Credit DerivativesTM  

Asset Swap Definition: The purchase of a fixed rate instrument, plus a position of paying fixed and receiving floating in an interest rate swap of the same maturity.
A dealer ordinarily arranges both the sale and the swap.
Example: An investor who wants to buy Freddie Mac debt with a floating coupon might buy Freddie Mac's fixed rate debt and pay fixed in an interest rate swap.
Application: The main reason for doing an asset swap is to tailor a bond's coupon stream to fit one's needs,
namely to convert a fixed coupon stream into a floating stream.
Pricing: The asset swap should trade at roughly the cost of the underlying fixed rate instrument,
because the interest rate swap should have zero value at inception.
Risk Management: The asset swap is a tool for converting from the risk of price fluctuations to the risk of payment fluctuations,
since the value of default riskless floating rate debt reverts to par at each reset debt.
Comment: Asset swap spreads are useful for pricing credit default swaps.

BISTRO Definition: An acronym for either of the following, depending on who's talking and who might be listening.
1. Broad Index Secured Trust Offering. J.P.Morgan's preferred vehicle for transferring a significant amount of diverse credit risk to an SPV.
2. BIS Total Rip Off. An alternative definition of unknown meaning.

Bond Guarantee Definition: A contract that puts the guarantor in place of the debtor, in case of debtor's default.
Thus, a guarantee seems to promise payment in full of the bond's interest and principal and is like bond insurance (q.v.) that pays off enough to make the borrower whole.
Of course, we have to ask, "Who guarantees the guarantor?"

Bond Insurance Definition: An insurance contract that promises the bondholder a payment (maybe not payment in full) in case the debtor defaults.

Chase Secured Loan Trust Note (CLST) Definition:Chase Bank's preferred vehicle for transferring a large amount of diverse credit risk into an SPV.

Collateralized Bond Obligation (CBO) Definition: A note or bond or tranches of notes and/or bonds that an SPV (q.v.) issues, in order to raise money to buy bonds that serve as collateral for the SPV obligations.
Application: The CBO gets the bonds off the balance sheet of the SPV's creator, in return for cash, and allows the creator to structure collateral and SPV obligations to provide the desired credit rating.

Collateralized Loan Obligation (CLO) Definition:A note or bond or tranches of notes and/or bonds that an SPV (q.v.) issues,
in order to raise money to buy loans that serve as collateral for the SPV obligations.
Application: The CLO gets the loans and attendant exposure off the balance sheet of the SPV's creator,
in return for cash, and allows the creator to structure collateral and SPV obligations to provide the desired credit rating.

Synthetic Collateralized Loan Obligation (CLO) Definition:A note or bond or tranches of notes and/or bonds that a lender issues,
plus related credit swaps, designed to reduce the lender's credit exposure and raise money, so it can make additional loans.
One or more credit swaps provide(s) credit protection for the loans, enhancing their cash flow as collateral.
The notes may include credit-linked notes, where the note-holders assume some of the credit risk of the underlying loans.
The lender ordinarily assumes as much as a few percent of the first credit loss.

Collateralized Mortgage Obligation (CMO) Definition:A note or bond or tranches of notes and/or bonds that an SPV (q.v.) issues,
in order to raise money to buy mortgage loans that serve as collateral for the note(s).
Application: The CMO gets the bonds off the balance sheet of the CMO's creator,
thus eliminating credit exposure, in return for cash, and allows the creator to structure collateral and notes to provide the desired credit rating.
Comment: The REMIC (q.v.) has replaced the CMO as the vehicle of choice for repackaging mortgage loans and getting them off a mortgage lender's balance sheet.

REMIC Definition:(q.v.).

Real Estate Mortgage Investment Conduit A structure with favorable tax treatment that the U.S. Congress created in 1986 for issuing CMOs (q.v.).

Commercial Credit Insurance Definition: Insurance that makes a business whole when its debtors default, such as when they fail to pay for goods and services they buy.
Particularly for smaller businesses, a credit insurance policy often includes guidance on credit policy, to reduce losses.
Application: A prime application is to make it easier for a business to raise financing, by reducing the uncertainty about its receipts.
Risk Management: Issuers of credit insurance ordinarily rely on diversification for risk management.

