TRANSFORM ANALYSIS FOR POINT PROCESSES AND APPLICATIONS IN CREDIT RISK

Authors


  • This is a significant revision and extension of an earlier paper by the first author entitled “The correlation neutral measure for portfolio credit.” This research was partly supported by a grant from JP Morgan Chase’s Academic Outreach Program, for which we are very grateful. We would like to thank Tom Bielecki, Xiaowei Ding, Darrell Duffie, Steve Evans, Lisa Goldberg, Monique Jeanblanc, Roger Lee, Alexander Shkolnik, Dmitry Smelov, Pascal Tomecek, and Stefan Weber for helpful discussions, comments, and suggestions. We would also like to thank three anonymous referees for their insightful reviews of this paper.

Kay Giesecke, Department of Management Science & Engineering, Stanford University, Stanford, CA 94305, USA; e-mail: giesecke@stanford.edu, web: http://www.stanford.edu/~giesecke.

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.

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