| This paper deals with the impact of structure of dependency and the choice
of procedures for rare-event simulation, on the pricing of multi-name credit
derivatives such as basket credit default swap. A copula-based simulation procedure for
pricing basket credit default swaps, under different structure of dependency, is
presented here. The choice of copula and procedures for rare-event simulation govern the
pricing of the basket credit default swap. Alternatives to the Gaussian copula are the
Clayton copula and t-student copula under importance sampling procedures for
simulation, which capture the dependence structure between the underlying variables at
extreme values and certain values of the input random variables in a simulation, and
have more impact, than others, on the parameter being estimated.
Credit derivatives are bilateral instruments designed to reduce and transfer credit risk from
the buyer to the seller of the instrument without selling the reference entity. They allow
investors and financial institutions to more effectively manage their exposures to credit risks.
The principal products referred as credit derivatives are credit default swap, credit linked
notes, total return swap, and credit spread options. The central product in the credit
derivatives market is the credit default swap. However, in recent years, structured credit
derivatives instruments such as basket default swap and Collateralized Debt Obligation
(CDO), have been growing in importance.
The CDO instruments are considered as a part of the recent financial
crisis. Many studies are devoted to single name credit derivatives. Hull et al. (2004) analyzed the impact of credit rating announcements in the pricing of credit default swap. Norden and Weber
(2004) analyzed the empirical relationship between credit default swap, bond and stock markets.
Ericsson et al. (2004) investigated the relationship between theoretical determinants of default
risk (firm leverage, volatility and the riskless interest rate) and actual market spread of credit default
swap, using linear regression. Abid and Naifar (2006a) explained empirically the determinants of
credit default swap rates using a linear regression. They found that credit rating, maturity,
riskless interest rate, slope of the yield curve, and volatility of equities explain more than 60% of
the total level of credit default swap.
In the recent years, more empirical studies are devoted to structured credit
derivatives instruments such as basket default swap and CDO. The most important problem in the
pricing of these instruments is modeling the structure of dependency of the default times. The
principal characteristic of Kendall's tau is that it remains invariant under monotone transformations.
Li (2000) used a Gaussian copula for modeling joint default times and then, pricing a first
to default swap. Other studies of elliptical copulas with higher tail dependence, such as the t-copula, can be found in Mashal and Naldi (2002). The Marshall-Olkin copula is a class of
copula functions based on the Marshall-Olkin shock model. In this model, individual defaults
are constructed from a series of independent common shocks. Previous studies on the use of
the Marshall-Olkin copula in the context of credit risk modeling include Wong (2000), Duffie
and Pan (2001), and Lindskog and McNeil (2003). Hull and White (2004) developed two
procedures for pricing tranches of CDO and nth to default swap. The first procedure involves
calculating the probability distribution of the number of defaults by time T, suited to the situation where companies have equal weight in the portfolio and recovery rates are assumed to be
constant. The second procedure consists of calculating the probability distribution of the total loss
from defaults by time T. |
