enhances market
transparency by reducing confusing variety of documentation.
The International Swaps and Derivatives Association (ISDA), which, through various
publications, has been considered a trendsetter in the derivatives arena by developing
master agreements, has developed standard documentation for some types of credit
derivatives. With eight different definitions of credit events that could have an impact on
the transaction ­ bankruptcy, credit event upon merger, cross acceleration, cross default,
downgrade, failure to pay, repudiation and restructuring ­ the documentation provides a
framework for future transactions. One of the principal aims of ISDA in developing the
definitions was to promote legal certainty in the market for credit default products.
Nevertheless it has to be recognized, that credit involves more variables than, say, interest
rates and thus the credit derivatives market will never be as uniform in its procedures as the
interest rate derivatives market.
3.5 The Application of Credit Derivatives
3.5.1 Portfolio Diversification
Credit derivatives allow access to previously unavailable credits. They can be used to
diversify across a range of borrowers in different regions to gain exposure to an asset
without owning it. From a risk management perspective the optimal portfolio to aim for is
well diversified and non-lumpy, but business strategies which focus on core clients create
the exact opposite portfolio. Many financial institutions traditional approach to the credit

Credit Derivatives
22
Structures and Applications
business was answering the question whether to lend or not to lend. A transformation to the
role of active portfolio managers requires a big change. Commercial banks will need to
operate more like investment banks: managing portfolios and marking prices to market.
(Currie (1998), p.123).
3.5.2 Limits
One of the clearest applications of credit derivatives is the synthetic reallocation of credit
risk between the loan portfolios of banks. From portfolio perspective, big problems can
arise from the banks' concentration on its core competency. Credit lines filled up with
loans, bonds and derivative portfolios can thus be freed up. Therefore, organizations that
are approaching established in-house limits on counterparty credit exposure could continue
to originate loans to a particular industry and use credit derivatives to transfer the credit
risk to a third party, without to undergo complex assignment procedures.
3.5.3 Concentration Risk
The use of credit derivatives may allow a banking organization to mitigate its
concentration to a particular borrower or industry without severing the customer
relationship. On a risk adjusted basis a loan to a major borrower might be unprofitable and
selling the loan in the secondary market may not be possible without disturbing customer
relationship.
A credit swap could solve the problem The relationship bank subscribes to the loan but
also enters a credit default swap agreement on the proportion of the loan it wishes to
hedge. The borrower never knows that its relationship bank no longer holds the risk and so
is happy to provide it with that additional high-margin business (see Parseley (1996), p.29).
Concentration risk can also be a reason for corporations to dispose large exposures to
individual customers. They also possibly need to hedge against emerging-market risk
where guarantees are not available or export agency cover is expensive.

Credit Derivatives
23
Structures and Applications
3.5.4 Hedging
Credit derivatives can be used for purposes such as risk management. The most
straightforward of these trades involve swaps used to create synthetic assets that do not
exist in the markets. The market can fail to supply investment opportunities in the required
maturity, or the constraints on the maximum term of an investment fund may restrict
investment to credit which only issue in longer maturities; i.e. a bank might have a two-
year line for a credit that issues only five-year debt. A credit swap can be tailored to create
a synthetic two-year asset indexed to the default risk of the five-year cash asset. A bank
might have a five-year line but be full out to the second year. A forward-start credit swap
could be used to plug the gap in the credit curve (see Parseley (1996), p.31).
On the other side of these types of trade are hedgers wanting either to hedge just part of an
exposure ­ rather than liquidate an entire position ­ or to hedge an exposure for a limited
period. A credit swap's notional principal and maturity can be tailored to provide the
amount and tenor of protection required.
3.5.5 Achieving Target Profiles
Banks use default swaps and total-return swaps to lay off exposures that do not meet their
return criteria and use the freed capital to invest in transactions that do. The buyers
typically are looking for leveraged or off-balance-sheet exposure, require synthetic assets
or are unable to buy the assets they require in the cash market because their funding costs
are too high.
Also nonbank institutions may serve as counterparties to credit derivative transactions with
banks in order to gain access to the commercial bank loan market. These institutions either
do not lend or do not have the ability to administer a loan portfolio.
Furthermore, institutions may use credit derivatives to lever their portfolios by assuming
credit exposures to different borrowers or industries without actually purchasing the
underlying assets.

Credit Derivatives
24
Structures and Applications
3.5.6 Arbitrage
Credit derivatives allow investors to exploit market mispricing of credit risk, discrepancies
between different markets' pricing of the same risk or simply different opinions.
3.5.7 Remaining problems
One central issue to be considered in dealing with credit derivatives is the existing basis
risk. In a credit swap on a bond for instance, the payment to the hedger on default is based
on a bid for the reference bond. If that bid does not accurately reflect its exposure ­
perhaps because the swap valuation is made one month after default but subsequent events
push the final recovery value much lower ­ a considerable difference between the actual
loss and the recoverable sum could arise.
As well an issue is the correlation beween a possible default of the offloaded exposure and
the contractual partner. The problem is, first, to evaluate the exact probability of joint
default so that the net post-swap credit exposure can be worked out and, second to find
enough uncorrelated counterparties interested in the credit risk that has to be sold (see
Parseley (1996), p.31).
Summarizing it must be emphasized, that working with credit derivatives requires a
commitment to an active portfolio management, to collect relevant data, to construct
suitable modeling systems, an understanding of the regulatory requirements, and a
management that understands the whole process (see Currie (1996), p.124).
3.5.8 Credit Derivatives and Regional Banks
Although the credit derivatives market is no longer a collection of one-off deals, true
liquidity is still confined to blue-chip risk. Theoretically, credit derivatives should be an
ideal product for regional banks. As their resources and geographical networks are limited,
they specialize in particular regions and sectors, building up dangerous concentration risks
in their portfolio. Nevertheless, that should make it easier to package many similar loans
with similar credit risks. Regional and local banks are also accustomed to combining
volume and spreading risk by sharing lending transactions overcoming difficulties of size.

