Transform Analysis for Point Processes and Applications in Credit Risk

24 Pages Posted: 19 Oct 2007 Last revised: 22 Jun 2016

See all articles by Kay Giesecke

Kay Giesecke

Stanford University - Management Science & Engineering

Shilin Zhu

Stanford University - Department of Statistics

Date Written: April 8, 2011

Abstract

This paper develops a formula for a transform of a vector point process with totally inaccessible arrivals. The transform is expressed in terms of a Laplace transform under an equivalent probability measure of the point process compensator. The Laplace transform of the compensator can be calculated explicitly for a wide range of model specifications, because it is analogous to the value of a simple security. The transform formula extends the computational tractability offered by extant security pricing models to a point process and its applications, which include valuation and risk management problems arising in single-name and portfolio credit risk.

Keywords: Point process, compensator, Laplace transform, measure change, credit derivative, portfolio credit risk

Suggested Citation

Giesecke, Kay and Zhu, Shilin, Transform Analysis for Point Processes and Applications in Credit Risk (April 8, 2011). Available at SSRN: https://ssrn.com/abstract=1021890 or http://dx.doi.org/10.2139/ssrn.1021890

Kay Giesecke (Contact Author)

Stanford University - Management Science & Engineering ( email )

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

Shilin Zhu

Stanford University - Department of Statistics ( email )

Stanford, CA 94305
United States

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