ÖCredit Derivatives from 1998
Our Credit Derivatives Pages: Current 1999 1998
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How do practitioners measure credit exposure (9/28/98)
Dear Dr Risk – How do practioners determine the amount of the exposure offset created by a long default swap, where the maturity of the default swap is less than the reference/underlying asset? I now for regulatory capital purposes there are policies set forth (eg: FSA in UK) which outline the conditions but was interested to know want how bank's actually record the offset? – Piet
Dear Piet – First, let's agree on terms. In my experience, a default swap matures when the underlying/reference note/bond matures. (Please see the definitions, below.) Maybe you're talking about a total return swap (TRS), which may mature before the reference instrument matures.
Different institutions measure credit exposure differently, but a typical way to incorporate a short-dated total return swap on a long-dated note or bond into computation of credit exposure is to add it to the portfolio of deals with the relevant counterparty or credit name. Then, run the credit VaR model, or other model, and see the change in exposure. This model typical computes a probability distribution of values for the relevant portfolio, out one, two, ... years, based on the assumption that the portfolio remains static the entire time. The credit exposure for each year is a fractile of that distribution, typically the 95th. Out to the TRS maturity the gain on the TRS will tend to offset a credit loss on the reference instrument, but at later dates the underlying risk will still exist, while the TRS is gone. The overall credit exposure is a function of the annual credit exposures. – Dr. Risk
Market skepticism about agency credit quality? (11/28/98)
Question: My question has to do with the widening of the spread between 10 year treasuries and mortgage rates. For as long as I can remember it has been 80/120 bases points over the 10 yr. T/B for a 30 year mortgage. A recent article in the NY Times said the spread has widened to over 200 B/P. If using either Fannie or Freddie as the issuer of the MBS with the implied guarantee of the US government how has the market assigned what appears to be a very high risk factor to this type of investment. [Today is 10/22/98.] I notice that the last question up-date was 9/28/98 so if you e-mail back a answer it would be appreciated. – Paul
Answer: I won't address your facts. I'll assume they are correct and try to explain how that could be consistent with rationality in the market. It's not clear that credit risk is the issue. I'll agree that Fannies and Freddies have little of that, although they don't have federal government guarantees, as far as I know, except for Fannie's limited "backstop authority".
The main issue here is the value of the borrower's prepayment option inherent in each loan that Fannie or Freddie buys. The more valuable that option, the more the borrower will pay for it. The borrower pays more by paying a larger coupon for a loan priced at par. The larger coupon leads to a larger yield to maturity and spread over the ten-year Treasury. Apparently, right now, that option is extremely valuable, which I don't find particularly amazing in this relatively uncertain world. See what has happened to volatilities in the Treasury bond market. I haven't looked, but would guess that they have risen.
Maybe the following illustration will be useful. If you buy
the ten-year, noncallable Treasury, trading at par, then your
coupon and yield to maturity will be a specific number, say 5%
for ten years. (I'm making this up. I don't know the real number
and don't really care. If you don't like 5%, use another number
and make the appropriate changes, elsewhere.) If you had bought
the ten-year, callable Treasury, trading at par, and its coupon
were also five percent, then three things could happen:
(a) rates could rise and you would take an immediate capital
loss, then receive your five percent, until maturity
(b) rates could remain the same and you'd collect your coupon to
maturity with no regrets
(c) rates could fall and the Treasury would exercise its call
option and take your notes back, forcing you to reinvest at a
lower coupon.
For the Treasury, it's a "heads, I win, and tails, the
lender loses" situation. The ten-year, noncallable Treasury
with a coupon of 5% would be a poor investment for you, but a
great funding coup for the the Treasury. The Treasury would be
happy to pay a higher coupon, in exchange for that call option,
and you'd be a fool not to demand it.
Similarly, the 30-year mortgage contains an embedded prepayment (American call) option. The lender demands a high coupon to pay for selling that option, and the borrower is willing to pay for the option that way. When the mortgage spread over the 10-year Treasury rises, it could be because of declining credit quality or because of increased time value for the embedded call option. – Dr. Risk
Vulnerable options (9/28/98)
Question #1: Dear Dr. Risk – What is a "vulnerable option" ? Enquiring minds want to know. – Alyce
Question #2: Dear Dr. Risk – I have found a definition of a "vulnerable option in a paper:
- Emilio Barone, Giovanni Barone-Adesi, and Antonio Castagna, "Pricing bonds and bond options with default risk," European Financial Management (Vol 4, No 2, 1998, pp.231-282).
