Credit Derivatives Last revised: March 02, 2002

New, this month:

  • 9/28/00 "Ask Dr. Risk!": "Corporate Finance Applications of Credit Derivatives", Accounting for Credit Derivatives, That Credit Derivative: Is It a Hedge, or Is It a Trade?
  • Dr. Risk's "Derivatives DictionaryTM": 
  • 9/28/00 Dr. Risk's Links: Vinod Kothari's
  • Dr. Risk's "Mathematical Appendix": "The World's Simplest Model of the Credit Spread"

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Archived Credit Derivatives Pages:    1999  1998

Ask Dr. Risk!

Dr. Risk promises you at least a brief response to your important question, as soon as he has a free moment. A question of sufficiently general interest to make it into the 'Zine, tends to generate a more comprehensive response. All questions and answers become the property of The William Margrabe Group, Inc. 

9/28/00 Credit Derivatives and Energy (9/28/00)

Dear Dr. Risk – I am an Intern and am keen to take up a position in Credit Derivatives in the energy co - what are the issues and things I am supposed to be aware of in the Energy Industry vis a vis Credit derivatives  – Shrikant

Dear ShrikantSince you are at the entry level in this industry, a basic knowledge of credit derivatives and of energy economics and finance would impress potential employers. They would ordinarily suffice to obtain an entry level position.

The risk management business has recently moved toward a unified look at risk management that includes credit and market risk. Researchers and practitioners are talking about unifying market and credit risk, at least. Look into that. A special case of this union of topics, where the market risk comes from movements in energy prices, is what you want. Firms are hiring chief risk officers who oversee market, credit, operational, legal, and other risks. That gives you something to work towards. – Dr. Risk 


9/28/00 Corporate Finance Applications of Credit Derivatives (9/28/00)

Dear Dr. Risk – I have to do a presentation in a few weeks titled "Corporate Finance Applications of Credit Derivatives". Do you have some suggestions as to where I might find some literature on this topic (e.g. links, papers, etc). – James

Dear JamesSorry, but Dr. Risk doesn’t know of a document called "Corporate Finance Applications of Credit Derivatives", etc. He can only speculate on your specific needs, but his speculation is that you have to prepare some sort of sales presentation to corporate clients about how you can help them with your credit derivatives capabilities. Most of the credit derivatives literature is from the point of view of the investor, but what’s important to the investor is important to the issuer, because it affects the price that the investor will pay for the issuer’s securities. So Dr. Risk can only suggest that that sort of approach might prove useful. Talk about how the issuer has one credit quality, the investor wants another, and you can step in the middle to help both parties achieve what they want. Dr. Risk 

Dear Dr. Risk – As it turns out, my presentation is merely to other people in our small group of
6!  This is our SVP's idea since our group only writes presentations (memos) on paper to a market risk committee.  We don't get the practise the valuable skill of public speaking. Hence our presentation series. Each of us has to discuss a different aspect of Credit Derivatives (one person does the intro, another person covers pricing models, etc, and my talk is on Corporate Finance Applications of Credit Derivatives). While I am not looking for a specific article with this title, I thought there might be some case studies/reports you could point me to that deal with this topic. thanks for your time. – James 

Dear JamesHow fortunate you are that your SVP is urging you to develop your public speaking skills. No article that comes to mind deals with the general topic of corporate finance applications of credit derivatives. Dr. Risk can only suggest following links from his credit derivatives page. The most promising link would probably be (the old link is obsolete), then do a search. The UBS link seems relevant.  

Of course, your definition of corporate finance is relevant. Dr. Risk’s definition includes discussions of the standard issues of investment, financing, dividend policy, leasing vs. buying, treasury operations, etc. Just look at every aspect of corporate finance, as you define it, see where credit is an issue, and envision how credit derivatives could do some good. Credit derivatives are relevant for investment in securities where the issuer makes a promise. They can be relevant for financing, where a borrower promises to repay a loan. They are relevant for the issue of leasing vs. buying, because a lease is a promise to pay. Treasury operations could depend heavily on credit quality -- yours or the issuer of paper that you buy. Credit derivatives may enhance the issuer’s credit quality to suit investor tastes, or may prove useful in guaranteeing a customer’s obligations under a long-term contract or lease.

Sorry that Dr. Risk can’t point you to a specific source. Dr. Risk 


9/28/00 Accounting for Credit Derivatives (9/28/00)

Dear Dr. Risk – I'm a Filipino doing a research about Total return swap and credit default swap for my company here I the Philippines.  This is very new to me and I've come across a lot of references about the subject.  but I haven't encountered on how to account for such transaction in our books.  Can you please point me to the right direction when it comes to Accounting for credit derivatives? – Edu

Dear EduDr. Risk has some good news and some bad news. First the good news. In the U.S. the Financial Accounting Standards Board and SEC are the major players in setting financial accounting standards. Both have web sites and our links page provides direct links to them. At the FASB site one can get much information about FAS 133 and 138, the latest pronouncements on accounting for derivatives, including credit derivatives, including a large booklet and course materials. 

Now, the bad news.

1. You’re in the Philippines. U.S. standards – such as they are – may or may not have any bearing on your country’s financial standards.

2. U.S. standards on accounting for credit derivatives aren’t the most straight forward. Dr. Risk has attended presentations where the experts hemmed and hawed on the subject. 

3. In the U.S. the best way to learn about this subject is to bring in your Big Six (Five?) accounting firm and get an incredibly expensive tutorial or attend a seminar for a merely expensive tutorial. Alternatively, buy the books from the FASB site and teach yourself, much as you might teach yourself brain surgery to take care of a tumor in your head.