Credit Derivatives
25
Structures and Applications
Credit derivatives tend to be worthwhile only for large volumes of at least $10m. Other
kinds of loans ­ to unlisted, unrated medium-size companies or the public sector ­ almost
never feature as the underlying assets in derivative transactions. There is too little demand
from investors. Yet these are exactly the kind of loans regional and local banks would like
to divest from their balance sheets to free up credit lines and increase returns. Medium-size
banks are still finding it virtually impossible to sell their risk in the form of default swaps,
CLOs or similar credit-backed instruments. That is not because they are smaller, or less
well-known than major European players, but because of the kind of exposures they have.
Regional and smaller banks have too little exposure to rated blue-chip credits to make them
palatable to investors (see Covill (1999), p.32).
The biggest problem of all is the absence of serious credit research on local borrowers.
Regional banks often find that their own corporate memory is the best available guide to a
borrower's creditworthiness ­ yet investors are naturally unwilling to take the bank's word
for it.
The solution, may be for smaller banks to join forces to offer an acceptable package of
loans for a CLO or other securitization; i.e. the local public-sector and cooperative banks in
the different countries rely on one or more head banks (Rabobank, Crédit Agricole,
German Landesbanken, ...). However, many of these public-sector banks still encounter no
pressure from their shareholders to improve their unimpressive return on assets. These
institutions exist primarily to provide reliable banking services to certain customers, and
the profit motive comes at a poor second on their list of priorities (see Covill (1999), p.34).
3.6 The Market for Credit Derivatives
Credit risk is one of the oldest and best-understood risks in finance. On the other hand it is
surprising that credit risk derivatives were not publicly introduced until 1992 at the ISDA
annual meeting in Paris. Interest rate and foreign exchange risk were little managed prior
to the 1970s, yet by 1992 interest rate and FX derivatives were well-developed. Why did
credit derivatives take so long to emerge?
One plausible explanation is that many credit-sensitive instruments are also interest rate-
sensitive, so the value of a credit derivative often requires more sophisticated models than

Credit Derivatives
26
Structures and Applications
for pure interest rate or FX derivatives. An example is a spread-based product, which
derives its value from a risky bond (factor 1) and a comparable treasury security (factor 2).
The technology necessary to price and hedge two-factor products is still under
development and modeling credit risk depends on discrete, not continuous events, so it is
more difficult to model than other capital market phenomena (see Iacono (1997), p.22).
The inherent lack of an accepted credit pricing model and the difficulties in modeling
parameters such as default risk, recovery rates and default correlation create an inherent
lack of transparency that discourages trading (see Das (1998), p.53).
Providers of credit derivatives are mainly investment banks. They need to manage their
portfolios on a much more dynamic basis than the commercial banks do their loan
portfolios. Investment banks also have smaller balance sheets, their portfolios are marked
to market daily and investment banks tend to move in and out of fashionable sectors more
quickly than syndicated lenders (see Parseley (1996), p.34). However, the largest potential
for the market of credit derivatives lies in the commercial banks after they have adopted a
more active way in managing their loan portfolios. Banks will increasingly have the ability
to choose whether to act as passive hold-to-maturity investors, or as proactive, return-on-
capital-driven originators, traders, servicers, repackagers and distributors of the loan
product. Currently however, only a handful of banks have truly integrated credit
derivatives within their overall financial management strategies, although many more have
used them to address one-off exposures.

Credit Derivatives
27
Structures and Applications
0
200
400
600
800
1000
1200
1400
1600
Notional ($ billion)
1990-
96
1997 1998 1999 2000 2001 2002
Year
Credit Derivatives - Size of Market
Estimate
Forecast
Illustration 8: Credit Derivatives ­ Size of Market
13
According to the British Bankers' Association, the global credit derivatives market has
grown to $586 billion in 1999 and will reach at least $893 billion by the end of 2000.
Approximately 40% of the market notional come from credit default swaps. (see
Finkelstein (2000), p.3). In the years ahead, as the use of these products becomes
widespread in the marketplace, we will see the development of more index products,
including regional and industry-related credit indices, to manage credit exposures more
effectively on a portfolio basis (see Masters (1997)).
In addition to commercial banks, a host of other institutional investors, including insurance
companies, investment banks, mutual and pension funds, corporates, money managers and
hedge funds, will become active participants in the market as well.
13
see Finkelstein (2000), p.3

Details

Seiten
Erscheinungsform
Originalausgabe
Jahr
2001
ISBN (eBook)
9783832447830
ISBN (Paperback)
9783838647838
DOI
10.3239/9783832447830
Dateigröße
3.9 MB
Sprache
Englisch
Institution / Hochschule
Leopold-Franzens-Universität Innsbruck – Architektur/Bauingenieurswesen
Erscheinungsdatum
2001 (November)
Note
1,0
Schlagworte
duffie singelton stochastic modeling kredit derivat
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Titel: Modeling Credit Risk and Pricing Credit Derivatives
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