It appears this term is used to mean options written by a defaultable party on either risk-free or defaultable options. I guess "vulnerable" makes sense in this case, because there is credit risk not associated with the credit risk of the underlying asset. – Alyce
Answers to #1 and #2: Dear Alyce – Thanks for asking your question of general interest about "vulnerable option" and supplying me with an authoritative answer to your own question. That's the kind of self-starting participation we could use more of around here. Professor Barone was kind enough to send me a copy of the paper, which I recommend highly. The introduction contained a highly readable review of the literature and a highly technical discussion of many of the important issues.
The topic of "vulnerable derivatives" is extraordinarily important. Strictly speaking, all derivatives are "vulnerable", because you can never be sure that your counterparty will pay you what he owes. The degree of "vulnerability" depends on the collateral backing up the counterparty's obligation to pay. This collateral can be of a general nature, including all the assets that creditors could go after in bankruptcy. The collateral can be more specific, such as all the contracts included in a bilateral netting agreement, the collateral backing a clearing house's guarantee of futures or futures options contracts, or the collateral for a specific deal.
As a practical matter, most derivatives are vulnerable. Today, even though specific collateral backs many swaps, it does not back all, and default is a constant threat of unknown dimensions for such deals. Standard pricing models don't begin to deal with this issue adequately. As Barone et al. write, more recent researchers have approached defaultable claims in two main ways: (1) the "structural", "firm value" approach, and (2) the "reduced-form", "hazard rate" approach.
The structural approach appears to me to convert a derivative product with an n-dimentional promised payoff into a derivative with an actual (n+m)-dimensional payoff, m³ 0. For example, a zero coupon bond is a promise to pay that may appear to have zero dimensions of risk, but actually has one, as Black-Scholes (1973) clearly explained. Implementing this approach can be difficult, because the number of risk factors can be large and sorting out the actual payoff function can be difficult, as when one needs to know the entire capital structure of a firm, in order to figure out the payoffs for senior and junior, subordinated debt. The approach may no be precise, if political or other complex considerations, in addition to the issues of positive net worth, influence the default decision.
The reduced form approach makes all the necessary assumptions to bypass the obvious complications of the structural approach. This might involve modeling default as a Poisson process, and the recovery rate as either given, time dependent, or stochastic.Advocates of this approach like the way it finesses the tough issues of the structural approach. However, one faces the problem of making sure that the assumptions are not arbitrary and misleading.
For a better theoretical understanding of the relevant issues and ways to deal with them, see the article by Barone, Barone-Adesi, and Castagna. I found an additional, textbook discussion of pricing and hedging vulnerable derivatives in Jarrow, Robert, and Turnbull, Stuart, Derivative Securities, Cincinnatti, South-Western, 1996, pp. 574 et seq.
For what it's worth, I prefer the adjective "defaultable" to "vulnerable", because it is more specific. I lean toward the structural approach, because the reduced form approach seems too subjective. Also, thanks to Markus Klaesner and Ingo Schneider for valuable counsel about vulnerable options – some of which goes beyond what I have mentioned here.
– Dr. Risk
Credit risk (7/28/98; revised 11/28/98)
Question: Dear Dr. Risk – I research a litterature survey of the credit risk: How is credit risk measured? – Stephane
Answer: Dear Stephane – The short
answer is, very badly.
1. The classic approach is that of "fractional
exposure", which is a forecast of potential market value of
a position – if positive. In its primitive form, this
doesn't encompass correlation among credit risks.
2. The state of the art model seems to be along the lines of VaR,
but with more mathematics, combining diffusion and Markov
matrices. JP Morgan's CreditMetrics takes this approach.
Currently, their model assumes that the forward curve is
constant, to isolate credit deterioration from market risk.
However, most credit deterioration comes from unfavorable market
moves.
3. An actuarial approach, which starts by modeling default as a
Poisson process, has its fans. CSFP's CreditRisk+ takes this
tack. I suggest that they rethink their model of correlation
among defaults.
4. Default rates rise (fall) during a recession (boom). In
principal, one might forecast the business cycle to gain insight
into default rates. Tom Wilson of McKinsey is pursuing this idea.
Unfortunately, decades of research have taught us only that the
stock market predicts the business cycle as well as everything
else combined, so I think that Wilson's explorations will lead to
dry holes.
5. Default is ordinarily a rational decision, where equity
holders decide not to exercise the option to keep a firm alive.
KMV has built an empire on this idea. The problem is quantifying
the underlying asset's value and volatility, as well as the
appropriate "strike" price.
Just about everything I've seen is highly suspect – not
the mathematical reasoning, only the assumptions from which it
derives. The problem is that much of the data you need to
calibrate the models is not observable. I hope to write more on
the topic later this summer or early in the fall, and I'll be
offering courses on managing credit risk
with credit derivatives in New York, Geneva, and London.
Meanwhile, look at the books on credit risk, mentioned above.
– Dr. Risk
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