Best of luck! Dr. Risk 


9/28/00 That Credit Derivative: Is It a Hedge, or Is It a Trade? (9/28/00)

Dear Dr. Risk – If Bank A sells a credit derivative to Bank B to take on the risk of a loan from Corp X. (That is Bank A is taking of the risk and Bank A does not have this loan or similar loan on its books).  Under what circumstances can this derivative be considered a hedge and under what circumstances can this be treated as trading? – David

Dear DavidWhen does your house provide shelter from the elements, and when does it provide an office for your business? It could provide both, and that could have implications for the way you live your life and what you put on your tax return. 

What's the context of your question? Why do you want to know? It matters. Is this a question about bank regulatory capital? Does it concern FAS 133? Are you concerned about basis risk for portfolio management? – Dr. Risk 


Credit Derivatives Pricing Paradox (7/28/00)

Dear Dr. Risk – I am working on a project that involves understanding of major influences on pricing, demand/supply dynamics and theoretical pricing considerations on credit default swaps.  Can you tell me an online source/book/publication that I can refer to.

[1] Also, one of the articles that I read mentioned that default swap quotes on some Investment Banks and corporates widened despite a rise in their stock prices, How can one explain this dynamic?

[2] Additionally, what would skew the pricing of credit default swap away from the credit spread on the underlying reference credit? Can we have a scenario wherein credit spread on the reference credit narrows whereas the default swap quotes on the reference credit widen? – Amberish

Dear Amberish – Your project sounds complex. You can find links to much free information about credit derivatives at You're the best judge of what suits your needs. 

Before explaining the phenomenon, let's clearly identify it. The coupon on credit-risky debt will ordinarily exceed the default-free rate for the same currency, tenor, and maturity, because of its positive probability of default and incomplete and/or untimely recovery. (For simplicity, ignore taxes, which also affect yield.) The yield spread of the reference credit over default-free debt is what the market charges as compensation for the cost of potential default. It is also what the market would pay to totally eliminate the potential default. Hence, the market would pay that spread to a totally solid seller of protection. If the protection seller were itself credit-risky, then it would have to either (a) require a smaller premium than the credit spread for promising to provide full protection or (b) charge the market credit spread and promise to provide full protection plus something. 

[1] You hypothesize that the debtor's share price rose and so did the cost of credit protection for its debt. That puzzles you, since you associate (a) a rise in the share price with an increase in the credit quality, (b) an increase in the credit quality with a decline in the credit spread, and (c) a decline in the credit spread with a decline in the quoted cost of a default swap. That is all true, ceteris paribus, so what else might change to muddy the waters? The provider of credit protection may also become more credit worthy, and this would allow it to charge more for its promised credit protection, ceteris paribus. Conceivably, the article you mentioned referred to a situation where the effect of improved credit quality of the provider of credit protection overwhelmed the effect of improved credit quality of the debtor. Dr. Risk admits that this sounds unlikely. 

[2] You hypothesize that the credit spread on the underlying reference credit decreased, but the premium on the credit default swap increased. As in [1], this means that the threat of loss decreased, but the value of protection increased. The most likely explanation for this is a simultaneous increase in the credibility of the provider of protection. Dr. Risk 


... and then Could Dr. Risk Wash Your Windows? (7/28/00)

Dear Dr. Risk – I am a student of business administration. I have got my diploma thesis and it deals with the topic of static hedging methods (options only) for stock and junk bond portfolios. I would be very greetful if you could propose a structure for my work and give an internet adress, where I can download articles of Journals (downloading working paper is possible, but Journals?)

In addition it would be very interesting if you could give an overview and describe the current situation of credit derivatives and new hedge products. – Eyüphan

Dear Eyüphan –  Dr. Risk has no doubt that you would be grateful if he would propose a structure for your work and give an Internet address where you could download articles of Journals. Dr. Risk would be grateful if Blythe Masters would propose a structure for HIS work, and would love to know where to download (for free, of course) all the print periodicals to which he now pays those annoying subscription fees.

Proposing a structure for your work is a job for you and your thesis advisor. Done properly, it requires much more time than Dr. Risk can devote to responding to a message. However, here are a few comments and questions. 

  • Your topic approaches specificity – that’s good! The ideal dissertation is what most ordinary people would find insanely specific, e.g., “The Role of the Fish Net in the Danish Herring Fishing Industry in the Latter Half of the 16th Century.”
  • What is a stock and junk bond portfolio? Is it a portfolio of many types of shares and junk bonds of many companies? Is it a portfolio of stock and one junk bond, both of one company? 
  •  Why do you choose not to find a static portfolio of options and stock (which is essentially an option on stock with a zero strike) with which to hedge the junk bond portfolio (a portfolio of junk bonds). 
  • If your junk bond portfolio has junk bonds of several companies, your static hedge will include some multivariate options that you’ll never see in the marketplace. Consequently, no one will ever apply that result from your dissertation.

The business model for most journals is to copyright their contents and charge subscribers for them. If they didn’t charge, they couldn’t survive. Consequently, you will ordinarily have to use a paid copy of the journal. A service that allows you to download articles will charge you and pay the journal. Dr. Risk has used ABI/INFORM to find and download articles from CD-ROM. Search for ABI/INFORM on the Internet and you may be able to access it on-line. Also, look at If you find a place to download a wide variety of articles for free, it may be pirating articles, which is not nice. Any minimally adequate university research library will subscribe to a service that makes all articles available to students on terms that satisfy the copyright holder. That may be ABI/INFORM, Lexis-Nexis, or something else. Contact your research librarian. You pay for that service via your university tuition fee.