Credit Default Swap (CDS) Definition: A derivative contract between a buyer and a seller of protection,
in which (a) the buyer of protection pays the seller a fixed, regular fee
and (b) the seller of protection provides the buyer with a contingent exchange that occurs
either at the maturity of the underlying instrument (note or bond)
or at the swap's date of early termination.
The trigger event for the contingent payoff is a defined credit event, which might be a default on the underlying instrument or other, related event.
The contingent exchange consists of the seller of protection paying the buyer the principal amount of the underlying instrument (says, 100), in exchange for the instrument (with value that we denote by B).
Cash settlement in the amount of 100 - B ≥ from the seller of protection to the buyer is an alternative to physical settlement.
Example: A German bank has a risky corporate loan on its books.
The bank pays a counterparty 1% of principal per year for a "put option" that has as its trigger the corporation's bankruptcy or insolvency.
Application: The buyer of protection may want to manage its risk or satisfy a regulator and reduce regulatory capital.
Pricing: Buying protection in a credit default swap is equivalent to shorting the credit risky underlying instrument and reinvesting the proceeds in a credit riskless instrument with the same sort of coupon (fixed or floating) and maturity.
Hence, the credit default swap should have the same value.
Risk Management: The CDS is a static hedging instrument.
Comment: Under specific circumstances, the CDS is equivalent to a TRR swap.

Credit Event Definition: A bankruptcy, default, failure to make payments, insolvency, restructuring of debt that hurts a class of creditors.

Default Correlation Definition: A statistical relationship between the values for two obligations of the binary random variable representing the obligation's default status (i.e., default / no default).
Example: We would anticipate a high default correlation between the debt of one Korean bank and the debt of its biggest borrower,
because if the borrower defaults it will stop making payments to the bank, which may have to default on its own debt.

Default Point Definition: The asset value at which at which a firm will default. Net worth may be zero at this point.
Application: Default point is a key parameter in the KMV methodology.

Default Probability The probability that a counterparty or debtor will fail to meet his obligations.

Distance-to-Default (DD) Definition:The number of standard deviations that asset value is from default point (q.v.).
DD = (Asset Value - Default Point) / (Asset Value x Asset Volatility).

Expected Default FrequencyTM(EDFTM)

KMV Corp.'s proprietary measure of the probability that a firm will default during a subsequent.
Currently, KMV computes EDFTM for the subsequent 1-5 years as a function of the firm's DD (q.v.), based on historical results for firms with a comparable DD.

Exposure The potential credit loss due to the face value of a loan to a debtor or the market value of a contract with a counterparty.

GKOs Russian government Treasury bills.

IANs Interest in Arrears Notes,
a tradable, current form of unpaid interest on bank loans that the former Soviet Union took out. Russia made two payments on these before the 1998 crisis. In 10/99 IANs traded at about 11 percent of par. Cf. Prins. (Craig Mellow, "Squeezing out the last ruble, Institutional Investor, 11/99, p. 77 ff.)

Letter of Credit (LC)

  1. The Circular Letter of Credit is a lot like a traveller's check that you can use only to get cash at a specific bank.
    You give your bank X yen (say) and it issues an LC for X yen.
    If you deliver the letter to a specified foreign bank, it gives you X yen or the equivalent in foreign currency (minus something for its trouble).
    The circular LC replaces the danger that a stranger will take your money at gunpoint with the danger that a bank will simply keep your money when you ask for it.
  2. In international trade Importer "opens" an LC with Importer's Bank.
    This means that Importer arranges with Importer's Bank (the "issuing bank") to issue an LC that is negotiable at Exporter's Bank (the "negotiating bank").
    The terms of the LC say that Exporter's Bank will deliver X yen (say) to the Exporter if Exporter presents the LC and satisfies its conditions.
    The conditions are things like presenting trade documents indicating that Exporter has delivered the goods at the right time and place, and in the right quality and quantity.
revocable (An irrevocable)LC is one that either (neither) the issuing bank or (nor) Importer can revoke. The negotiating bank will honour a confirmedLC, even if the issuing bank fails to pay.
The negotiating bank will honor an unconfirmed LC only if the issuing bank pays.
Thus, the confirmed Letter of Credit has a significant component of credit risk to it. The negotiating bank takes the issuing bank's credit.
This eliminates the need for Exporter to take Importer's credit.
Basic business sense indicates that the negotiating bank gets some money for taking that risk, and that the greater the risk, the greater the money.

