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Dynamic Factor Copula Model

by Ken Jackson of the University of Toronto,
Alex Kreinin of Algorithmics, Inc., and
Wanhe Zhang of the University of Toronto

March 7, 2010

Abstract: The Gaussian factor copula model is the market standard model for multi-name credit derivatives. Its main drawback is that factor copula models exhibit correlation smiles when calibrating against market tranche quotes. To overcome the calibration deficiency, we introduce a multi-period factor copula model by chaining one-period factor copula models. The correlation coefficients in our model are allowed to be time-dependent, and hence they are allowed to follow certain stochastic processes. Therefore, we can calibrate against market quotes more consistently. Usually, multi-period factor copula models require multi-dimensional integration, typically computed by Monte Carlo simulation, which makes calibration extremely time consuming. In our model, the portfolio loss of a completely homogeneous pool possesses the Markov property, thus we can compute the portfolio loss distribution analytically without multi-dimensional integration. Numerical results demonstrate the efficiency and flexibility of our model to match market quotes.

Keywords: Dynamic correlation, Correlation smile, Factor copula, CDOs.

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