For a free overview of the credit derivatives industry, please see the links at, elsewhere on this page. – Dr. Risk 


Credit Derivatives Forum (7/28/00)

Dear Dr. Risk – my name is Walter and I am an italian student. I'm starting to elaborate my theses degree about Credit Derivatives, and I'm searching every kind of material. I saw that many italian student sent you some requests about this theme. Could you please send me their e-mail, so i can countact them for some suggestion or advices. Thank you very much for your attention. – Walter

Dear Walter– Dr. Risk has noted that a high proportion of those writing him about credit risk and credit derivatives are Italian students. Why is that? Regardless, it sounds to me as though a forum, where people can share their interests and information would help you. Dr. Risk hopes to start one soon, so people can send messages that we will make public, allowing public responses and threads of conversations that continue, etc. We can't honor your request for the someone else's e-mail address, because we honor the confidentiality of those who write us. – Dr. Risk 


Default Correlation (7/28/00)

Dear Dr. Risk – I am now sutdying credit derivative as a trainee.And started with credit default swap.then I found problem how to reflect credit quality of the protection provider to the price of the credit default swap.And how to reflect the correlation between default probability of credit reference entity and the protection provider.If you have any advice to those problems. Please help.Thanks. – Makato

Dear Makato – "A rising tide raises all boats, but a typhoon can sink entire fleet." – Dr. Risk 

Kublai Khan's Mongol invasion fleets ran into storms en route to Japan in 1274 and 1281, and lost many ships each time. Western lenders in Asian credit markets during 1997 and 1998 experienced a high proportion of defaults, and that illustrates default correlation. 

The basic pricing model for a credit default swap consists of finding the cost of constructing static hedge against the credit exposure. Namely, the credit default swap provides protection that equals the excess of the payoff of a default-free bond over the payoff of a credit-risky bond with the same coupon, maturity, and other terms. Consequently, in a perfect market the cost of the protection should equal the difference in bond prices.

Your question focuses attention on a crucial assumption of this model: the protection provider will meet its obligations. However, (a) in theory, the protection provider might default, and (b) in practice, protection providers have defaulted on many occasions. The most notable, recent example of this was during the Asian meltdown of 1997-1998. In several cases, an Asian bank defaulted on its obligations to deliver protection to western lenders and bondholders after debtors from the bank's country defaulted. Economic troubles in the country and decline in its currency value were latent factors that hurt both the country's dollar (say) debtors and the banks. The standard term for the degree to which the debtors and guarantors default simultaneously is default correlation, which has different precise definitions in different models of default. Due to default correlation, the market price for this imperfect credit protection should be less than the basic model indicates. 

The books available on credit derivatives are not strong on this topic, but you might want to have access to the little they say. You can find a selection at "Books", below. The best information I’ve seen on this topic has been at conferences, where people talk about pricing credit derivatives. You might want to attend some conferences and take some courses that offer that material. I don’t have any free Internet links about this material at this point. – Dr. Risk 


Pricing Credit Derivatives (6/28/00)

Dear Dr. Riski have 4 questions:
i) What are the currently used models "in real life" for pricing Credit Default Swaps
ii) What are the currently used models "in real life" for pricing Total return swaps [e. g. Longstaff/Schwartz or Jarrow/Turnbull]
iii) What are the currently used models for pricing corporate loans (fixed interest); especially, when there is no public rating (and also no credit spreads) available
 iv) Do you prefer one of the portfolio models (CreditMetrics, CreditRisk+, CPV, KMV, KAMAKURA)? If yes, why?

Dear Michael – 

i) Practitioners use a no-arbitrage, static hedging argument to price credit default swaps off liquid asset swaps. If the asset swap (or equivalent) isn't available, then a price for the credit default swap isn't available. I discuss this elsewhere on the credit derivatives page, I believe. Although the models are simple, one benefits from having "street smarts" when using them. 

ii) Pricing total return swaps uses the same no-arbitrage, static hedging argument used for credit default swaps. The only difference is that the replicating portfolio for a total return swap is simply long (short) the credit risky bond and short (long) the floating rate bond of impeccable credit quality -- or equivalent. You won't see practitioners using Longstaff/Schwartz, Jarrow/Turnbull, or Duffie-Singleton. It would make about as much sense as using string theory to plan a moonshot. The elegant theories require data that don't exist. So the user has to make up numbers to use the model for pricing.

iii) The current model for pricing corporate loans is to charge interest as a function of the bank's internal credit rating. Moody's has products to help lenders do this more rationally and consistently. Perhaps, others do, as well.

iv) What is CPV? Last time I tried to find out Kamakura's basic approach, they wouldn't release it, until they released their product. Do you have a source for that information? – Dr. Risk 


Can Kantonalbanken Bank on Credit Derivatives?  (6/28/00)

Dear Dr. Risk – I'm a swiss finance student and i write a thesis about applications of Credit Derivatives in Kantonalbankenportfolios. Kantonalbanken are small  to medium-sized regional commercial banks and their credit portfolios consist mainly of low quality, non rated regional loans. I see a bunch of problems in using credit derivatives for this type of loans: they're not actively traded, so there's no market price. These lenders normally don't have exchange traded debt or equity that you could use as a reference asset. Correlation-data on credit losses dont exist and the loan provisions are secret and different among the institutions.

How would it be possible to overcome these problems and to use credit derivatives such as total-return-swaps or default-swaps (-options) as tools for diversifying the portfolios? – Marc

Dear Marc – Thanks for your carefully thought out and expressed letter.

You've done an excellent job of laying out serious problems with applying credit derivatives for hedging and arbitrage pricing in your particular case. In a nutshell, you're telling me that a prospective hedger can't find an appropriate hedging instrument for credit risk, and that the market is so sparse that the parameters that a reduced form pricing model would use are not available.

Then you talk about diversifying the portfolios, also appropriately. In the context of Markowitz portfolio theory, if you can't hedge, maybe you can diversify. If you can diversify enough, then you can eliminate risk and price the diversified portfolio just as you would price credit riskless debt. In your case, an obvious solution is to have the Kantonalbanken share their risk via total return swaps. The ultimate application of that idea would see each Kantonalbank with a share of the overall portfolio equal its share of total value. In essence, each Kantonalbank would be a marketing agent and the Kantonalbanken system would share a common portfolio.

