A Top-Down Approach to Multi-Name Credit

Operations Research, Forthcoming

34 Pages Posted: 15 Mar 2005 Last revised: 15 Jun 2016

See all articles by Kay Giesecke

Kay Giesecke

Stanford University - Department of Management Science & Engineering

Lisa R. Goldberg

University of California, Berkeley; Aperio Group

Xiaowei Ding

Stanford University

Date Written: August 11, 2009

Abstract

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.

Keywords: correlated defaults, point process, random thinning, single-name hedging, top-down model

JEL Classification: C00, C12, C13, C15, C51, C52, C53

Suggested Citation

Giesecke, Kay and Goldberg, Lisa R. and Ding, Xiaowei, A Top-Down Approach to Multi-Name Credit (August 11, 2009). Operations Research, Forthcoming, Available at SSRN: https://ssrn.com/abstract=1142152 or http://dx.doi.org/10.2139/ssrn.1142152

Kay Giesecke (Contact Author)

Stanford University - Department of Management Science & Engineering ( email )

475 Via Ortega
Stanford, CA 94305
United States
(650) 723 9265 (Phone)
(650) 723 1614 (Fax)

HOME PAGE: http://https://giesecke.people.stanford.edu

Lisa R. Goldberg

University of California, Berkeley ( email )

Department of Statistics
367 Evans Hall
Berkeley, CA 94720-3860
United States

Aperio Group ( email )

3 Harbor Drive
Suite 315
Sausalito, CA 94965
United States

Xiaowei Ding

Stanford University ( email )

Stanford, CA 94305
United States

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