Factor Copula Method Based On Stable Distribution And Its Application To CDO Pricing

The Gauss factor copula model is the standard model in financial industry for CDO pricing and risk measurement. However, because of the heavy tail feature of financial data, this model can not match all market quotes of the standard CDO tranches, and there exists implied correlation smile and other phenomena which are not consistent with the model assumptions. This paper introduces the stable distribution, which is characterized of heavy tail, to describe the financial risk factor, studies the decomposition theory of stable distribution variables, builds the factor copula method based on stable distribution, and applies it to CDO pricing for both homogeneous and non-homogeneous asset portfolios. Meanwhile, the stable distribution is a four-parameter distribution and there is no explicit density function, which brings the model great computational task and complexity. This paper studies and designs high efficient algorithms for reducing the model’s complexity and increasing its applicability. Then this paper conducts further theoretical research on the stable factor copula model, and it is shown that this model has more advantages over the current models in pricing and risk measurement. Finally, this paper performs empirical studies based on the model for the CDO market, and the results again show that this new model has better fitting effect and behaves better than the current models, which is in line with the theoretical conclusions.