Of course, this obvious solution has some problems. The biggest one is to remove from each Kantonalbank the cost of making bad loans. I would anticipate that such portfolio sharing would lead to a rise in bad loans. Also, even global diversification could never totally eliminate a "market factor" in credit risk, which rises and falls with the business cycle. Surely the Swiss economy has sufficient ups and downs to lower and raise the default rate and raise and lower credit quality. 

The Kantonalbanken might look abroad for diversification by doing total return swaps with lenders in other countries, even on other continents. That would provide significant diversification, but wouldn't remove the impact of the credit market factor. – Dr. Risk 


SPV, SUV, STD, ... S T U V ... ? (5/28/00

Dear Dr. RiskI am interested in learning about "special purpose vehicles" or "special purpose entity",  what is the best way to pursue this educational quest?Jim

Dear Jim The most authoritative source would be some documents from someone involved in such a deal. Might be hard to come by. A little easier to get would be some sales literature on a product that employs and SPV. For example, try to get literature on BISTRO directly from J.P. Morgan. If you know any Chase salespersons, you might make a similar request to them, mutatis mutandis. Maybe you could get literature on a Chase Secured Loan Trust Note (CLST). You could go to “Dr. Risk’s Bookshelf.” The Handbook of Credit Derivatives has probably the most coverage of SPVs, although I wouldn’t call it extensive. In particular, it has about a page on the the J.P.Morgan BISTRO product. Other mentions crop up throughout the book. I don't think the other credit derivatives books discuss SPVs more than a page or two. Dr. Risk


Dr. Risk Picks the Most Attractive Models (4/28/00)

Dear Dr. Risk – what do you think basically about pricing the default-risk of loans by using option models like Black/Scholes, Geske, Longstaff/Schwartz etc. Is there any model you prefer? If yes, what are the reasons (e. g. empiricial tests)? – Maria

Dear Maria – In Dr. Risk’s experience, what really works – in at least a few cases, when you have a rich debt market – is the simple arbitrage-free pricing model that prices the credit default swap in terms of an asset swap. The problem is that the market often does not provide the liquid instruments you would want to replicate the credit default swap. Debt markets, particularly corporate debt markets, are notoriously thin. However, this no-arbitrage model works in many cases and explains why 60%-80% of credit derivatives are default swaps, total return swaps, and structured notes with those embedded swaps.

Dr. Risk likes the Black-Scholes-Merton and Geske approaches, also. Those models have proven robust, and Dr. Risk’s guts tell him that they can be robust in this application. However, often the capital structure is complicated, so these models are only crude approximations or require data that are not available. Nevertheless, KMV (using an extended version of the BSM model) and Geske seems to have teased out some useful results.

Reduced form models are beautiful and elegant. Dr. Risk admires their sophisticated and ingenious structures, the way he admired the Black-Scholes model when he was young and it was mysterious. The information required for constructing the term structure of risk neutral probabilities of default (given recovery rates) might even be available for companies with much outstanding public debt. However, recovery is a complex process, and the historical data available for modeling recovery are crude and inadequate. Getting adequate data for such models appears hopeless to me for the foreseeable future. Dr. Risk makes this extremely pessimistic statement at every opportunity, waiting for someone to respond, “Oh, no. We have excellent data. You can bank on this reduced form model.” So far, it hasn’t happened.

Dr. Risk is not familiar with empirical tests of these models, except for KMV’s work on “Expected Default Frequency” (EDF) and Geske's work on default probabilities. Maybe Dr. Risk just needs to read more. However, what traders actually use is a key empirical result that speaks volumes. – Dr. Risk

Dear Dr. Risk – thank you ver y much for your prompt and interesting answer. I like to tell you something to the background of my problems concerned pricing the risk of corporate loans. In Germany the risk management of banks ist not so developed like in the states or in the U. K.  A major problem ist that availability of data (e. g. public ratings).

A very interesting discussion in Germany is: Should the loans that a bank gives to corporates (small, middle and big) be priced by internal rating (expected loss ...) or is there a possibility to price the loans by a option-model? (So the banks have to solve the same question like the traders of credit derivatives (the risktakers), but in Germany there is nearly no credit derivative market for the smaller and medium sized banks) From the mathematical view we prefer option models but our investigations were quite disappointing.

For further research we think about substituting the black/scholes model against mor complicated models (e. g. mixed-jump-diffusion, levy, ..). But we are insecure about the practicability (more parameters to estimate, more complexity of the models, loosing uniqness of the martingale measure,...) because many of our bank clients are small and medium-sized.

If i understand your answer right, you also think that this "high-sophisticated" models cannot be succesfull apllied in the near future?  – Maria

Dear Maria – The lack of public debt with credit ratings is a major difference between US and German markets. It makes the credit derivatives business in German dangerous, and rewards banks that nurture their relationships with customers.

Your excellent point deserves emphasis: “the banks have to solve the same question like the traders of credit derivatives … but in Germany there is nearly no credit derivative market for the smaller and medium sized banks”. It suggests that the credit derivatives people, with all their complicated option pricing, may have something to learn from the lowly credit officer and his antiquated methods.

