THE
WILLIAM MARGRABE GROUP, INC., CONSULTING, PRESENTS 
 Credit Derivatives Last revised: March 02, 2002New, this month:
On this page:Ask Dr. Risk!^{TM}  Books  Essays  Humor  Links  Mathematical Appendix  Presentations  Puzzles  Derivatives Dictionary^{TM} Archived Credit Derivatives Pages: 1999 1998Ask 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
Shrikant– Since 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. 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
James – Sorry, 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. Dear Dr. Risk – As it turns out, my
presentation is merely to other people in our small group of Dear
James – How 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 www.derivativesstrategy.com
(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 longterm contract or
lease. Sorry that Dr. Risk can’t point you to a specific source. 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 Edu – Dr. 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! 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 David – When 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. Dear Amberish – Your project sounds complex. You can find links to much free information about credit derivatives at http://www.margrabe.com/CreditDerivatives.html#Links. You're the best judge of what suits your needs. Before explaining the phenomenon, let's clearly identify it. The coupon on creditrisky debt will ordinarily exceed the defaultfree 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 defaultfree 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 creditrisky, 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?) 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.
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 CDROM. Search for ABI/INFORM on the Internet and you may be able to access it online. Also, look at http://www.lexisnexis.com. 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, LexisNexis, 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 www.margrabe.com/CreditDerivatives.html#Links, 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 email, 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 email 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 defaultfree bond over the payoff of a creditrisky 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 19971998. 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. Risk – i
have 4 questions: Dear Michael – i) Practitioners use a noarbitrage, 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 noarbitrage, 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 DuffieSingleton. 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 mediumsized 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. Correlationdata 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 totalreturnswaps or defaultswaps (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. Risk – I 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 defaultrisk 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 arbitragefree 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 noarbitrage 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 BlackScholesMerton 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 BlackScholes 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 optionmodel? (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. mixedjumpdiffusion, 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 mediumsized. If i understand your answer right, you also think that this "highsophisticated" 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 BlackScholesGeske 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 nonexistent. 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 nonperforming 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 nonperforming 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 nonperforming 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 nonperforming 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, nonperforming 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 nonperforming loan portfolio – which is already in default. A total return swap could have an underlying nonperforming 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 nonperforming loans. Dr. Risk doesn't see any absolute reason for excluding nonperforming 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 lowgrade loans on their books and transfer out credit risk of highergrade loans, because BIS regulations provide that strange incentive. Maybe nonperforming 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 nonperforming 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 (R_{Bt}) and shares (R_{St}) and the (arbitrary) exogenous variables X_{t} and Y_{t }(don't ask what they are) would be: R_{Bt} = a_{1}
+ a_{2 }R_{St} + a_{3} X_{t}
+ u_{1t} where u_{it} 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: R_{Bt} = c_{1}
+ c_{2 }X_{t} + c_{3} Y_{t}
+ v_{1t} 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 MertonGeskeKMV "structural model" of the probability of default uses a pair of simultaneous equations and an identity, such as S = BSM(A,VOL_{A},r,K,T) 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 lefthand side of the equation – as some sort of timeseries process. This allows the modeler to price an issue of creditrisky 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:
– 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:
Then we have the following binomial tree for the bond’s value:
100 (1+c_{1}) 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: Let l
= 1r
denote the loss rate. Rearranging the pricing
equation, we get The creditrisky coupon is As either the probability of default or the loss rate go to zero,
all of which are believable features of the model. We can easily extend this model in several directions:
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
Pricing
Market
Structures
Risk Management
Other
Derivatives Dictionary^{TM }Terms and definitions relating to credit derivatives are below. The main Derivatives Dictionary^{TM} is here.
EssaysPricing 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, creditrisky floatingrate note (FRN). The CDS payoff is “B(T) – P_{FRN}(T) = 100 – P_{FRN}(T)”, where B(T) is the value of a defaultfree FRN and P_{FRN}(T) is the value of the underlying, risky FRN. B(T) = 100% of par, because the model assumes that the defaultfree 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, creditrisky fixedrate note (FxRN) off the price of a replicating portfolio. The wrinkle here is that the payoff function is not “100 – P_{FxRN}(T)”, but “B(T) – P_{FxRN}(T)”, where B is the market value of a defaultfree 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 defaultfree note might deviate significantly from 100. AssumptionsCredit Default Swap (CDS)The CDS pays
off at default the dollar loss on the underlying note: Other assumptions
AnalysisFigure 1 defines the cash flows associated with some relevant positions in the underlying, creditrisky 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):
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 ontherun. 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 creditrisky 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.
Underlying Creditrisky FRNThis is more of a pure credit play. Any problem with interestrate market risk is minimal, because the underlying, creditrisky note is an FRN. Model 1Replicating Portfolio
Caveat
Model 2Replicating Portfolio
Caveats
Caveat
Model 4Replicating Portfolio
Caveat
Books
Dimitras N. Chorafas. Credit
Derivatives and the Management of Risk. / Hardcover / Published September 1999
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 Amazon.com to buy books, such as Credit Derivatives: A Guide to Instruments
and Applications (Wiley Series in Financial Engineering)
Credit Derivatives:
Trading & Management of Credit & Default Risk (Wiley
Frontiers in Finance)
Documentation For
Derivatives: Credit Support Supplement
Frontiers in Fixed Income
Management: The StateOfTheArt in Credit Risk, Derivatives
Valuation and Portfolio Strategies
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. PuzzlesThe following are exercises supplementary exercises for students who were in Dr. Risk's twoday 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 BondA 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?
Muni Bond YieldsGeorge 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, 30year 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, 30year 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 SwapsWhat is the standard way that traders price credit default swaps? Is it a "structural" model, a "reduced form" model, or something else? HumorPlaying Safe with Credit Derivatives (4/28/00)Q: How is a credit swap is like a condom? A: Three ways:
PresentationsWilliam Margrabe's Presentations on Credit Risk and Credit DerivativesIf you're interested in having a one or twoday presentation on credit risk, credit derivatives, or managing credit risk with credit derivatives at your institution, please contact Dr. Risk.
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