22-Credit Risk Model Derivs Page 711 Wednesday, February 4, 2004 1:12 PM
Credit Risk Modeling and Credit Default Swaps 711Several models have been suggested for pricing single-name credit
default swaps.^36 These products (before we take into account the valua-
tion of counterparty risk) are generally regarded as the “cash product”
that can be directly evaluated off the default probability curves. No
parametric modeling is necessary. This is just like the coupon bond val-
uation which is model free because the zero-coupon bond yield curve is
all that is needed to price coupon bonds.General Framework
To value credit derivatives it is necessary to be able to model credit risk.
The two most commonly used approaches to model credit risk are struc-
tural models and reduced form models. The latter do not look inside the
firm. Instead, they model directly the likelihood of a default occurring.
Not only is the current probability of default modeled, some researchers
attempt to model a “forward curve” of default probabilities which can
be used to price instruments of varying maturities. Modeling a probabil-
ity has the effect of making default a surprise—the default event is a
random event which can suddenly occur at any time. All we know is its
probability of occurrence.
Reduced form models are easy to calibrate to bond prices observed
in the marketplace. Structural-based models are used more for default
prediction and credit risk management.^37
Both structural and reduced form models use risk-neutral pricing to
be able to calibrate to the market. In practice, we need to determine the
risk-neutral probabilities in order to reprice the market and price other
instruments not currently priced. In doing so, we do not need to know
or even care about the real-world default probabilities.(^36) See, for example, John Hull and Alan White, “Valuing Credit Default Swaps I,”
working paper, University of Toronto (April 2000) and “Valuing Credit Default
Swaps II: Counterparty Default Risk,” working paper, University of Toronto (April
2000); and Dominic O’Kane, “Credit Derivatives Explained: Markets Products and
Regulations,” Lehman Brothers, Structured Credit Research (March 2001) and “In-
troduction to Default Swaps,” Lehman Brothers, Structured Credit Research (Janu-
ary 2000).
(^37) Increasingly, investors are seeking consistency between the markets that use differ-
ent modeling approaches, as the interests in seeking arbitrage opportunities across
various markets grows. Ren-Raw Chen has demonstrated that all the reduced form
models described above can be regarded in a non-parametric framework. This non-
parametric format makes the comparison of various models possible. Furthermore,
as Chen contends, the non-parametric framework focuses the difference of various
models on recovery. See Ren-Raw Chen, “Credit Risk Modeling: A General Frame-
work,” working paper, Rutgers University, 2003.