Transform Analysis for Point Processes and Applications in Credit Risk
24 Pages Posted: 19 Oct 2007 Last revised: 22 Jun 2016
Date Written: April 8, 2011
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
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