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| A Top-down Approach to Multi-name Credit by Kay Giesecke of Stanford University, and June 6, 2008 Abstract: A multi-name credit derivative is a security tied to an underlying portfolio of corporate bonds or other credit-sensitive securities. It enables investors to buy and sell protection against the default losses in the portfolio. The value of a multiname derivative depends on the distribution of portfolio loss at multiple horizons. Intensity-based models of the loss point process that are specified without reference to the portfolio constituents determine this distribution in terms of few economically meaningful parameters, and lead to tractable credit derivatives valuation relations that can be addressed by a variety of efficient methods. This paper proposes random thinning to extend the reach of these models beyond the portfolio level. Random thinning decomposes the portfolio loss process into the sum of its constituent loss processes, and allocates aggregate portfolio risk to sub-portfolios. We show that any loss process can be thinned, and that the associated thinning process is a probabilistic model for the next-to-default. We derive a formula for the constituent default probability in terms of the thinning process and the portfolio intensity, and show how to evaluate it for a large family of portfolio intensity models. This formula facilitates consistent pricing and calibration of constituent and portfolio credit derivatives, which we demonstrate by fitting a familiar stand-alone model of the portfolio loss to market rates of CDX index, tranche and constituent single-name credit swaps. Keywords: dependent defaults, portfolio loss, credit derivative, point process, compensator, intensity, random thinning. Books Referenced in this Paper: (what is this?)
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