Pricing Models For Credit Derivatives
These days, it's possible to call up five or six dealers and get a price
quote for the credit structure of your choice. But do you need your own
special pricing models to evaluate those prices?
Most major dealers argue that it is possible to evaluate credit derivatives
by simply considering the price of their underlying assets. But dealers
go beyond this when they price deals themselves. "All the major dealers
have their own proprietary models for pricing credit products," admits
one New York credit derivatives dealer. If the dealers can benefit from
this sort of modeling, why can't end-users?
There are several good reasons why a theoretical method of pricing credit
would help anyone in the credit derivatives market. A theoretical model
allows people to evaluate dealer prices, and to ascertain how much of the
price they pay is really extra cash for their dealers. A model could also
be the first step toward running risk management simulations on a portfolio
of credit derivatives; in these simulations, users might stress various
market factors and see how their portfolio performs. Finally, a theoretical
pricing model for common types of credit derivatives would make the pricing
of these products more transparent.
The problem is that there is no industry-standard way to price credit.
So far, only two companies have been working on the problem long enough
to make any headway: San Francisco-based KMV Associates and Tokyo-based
Kamakura. KMV Associates, founded in 1990, offers off-the-shelf software
capable of estimating default probabilities and managing portfolios of default
risk; this software is in production at many large international banks.
Kamakura, meanwhile, is a risk management consulting and software development
firm that is now developing a credit pricing module.
These two companies, however, have quite different philosophies in terms
of the relationship between fluctuating interest rates and default probabilities,
whether or not this relationship can be reliably calculated given the data
now available on secondary credit markets-and, in fact, whether or not credit
can be accurately priced at all given data-related constraints.
Kamakura, which has yet to offer an over-the-counter credit pricing module,
is developing software based largely on the research of Robert Jarrow, the
firm's head of research and a professor at Cornell University's Johnson
Graduate School of Management. Jarrow, in conjunction with professor Stuart
Turnbull of Queens University in Canada, published an early version of the
Jarrow-Turnbull model in 1993 that described a general methodology for pricing
credit and credit-based structures. Later, in 1995, Jarrow and Turnbull
published an extended version of the earlier model, which used historical
data to estimate specific parameters in the model.
According to Jarrow, the Jarrow-Turnbull model incorporates multifactor
interest rate analysis, and attempts to quantify the relationship between
interest rate fluctuations and default probability over time. He emphasizes
that this cross-market relationship is important to capture accurately the
value of a credit-based instrument. For example, rising interest rates are
known to cause problems for highly leveraged companies. Certainly, the way
a credit investment might perform under a different interest rate environment
is valuable information for the potential investor.
"Assuming that interest rates are constant is a heroic assumption,"
says Don Van Deventer, president of Kamakura, who cites an analogy from
the mortgage market. According to a recent study by the Federal Reserve,
much of the seemingly irrational behavior of home borrowers who did not
refinance under favorable interest rate conditions was, in fact, a result
of the asset value of their homes. If the value of the house was less than
the balance of the mortgage, then borrowers would not refinance. According
to Van Deventer, similar principles are at work in the corporate borrowing
market-the asset valuation of the corporation in question and the level
of interest rates are both critical to refinancing decisions. He emphasizes
that both factors must be taken into consideration in order to accurately
value credit derivatives.
However, Stephen Kealhofer, one of KMV's founding directors, says, "At
a conceptual level there may well be an important relationship between interest
rates and default probabilities, but the empirical evidence for it is weak."
Kealhofer explains that KMV uses equity prices as a key input to its model
for estimating default; according to KMV's research, interest rate effects
are to a great extent embedded in these equity prices.
Over the past few years, KMV has attempted to boost the accuracy of its
software by testing methods that include an explicit interest rate factor
in addition to equity prices. However, the results were less than encouraging.
He says, "We have not been able to find much of any consistent relationship
between interest rates and default risk after taking equity prices into
And, adds Kealhofer, the extent of interest rate effects on default probabilities
may be relatively mild. He says, "The corporate capital structure consists
of interest-sensitive assets and liabilities, which in many cases create
a natural hedge against interest rate fluctuations." And, at the asset
level, KMV's research has found that most firms' assets exhibit only a modest
level of interest rate sensitivity. Still, KMV's software does incorporate
a correlation factor that represents the relationship between interest rate
fluctuations and asset value.
What KMV does not endorse, however, is the value of correlations between
interest rates and credit quality based on incomplete data. According to
KMV vice president Mac McQuown, known variables that affect credit spreads
include default probability, interest rate fluctuations and time. Likewise,
there may be other dimensions, such as liquidity, which have yet to be adequately
quantified. "Interpreting motion across three dimensions-default, interest
rates and time-is as much an empirical problem as it is a theoretical one,"
says McQuown. Using Bridge's (formerly EJV) indicated credit spread data-which
is arguably one of the best such data sets in existence today-in research
efforts over the past year, KMV has concluded that even this data is "too
noisy" to allow any firm conclusions on the relationship between credit
migrations and interest rates.
So far, KMV does not offer a credit valuation model. Although the firm
has developed several prototype models intended to predict future corporate
bond prices, none of these models has been deemed "ready for prime
time." Adds McQuown, "This topic is very complex, and its resolution
depends on the availability of better data."
KMV is currently the only firm actually offering stand-alone credit-pricing
software, but other companies are busy developing modules for their systems
as well as trying to build effective credit-valuation models. "Our
methodology is in production at many large financial institutions today,"
notes McQuown. "There are many things that have to happen after a
model is published in academic journals before it can be judged as appropriate
for use in a live trading environment." We'll just have to wait and