Abstract
Pricing complex financial derivatives such as collateralized debt obligations (CDO) is considered as the main reason triggering the 2008 financial crisis. The correlation structure related to the credit risks involved in a portfolio for pricing issues have been tried to overcome via a Gaussian copula framework first introduced by David Li (2000). This approach regards the correlation among the credit risks as normally distributed (tied with a Gaussian copula framework), enabling us to derive analytical solutions. However, despite its simplicity, this approach is far from reality, which caused mispricing of the tranches of CDOs. This phenomenon is called the correlation smile. This paper takes the correlation smile issue by considering a Levy copula framework. When this is introduced to pricing equations, one can see that the correlation smile is “corrected”. Thus, a more accurate model of pricing the above-mentioned tranches is introduced.
Highlights
Credit derivatives market drew quite a lot of attention beginning from 1998 and experienced a vast growth until the financial market crises in 2008
The correlation structure related to the credit risks involved in a portfolio for pricing issues have been tried to overcome via a Gaussian copula framework first introduced by David Li (2000)
A collateralized debt obligation (CDO) is another extensively used credit derivative which is usually regarded as the main instrument triggering the 2008 world financial crisis
Summary
Credit derivatives market drew quite a lot of attention beginning from 1998 and experienced a vast growth until the financial market crises in 2008. In addition to all these, there was another quite important issue which was not taken seriously by the investment banks due to possible computation complexities The pricing of these CDOs is not obvious in the sense that the expected time of defaults of the loan payers has to be taken into account. It was the first attempt introduced by David Li (2000) that the correlation structure can be represented by a single common factor “a” yielding a single factor Gaussian copula framework enabling the practitioners to compute the price of these complex financial derivatives. This computation technique inherited a major drawback which came to surface at the financial crisis.
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