Dr. Risk doesn't think the problem is using diffusion, rather than jump diffusion. His guess is, the problem lies in the data. After you solve the data problem, your theory will work much better. In your case, with no debt market, just a bilateral loan market, the reduced form models are hopeless. The Black-Scholes-Geske approach you are trying has more promise. How much promise depends on the data. – Dr. Risk

Dear Dr. Risk – What ist the practise in the states for pricing the credit risk of non rated companys? (Expected loss via expected default probability?) – Maria

Dear Maria – Lenders have priced credit risky debt for at least many decades without resorting to any sort of explicit option pricing model. Mostly, they use rules of thumb, based on experience. For example, revenue as a percent of fixed expenses, asset value / debt, etc. Also, they rely on the underwriting opinions of loan officers and loan committees, depending on the size of the loan. The more sophisticated lenders use statistical models, such as discriminant functions. Their risk management is primitive to non-existent. Of course, from time to time, the herd instinct leads them astray. For that and other reasons credit problems explode in their midst. Dr. Risk imagines that German lenders use a similar process, with similar results. German lenders have much experience in building relationships and using them to gather information on which to base loan decisions. – Dr. Risk


Why Writing Life Insurance on a Dead Man Can Be a Winning Idea, and Related Credit Issues (4/28/00)

Dear Dr. Risk – I am interested in knowing if credit derivatives are used apart from performing loans also for non-performing loan portfolios (i.e. defaulted counterparties) in order to transfer (partially or totally) the risk (related to the amount and time of credit recovery)  to another counterparty (by the way of asset swap or an option). My hypothesis is that credit derivative on non-performing loans could be employed in place of securitization. For these portfolios credit derivative could be more efficient since there are less costs for setting up and arranging the transactions compared to securitization.

Is this true ? Could you provide me with some helpful sources & information on this subject ? Maria

Dear Maria – Credit protection through a credit derivative is practically equivalent to insurance. Consequently, a credit derivative that has underlying non-performing debt is like a life insurance policy written on a dead person. Dr. Risk thinks it makes sense for an insurance company to write a life insurance policy on a dead person, but it may not make sense for a credit derivatives desk to offer credit protection on non-performing debt. 

Why is credit protection via purchase of a credit swap like a life insurance policy? In each case, you have a loss, and the "insurance" (life insurance policy or credit derivative) makes you whole. As a practical matter, that’s insurance. As a legal matter, it’s not. "Insurance" is the word that the credit derivative salesperson dares not speak, because that could lead to a violation of insurance regulations. In a worst case scenario, the credit derivatives salesperson who uttered that word might even end up in jail.

While it may seem obvious why someone would want to buy a life insurance policy on a dead person, why would any company write such a policy? While buying such a policy may sound preposterous, like something that the mob might do, it’s a legitimate business practice. Dr. Risk recalls that a hotel company bought such a policy on dead customers after a horrible hotel fire. You can imagine that it was an expensive policy! The people were dead and the hotel company would certainly have to compensate their survivors. However, the level of compensation was (a) uncertain and (b) dependent on the outcome of negotiations. The hotel company decided to pay a predetermined amount to turn the problem over to a life insurance company that customarily dealt with that sort of uncertainty and negotiation. For the right price, the insurance company was delighted to take on the risk and the negotiations. 

What sort of credit derivative could have underlying, non-performing debt? Credit derivatives have payoffs that depend on some aspect of credit quality. A credit default swap typically pays off at the occurrence of a "credit event" that amounts to a default, so would not be suitable for trading exposure to a non-performing loan portfolio – which is already in default. A total return swap could have an underlying non-performing loan portfolio.

So, have you come up with a new line of business for credit derivatives desks? Dr. Risk has his doubts. First, look at what the pros are doing. Recently, Dr. Risk has heard – on separate occasions – Blythe Masters (JP Morgan) and Dennis Oakley (Chase Bank) discuss how they run their credit derivatives businesses. Since 1997, both banks have on several occasions used credit derivatives to transfer significant amounts of credit risk to SPVs. JP Morgan has used the BISTRO (Broad Index Secured Trust Offering) structure for this purpose, and Chase has used synthetic collateralized loan obligations (CLOs) and the Chase Secured Loan Trust Note (CLST). Part of the charm of using credit derivatives to transfer the risk is the efficiency you mention. Dr. Risk doesn't recall that either Blythe or Dennis specifically mentioned using these structures to transfer exposure to non-performing loans.

Dr. Risk doesn't see any absolute reason for excluding non-performing loans from these structures, but let’s think about it. What could be wrong with the idea, from a business point of view? Maybe such loans are relatively few, scattered, and uneconomical to package. Maybe banks keep the low-grade loans on their books and transfer out credit risk of higher-grade loans, because BIS regulations provide that strange incentive. Maybe non-performing loans raise significant regulatory, tax, accounting, or other issues.

Maybe this sort of arrangement would magnify a problem that is already inherent in credit derivatives: separation of actions from consequences. By now, all competent adults should know that actions have consequences, and there are advantages of letting the actor reap the consequences of his action. Unfortunately, credit derivatives weaken that connection.

Let’s get more specific about the relevant actions and consequences. In a non-performing loan, managing the workout is crucial, but difficult. Dr. Risk’s experience observing default has been more in the area of real estate, although as a favor to a friend, Dr. Risk is trying to help a person who has defaulted on an amazing amount of credit card debt. (A financial counselor who deals with this problem frequently said to the insolvent one, "I've only seen one other case this extreme. I'll have to go back into that file and see what we can do for you.") Banks are notoriously poor, sometimes even incompetent when it comes to maximizing the value of real estate, owned (REO). Real estate management is a tough game fought every day over nickels and dimes that add up to huge sums over time and space. The typical bank that finds itself with REO after a real estate crash isn’t prepared to deal with this sort of alien minutia. Dr. Risk suspects that this is true with other sorts of loans. Put this problem together with the fact that the lender might supervise the workout, while a credit derivatives counterparty reaps the benefits of a job well done, and you might have an expensive conflict of interest.

