A Top-Down Approach to Multi-Name Credit

A multi-name credit derivative is a security that is tied to an underlying portfolio of corporate bonds and has payoffs that depend on the loss due to default in the portfolio. The value of a multi-name 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 computationally tractable derivatives valuation problems. However, these models are silent about the portfolio constituent risks. They cannot be used to address applications that are based on the relationship between portfolio and component risks, for example constituent risk hedging. This paper develops a method that extends the reach of these models to the constituents. We use random thinning to decompose the portfolio intensity into the sum of the constituent intensities. We show that a thinning process, which allocates the portfolio intensity to constituents, uniquely exists and 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 develop a semi-analytical transform approach to evaluate it. The formula leads to a calibration scheme for the thinning processes, and an estimation scheme for constituent hedge sensitivities. Our empirical analysis for September 2008 shows that the constituent hedges generated by our method outperform the hedges prescribed by the Gaussian copula model, which is widely used in practice