reference entities to investors willing to assume the risk in exchange for the beneﬁts.
Credit derivatives havebeen widely criticised and misunderstood in the wake of the global
ﬁnancial crisis; however, their important role in credit risk hedging and management
should not be overlooked. CDOs and BDSs are the two most important credit risk
management instruments, but they are also the most complicated, since the dependence
structure and joint distribution between the underlying obligations must be determined.
Determining the dependence structure between ﬁnancial assets is an important problem
for both researchers and practitioners. It is useful in multi‐asset derivative pricing, portfolio
selection, and portfolio risk management. Linear correlation has traditionally been used to
model dependence because of its simplicity in calculation and understanding, but it is
satisfactory only within the Gaussian or elliptical frameworks (Embrechts et al., 1999).
Increasingly, copulas have been widely used to model dependence because of their
advantages in characterising nonlinear and tail dependence and constructing multidimen-
sional distribution functions. However, most of the related literature is based on static
copulas, among which static Gaussian copulas are especially common (e.g., Li, 2000).
However, most ﬁnancial datasets cover long periods and economic factors can
therefore induce changes in the dependence structure. There are two ways to consider the
change of dependence structure when employing copulas: One is to consider the change
of copula parameters while the copula family keeps the same and the other one is to
consider the change of copula family. Patton (2006) considered the change of copula
parameters by assuming that the dependence measure is a function of the conditional
volatilities of the underlying ﬁnancial variables. He used this so‐called time‐varying
copula method to model the dependence structure between two exchange rates and
showed through empirical examples that the time‐varying copula model behaves better
than the static one. Wu and Liang (2011) incorporated time‐varying copulas into a range‐
based volatility model to describe the dependence structures and volatility of stock and
bond returns. Guégan and Zhang (2010) considered changes in both the copula family and
the copula parameters. They used tests based on conditional copulas and goodness‐of‐ﬁt
(GOF) to determine the type of change and then applied their approach to compute the risk
measures VaR and ES for a portfolio of Standard & Poor’s 500 and NASDAQ indices;
that is, the authors dealt with two‐dimensional copulas.
The dynamic conditional correlation (DCC) model introduced by Engle (2002) is another
time‐varying model used for correlations and dependence structures. This model is a new
kind of multivariate GARCH model that allows the correlation matrix to vary with time.
Cappiello et al. (2006) subsequently presented the asymmetric generalised DCC model to
study conditional asymmetries in correlation dynamics and applied their model to analyse the
behaviour of international equities and government bonds. The DCC and asymmetric
generalised DCC models are good but are built on the assumption of normality. In contrast,
the dynamic copula model is not restricted by the assumption of marginal distributions.
In this paper we analyse the change of copulas, as Guégan and Zhang (2010) did, but we
deal with six‐dimensional copulas and then apply the dynamic copula method to the
pricing of a six‐dimensional BDS. There are two main approaches to pricing credit
derivatives: the structural approach initiated by Merton (1974) and the reduced‐form
approach proposed by Jarrow and Turnbull (1995). Recent related papers include those of
Brennan et al. (2009) and Bedendo et al. (2011). In pricing multi‐name credit derivatives,
a critical problem is to model the default correlation and copulas have been widely used
for this purpose. A milestone in this ﬁeld is the work of Li (2000), who used a Gaussian
copula to model the default correlation and price multi‐name credit derivatives. This
© 2013 John Wiley & Sons Ltd
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