You can find information about credit derivatives on “Dr. Risk’s Bookshelf.” The credit derivatives teams at Chase and JP Morgan have been generous sources of literature, so if you’re a customer or potential customer, you might contact them. – Dr. Risk


Structural and reduced form models (4/28/00)

Dear Dr. Risk – We are wondering why "reduced form models" for pricing of credit derivatives is called reduced form? – Andy & Matt

Dear Andy & Matt – While "reduced form models" may sound a bit pretentious and even outré to most of us mere mortals, it rolls naturally and easily off the tongue of everyone who got 800 on his math SAT and aced econometrics at the graduate level. Dr. Risk doesn't think the mathematics of simultaneous equations in econometrics and simultaneous equations in credit risk are isomorphic (i.e., matching piece by piece, process by process), but somebody apparently thought they were similar enough to describe them with the similar language. 

Reduced form and structural equations are two ways that the econometric literature expresses systems of simultaneous equations. A pair of structural equations relating the endogenous rates of return on bonds (RBt) and shares (RSt) and the (arbitrary) exogenous variables Xt and Yt (don't ask what they are) would be: 

RBt = a1 + a2 RSt + a3 Xt + u1t 
RSt = b1 + b2 RBt + b3 Yt + u2t 

where uit denotes an error term. 

If you manipulate the structural equations properly, you can solve for the rates of return on bonds and shares in terms of the independent variables X and Y, obtaining the reduced form equations:  

RBt = c1 + c2 Xt + c3 Yt + v1t 
RSt = d1 + d2 Xt + d3 Yt + v2t 

Of course, the c's and d's are functions of the a's and b's, and the v's are functions of the u's. 

In the case of credit derivatives, the Merton-Geske-KMV "structural model" of the probability of default uses a pair of simultaneous equations and an identity, such as 

B = S - A

and requires solving the equations simultaneously for the only unknowns, 

A = B + S

en route to solving for the desired probability of default. 

In contrast, a typical "reduced form" model prices credit risky debt by simple discounting, using an adjusted rate of interest, and might model the credit spread simply and directly – i.e., alone, on the left-hand side of the equation – as some sort of time-series process.  This allows the modeler to price an issue of credit-risky debt without simultaneously pricing all the debt in the firm's capital structure. However, if one deduces the term structure of default probabilities, that has for Dr. Risk the same flavor as a structural model. 

Other differences:

  •  In econometrics, one might use structural equations to conceive a set of relationships, then use reduced form equations to estimate them. In the credit area, some people look at the credit problem from the point of view of structural equations, other from reduced form equations. However, the structural equations that some people use are not equivalent to the reduced form equations that others use.

  • In econometrics, all the equations are typically linear, although perhaps in logarithms or differences. In credit the equations are ordinarily nonlinear.  

Dr. Risk


Mathematical Appendix Below, you'll find mathematical analysis of credit derivatives. You'll find more mathematical finance here.

The World's Simplest Model of the Credit Spread (7/28/00)

Fairly obviously, the credit spread depends on the probability distribution for the possible levels of severity of default. Let's consider the simplest possible case: 

  • Time consists of one period that starts "now" and ends one year "later". 
  • The default-free and credit-risky debt mature at the end of one year. 
  • The tenor for the coupon is one year. Let c1 denote the coupon rate. 
  • The bond defaults, with risk-neutral probability p. If it defaults, the bondholder recovers the fraction r of the promised payment of interest and repayment of principal. 
  • The bond sells now for par. 

Then we have the following binomial tree for the bond’s value: 

            100 (1+c1)
            100 (1+c1)

We derive our pricing equation from the assumption that the price of the bond equals the discounted, expected (using risk neutral probabilities) payoff after one period. The pricing equation for the bond is:
100 = [p 100 (1+c1) r + (1-p) 100 (1+c1)] / (1+r)  

Let l = 1-r denote the loss rate. Rearranging the pricing equation, we get 
1+r = (1+c1) [
p r + 1-p ] = (1+c1) [1 - p (1-r)]  = (1+c1) [1-p l]. 
Hence, the ratio of the promised wealth relative for the credit-risk debt to the promised wealth relative for credit-riskless debt is
(1 + c1) / (1+r) = 1 / (1 - pl), 
1 + c1) = (1+r) / (1 - pl). 
The promised wealth relative equals the riskless wealth relative, grossed up to reflect the probability and magnitude of possible default.  

The credit-risky coupon is
c1 = (1+r) / (1-pl) - 1 = (r +pl) / (1-pl),
namely, the risk-free rate, plus a premium to reflect the probability and magnitude of default, all grossed up to reflect the probability and magnitude of possible default. 

The credit spread is 
c1 - r = (r + pl) / (1-pl) - r = [(r + pl) - r + r pl)] / (1-pl
= (1+r) pl (1 - pl),
which reflects the probability and magnitude of default, the fact that that default comes one period in the future, and a gross-up factor that reflects the probability and magnitude of default. 

As either the probability of default or the loss rate go to zero,

  • the ratio of wealth relatives goes to one
  • the credit-risk coupon approaches the riskless rate
  • the credit spread approaches zero,

all of which are believable features of the model. 

We can easily extend this model in several directions: 

  • allowing multiple periods and coupon tenors of less than one year
  • deducing the probability of default from the credit-risky coupon

and we may do that in the coming months. 

Of course, the model has its limitations. For example, the binomial probability distribution for loss rate is simplistic. Unfortunately, relaxing the binomial assumption is difficult. Amazingly, the extensions of the basic model seem to be state of the art for practical, reduced form models. 


Links Links related to credit derivatives are below. Links related to other financial topics are here.