LINS Loan Identification Number System.
The trademark for a system that establishes a unique number for each loan. Each loan is to its LIN as each security (e.g., share or bond) is to its CUSIP number.

Loss, Given Default The magnitude of the loss due to a counterparty or creditor's default. The term seems redundant, because "loss, given no default" would be zero, under a reasonable definition.

Materiality Clause In a contract, a clause that stipulates when an event or action is significant.
In a credit derivatives contract, the materiality clause specifies when a credit event is significant.
Typically, if a credit event occurs along with a drop in the price of the reference instrument, then the event is material.

Migration Risk The risk of loss due to a change in an obligation's credit rating.
[Not to be confused with the possibility that the entire population of Mexico will decide to migrate to the more attractive economic and political environment in California, Arizona, New Mexico, and Texas.]

Portfolio [credit] Risk The magnitude of the potential loss due to default by any or all counterparties and/or creditors,
as opposed to the potential loss due to default by a single counterparty or creditor on a single obligation.
Cf. standalone risk.

Prins Principal notes, tradable, bondlike current form of bank loans that the former Soviet Union took out.
Russia made two payments on these before the 1998 crisis.
In 10/99 Prins traded at about 9 percent of par.
Cf. IANs. (Craig Mellow, "Squeezing out the last ruble, Institutional Investor, 11/99, p. 77 ff.)

Reference Entity The person, corporation, government, etc. whose credit quality is the credit derivatives underlying risk factor.

Reference Obligation The note, bond, or other obligation that the reference entity issues, insures, or guarantees.

Standalone Risk The risk of loss on a single loan or other contract, ignoring portfolio effects. Cf. portfolio [credit] risk.

Total Rate of Return (TRR) Swap (TRORS) Definition:A derivative contract that simulates the purchase of an instrument (note, bond, share, etc.)
with 100% financing, typically floating rate.
The contract may be marked to market at each reset date, with the total return receiver receiving (paying) any increase in value of the underlying instrument, and the total return payer receiving (paying) any decrease in the value of the underlying instrument.
Cash settlement is the norm for the total return swap.
Example: A U.S. regional bank that wants to invest in Patagonian debt quickly can be the TRR receiver in swap with Patagonian debt as the underlying instrument.
Application: A couple of prime motivations for being TRR receivers are (a) arranging 100% financing and (b) surmounting hurdles to ownership of the underlying instrument.
Pricing: Price the TRR swap roughly the same as the replicating portfolio of (a) long position in the underlying credit risky instrument and (b) short position in the financing instrument.
Risk Management: The TRR swap is a static hedging instrument.
Comment: Under specific circumstances, the TRR swap is equivalent to a CDS.

Vulnerable Option

  1. "An option on a defaultable instrument, subject also to their issuer's default risk. Ex: A put issued by a shaky bank on a corporate bond issued by a third party."
    (Giovanni Barone-Adesi, 9/10/98.)
  2. An option "subject to the additional risk that the writer of the [option] might default."
    (Robert J. Jarrow and Stuart Turnbull, Derivative Securities, Cincinnati, South-Western, 1996, p. 575.)
  3. An option that may not pay off as the contract specifies, because of a possible default by one of the counterparties.
Example: You buy an OTC, deep OTM S&P 500 index put option from a hedge fund. The market tanks and stays there until expiration. You try to collect your winnings, and the hedge fund folds.
Pricing: The usual pricing model for an equity index option has a single risk factor. When the counterparty might default, the option's value depends on at least another risk factor, the counterparty's equity.
Risk Management: The derivatives market ordinarily handles vulnerable derivatives in any of three ways: (1) the "ostrich approach", pretending that the counterparties can't default, (2) the "creditor enhancement approach", putting the deal on the books of AAA subsidiaries, and (3) the "secured lending approach", putting up collateral to secure each counterparty's position.
Comment: I prefer the term, "credit risky derivative", which seems more transparent.