  Brady Bonds




  Risk Management



Derivatives DictionaryTM  

Terms and definitions relating to credit derivatives are below. The main Derivatives DictionaryTM is here

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.
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).
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. 
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.
Real Estate Mortgage Investment Conduit (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 ³ 0 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. 
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. 
Russian government Treasury bills.
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
1. The circular LC is a lot like a traveler's check that you can use only to get cash at a specific bank. You give your bank X lira (say) and it issues an LC for X lira. If you deliver the letter to a specified foreign bank, it gives you X lira 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 lira (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.
A revocable (An irrevocable ) LC is one that either (neither) the issuing bank or (nor) Importer can revoke.
The negotiating bank will honor a confirmed LC, 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 LC 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.
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.
Russian government Treasury bonds.
Long term, hard currency bonds that the Russian Ministry of Finance issued. Known as "Taiga" bonds or "MinFins".
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.  
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, private email correspondence, 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.



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 don’t 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

  • All the FRNs in this discussion have a par value of 100 and pay coupons that are LIBOR plus a spread, L + SFRN. The default-free FRNs have a market value of 100 at each reset date. 

  • All the FxRNs in this discussion have a par value of 100 and pay fixed coupons, CFxRN

  • The interest rate swaps have notional mount of 100. They’re all on-the-run, hence have initially a market value of zero. 

  • The “AAAA” rating is not something you’ll see in literature from Moody’s or Standard & Poor’s. However, the market recognizes that some names are better than others, and some are much better than the rest of the best. These are the “AAAA” names that have credit quality similar to Treasuries.


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, let’s consider only the first five simple positions, not the replicating portfolio positions in rows (6) –(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 instrument’s initial cost. 

The “Periodic CF” is a fixed or floating coupon, except for the IRS – there, it’s 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” FRN’s 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 FRN’s terminal value is not 100 because of default risk. The risky FxRN’s 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

  • Buy a “AAAA”-rated FRN and short the credit-risky FRN with the same maturity. 
  • The “recovery” payoff at the common maturity equals the excess of the terminal value of the “AAAA” note over that of the credit-risky FRN. Presumably, the “AAAA” note will be at par. 
  • The up-front cost is the excess of the AAAA note cost over the cost of the FRN. 
  • The periodic cost of the protection is the excess of the credit-risky FRN’s spread over LIBOR over the AAAA FRN’s spread over LIBOR.


  • The AAAA note is not completely default-free. Thus, the “arbitrage” is not perfect. 

Model 2

Replicating Portfolio

  • Buy a US Treasury note that matures when the underlying, credit-risky FRN matures. 
  • Pay fixed on an IRS to create a synthetic AAAA FRN. 
  • Short the underlying, credit-risky FRN. 
  • The up-front cost is the excess of the Treasury note cost over the cost of the FRN. 
  • The periodic cost of the protection is the excess of the coupon on the IRS over the excess of the Treasury coupon over the spead over LIBOR of the credit-risky FRN.


  • The IRS has a positive probability of default.
  • The swap spread may change, creating basis risk.
  • This assumes that the difference in coupons is due to probability of default. In fact, it may by due at least partially to differences in taxation or li


  • Buy a Treasury that matures at the underlying note’s maturity.
  • Short the underlying, credit-risky note. 
  • The promised cash flow at maturity is the dollar loss on the underlying note. 
  • The up-front cost equals the excess of the Treasury note cost over the FxRN cost.
  • The periodic cash flow through maturity is the excess of the credit-risky fixed coupon over the Treasury coupon.


  • This assumes that the only possible default is at the underlying note’s maturity. If default comes earlier, then the Treasury may not trade for par, and the “replicating portfolio” may not replicate the CDS, creating a “basis risk”. 
  • This assumes that the difference in coupon is due to probability of default. In fact, it may by due at least partially to differences in taxation or liquidity.

Model 4

Replicating Portfolio

  • Buy a “AAAA” corporate FRN that matures at the underlying note’s maturity. 
  • Swap the floating coupon to fixed by receiving fixed in a vanilla IRS. 
  • Short the underlying, credit-risky FxRN
  • The promised cash flow at maturity is the dollar loss on the underlying note. 
  • The up-front cost is the excess of the AAAA note cost over the cost of the FxRN. 
  • The periodic cost through maturity is the excess of the credit-risky coupon over the sum of the par swap coupon and the “AAAA” spread over LIBOR. 


  • The swap spread may change, creating basis risk. 
  • If default occurs before maturity, then the Treasury may not trade at par, and the “replicating portfolio” may not replicate the CDS, creating a “basis risk”. 
  • This assumes that the FRN price reverts to par at each coupon reset date. The contractual spread over or under LIBOR may not always be current, and the FRN price may drift away from par. Thus, we’ll have a small version of the main problem with Model 1. 



Dimitras N. Chorafas. Credit Derivatives and the Management of Risk. / Hardcover / Published September 1999
"I just learned about this one and have only glanced at it. It is not overly technical and includes several relevant anecdotes about the unpleasantness of September 1998, including at least two about LTCM.  – Dr. Risk"



Question: Dear Dr. Risk – I'm looking for a credit derivatives primer for a headhunter friend who knows nothing about derivatives. Tough order 'cause all the information is a.) expensive, and b.) overkill for what he needs (he doesn't need to understand derivs maths, for example). Any suggestions? Of course something short, sweet, and free is preferable. – Jolene

Answer: Dear Jolene – I've got some good news and some bad news. First, the bad news: There is no such thing as a free lunch, and there is no such thing as free information.

Now, the good news. You picked a good time to ask Dr. Risk about credit derivatives. I've got three main suggestions for your friend. Although none of them is free, the first choice doesn't cost significant money out of pocket. Your friend can choose the optimal amount of time and money to spend to produce knowledge about credit derivatives.

1. If he goes to the library and looks at some back issues of either Derivatives Strategy or Risk, going back the last year or two, he will find extensive coverage of credit derivatives for free.