OFZs Russian government Treasury bonds.

OVZs Long term, hard currency bonds that the Russian Ministry of Finance issued. Known as "Taiga" bonds or "MinFins".


Pricing Credit Default Swaps (5/28/00)

The most commonly used and reliable models for pricing credit derivatives price are for pricing a credit default swap (CDS) for an underlying, credit-risky floating-rate note (FRN).
The CDS payoff is B(T) - PFRN(T) = 100 - PFRN(T) ,
where B(T) is the value of a default-free FRN and PFRN(T) is the value of the underlying, risky FRN.
B(T) = 100% of par, because the model assumes that the default-free FRN resets to par at each reset date.
Its premium is some constant, periodic rate.
The pricing model for this CDS assumes that the CDS value is the cost of a replicating portfolio.
Two replicating portfolios have potential for use in the pricing model, and we discuss both.
As good as these models are, they are not perfect, because they do not handle some relevant details.
Science leaves room for skill and guts.

We develop two similar models for pricing a CDS for an underlying, credit-risky fixed-rate note (FxRN) off the price of a replicating portfolio.
The wrinkle here is that the payoff function is not 100 - PFxRN(T) ,
but B(T) - PFxRN(T) ,
where B is the market value of a default-free note that is "comparable" to the FxRN - same coupon, same maturity.
This isolates the credit risk of the FxRN from its market risk.
Note: If the default occurs before maturity, and interest rates have moved significantly, then the value of the default-free note might deviate significantly from 100.


Credit Default Swap (CDS)

The CDS pays off at default the dollar loss on the underlying note:
Payoff = 100 - PFRN(t)
Payoff = 100 - PFxRN(t).

The cost of that payment is a periodic rate, similar to a bond or note coupon:
Premium = CCDS

Other Assumptions


Figure 1 defines the cash flows associated with some relevant positions in the underlying, credit-risky debt and other instruments and portfolios.
The "Position" column names the position.
For now, letís consider only the first five simple positions, not the replicating portfolio positions in rows (6) to (9):

  1. receive fixed in an interest rate swap (IRS)
  2. buy a U.S. Treasury note
  3. buy a "AAAA" FRN
  4. buy a risky FRN
  5. buy a risky FxRN

The "Initial CF" column denotes the initial outlay for getting into the position in the previous column.
For the swap, Initial CF = 0, because the swap is on-the-run. The other initial cash flows are negative in the amount of the instrumentís initial cost.

The "Periodic CF" is a fixed or floating coupon, except for the IRS, there, it is an exchange of floating coupon for fixed.

The "Terminal CF" for the IRS includes a term for its MTM value, because we need to allow for the "terminal" date to precede the maturity of the underlying note, if default occurs. The terminal prices of the IRS and UST are not 100, because of market risk for early default of the underlying credit-risky note. The "AAAA" FRNís value is 100 at any reset date. Of course, this is an oversimplification, because either its credit quality might change or default might not occur at a reset date. The risky FRNís terminal value is not 100 because of default risk. The risky FxRNís terminal value is not 100 because of default and market risk.




Initial CF

Periodic CF

Terminal CF


Rec. Fxd., IRS













100 + L + SAAAA


Buy Risky FRN





Buy Risky FxRN















(3) - (4) - Model 1

PFRN(0) - PAAAA(0)


100 - PFRN(T) + SAAAA - SFRN


(2) - (4) + (1) - Model 2

PFRN(0) - PUST(0) 














(2) - (4) - Model 3

PFxRN(0) - PUST(0) 


PUST(T) - PFxRN(T) + CT - CFxRN 


(3) - (4) + (1) - Model 4

PFxRN(0) - PAAAA(0) 



Underlying Credit-risky FRN

This is more of a pure credit play. Any problem with interest-rate market risk is minimal, because the underlying, credit-risky note is an FRN. 

Model 1

Replicating Portfolio


Model 2

Replicating Portfolio



Model 4

Replicating Portfolio