2. He might consider going to to buy books, such as

Credit Derivatives: A Guide to Instruments and Applications (Wiley Series in Financial Engineering)
Janet M. Tavakoli / Hardcover / Published 1998
Amazon Price: $48.96 ~ You Save: $20.99 (30%) ~ Usually ships in 24 hours
"I bought it from It was interesting, informative, and worth the price. More readable than Das.  – Dr. Risk"
Buy the Book Today!


cover Credit Derivatives: Trading & Management of Credit & Default Risk (Wiley Frontiers in Finance)
Satyajit Das (Editor) / Hardcover / Published 1998
Amazon Price: $79.95 ~ Usually ships in 24 hours
"I bought it from It was more technical than Tavakoli, and worth the price. – Dr. Risk"
Buy the Book Today!


cover Documentation For Derivatives: Credit Support Supplement
A Gooch, L Klein / Paperback / Published 1995
Amazon Price: $135.00 (Special Order)
Buy the Book Today!


Frontiers in Fixed Income Management: The State-Of-The-Art in Credit Risk, Derivatives Valuation and Portfolio Strategies
Ho, Thomas S. Gat Fixed-Income Conference 1994, Amelia Island, FL / Hardcover / Published 1995
Amazon Price: $65.00
Buy the Book Today!



"More readable than Das, but doesn't quite have Tavokoli's voice of experience." – Dr. Risk


"Much, excellent material: institutional stuff, equations, ... Excellent!" – Dr. Risk


"An interesting survey with broad coverage and no equations that I saw". – Dr. Risk"


3. For somewhat more money, this fall, he can attend my seminar on the subject in New York, Geneva, or London,. Details appear in The Derivatives 'Zine on the "Derivatives Calendar". While I don't anticipate seeing your friend, thanks for giving me a reason to mention my coming appearances.
Dr. Risk



The following are exercises supplementary exercises for students who were in Dr. Risk's two-day course on "Credit Derivatives for Credit Risk Management". If you were registered in the course and want a copy of the solutions and other materials as I prepare them, please send Dr. Risk a message that contains your name (as registered) and "Please send credit derivatives materials" or other specific request. If you don't mind, Dr. Risk will put you on his credit derivatives mailing list and send you other materials as they become available.

The Perpetual Zero Coupon Bond

A favorite question that Bankers Trust employees posed to job candidates in the late 1980s or early 1990s was the following: You have to make a market in a company's perpetual zero coupon bonds. What should they be worth? Or, if you can't figure out the exact price, how would you go about pricing them?

(Partial) Solution: Galen Lee of Columbia University offers this partial solution: "Hey, has anyone solved that zero coupon perpetual bond puzzle yet? I have thought about it and my answer goes along something like: the bond will only pay off when the company goes into default, so we'll price it by replicating its payoff from some sort of credit default swap or credit insurance, with adjustments for any liquidation values in the company's assets (its not enough that the company goes bust, it must have enough assets to pay off its bondholders first). Is that an approach you would take?"

So far, so good. Now make some reasonable – or at least industry standard – assumptions and flesh out the solution.
Dr. Risk

Muni Bond Yields

George Strickland, assistant portfolio manager for Thornburg Bond Funds of Sante Fe, NM, said that muni bond market conditions in early September, 1998, meant that an investor could, essentially, get the muni bond tax exemption for free, and "I have never seen this relationship so cheap." For example, on 9/10/98, Michigan State Hospital Finance Authority issued new, 30-year bonds, price to yield 5.40% – 104% of the long bond yield of 5.17%. Moody's Investors Service Inc. rated the bonds as A3 and S&P rated them as A-. According to Delphis Hanover Corp., which tracks bond yields, on 9/11/98 the Treasury long bond yield was 5.23% and AAA, 30-year municipal bond yields were 96.6% of that, rather than 85%, the average over the previous 10 years. (Dena Aubin, "Muni Bonds' Yields Appear Attractive, But Recent Buying Is Up Only Slightly," Wall Street Journal, 9/14/98.)

What do you think about this apparent "buy signal"?

Pricing Credit Default Swaps

What is the standard way that traders price credit default swaps? Is it a "structural" model, a "reduced form" model, or something else?



Playing Safe with Credit Derivatives (4/28/00)

Q: How is a credit swap is like a condom?

A: Three ways: 

  • You don’t need them if there’s no chance you’ll get screwed.
  • Professionals tend to use them. Bank-to-bank credit swaps are far more common than credit swaps involving retail customers. The main reason’s probably the ridiculous BIS capital charges.
  • Good quality is important. If it breaks, you might end up with a bad condition. In the worst case, product failure can kill you.



William Margrabe's Presentations on Credit Risk and Credit Derivatives

If you're interested in having a one- or two-day presentation on credit risk, credit derivatives, or managing credit risk with credit derivatives at your institution, please contact Dr. Risk.

COURSE OUTLINE for "Managing Credit Risk with Credit Derivatives."

Day One – Credit Risk Measurement and Management
Morning Session – Overview
What is Credit Risk?
Why is Credit Risk Important?
How can we measure Credit Risk?
How can we manage Credit Risk?
Afternoon Session – Models
Modeling credit exposure
RiskMetrics Group’s CreditMetricsTM
CSFP’s CreditRisk+
KMV’s expected default frequency
Tom Wilson's (McKinsey) maco approach to probability of default

Day Two – Credit Derivatives
Morning Session – Overview
What are the main Credit Derivatives structures?
Total return swaps, credit default swaps, and structured notes
Credit spread derivatives
First-to-fail, tranched, and other basket derivatives
Exotic credit derivatives
How do Credit Derivatives work?
How can we can apply Credit Derivatives?
Afternoon Session – Models
Arbitrage pricing of credit derivatives
Correlation of credit risks
Deriving risk neutral probability of default from riskless and risky term structures
The "structural" or "contingent claim" approach to pricing credit derivatives
The Black-Scholes-Merton model
The "reduced form approach" to pricing credit derivatives
The Jarrow-Turnbull (1995) model

Other Coming Conferences and Presentations



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