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Author Giesecke, Kay ♦ Tomecek, Pascal
Source CiteSeerX
Content type Text
File Format PDF
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Time Change ♦ General Point Process ♦ Timechanged Hawkes Process ♦ Continuous Path ♦ Generates Sub-models ♦ Jp Morgan ♦ Time-changed Poisson Process ♦ Random Environment ♦ Multi-name Credit Modeling ♦ Point Process ♦ Dependent Event ♦ Individual Firm ♦ Self-affecting Point Process ♦ Economic Environment ♦ Special Case ♦ Global Derivative Research Group ♦ Classical Family ♦ Observable Information ♦ Standard Poisson Process ♦ Tractable Way ♦ Stochastic Process ♦ Economy-wide Default Process ♦ Time-change Technique ♦ Classical Hawkes ♦ Inaccessible Arrival
Description 2005, Working Paper, Cornell University. - Project 2 Modeling and Predicting the Volatility
Meyer (1971) showed that any point process whose compensator has continuous paths that increase to ∞ can be time-scaled to a standard Poisson process. In this article we consider the converse to this result. We construct a time change with continuous paths increasing to ∞ that transforms a standard Poisson process into a general point process with totally inaccessible arrivals and compensator given by the time change. The time change generates path-dependent or self-affecting point processes whose dynamics depend on the information generated by the arrivals of the process as well as other observable information describing the state of the random environment. The classical Hawkes and doubly stochastic processes are special cases. Timechanged Hawkes processes are shown to combine the best features of these classical families is a flexible and tractable way. We conclude by introducing time-change techniques to multi-name credit modeling. We describe the economy-wide default process as a time-changed Poisson process, whose arrivals are temporally clustered due to contagion and depend on the economic environment. Random thinning generates sub-models for individual firms and portfolios of firms. ∗ This research is supported by grants from the Global Derivatives Research Group at JP Morgan
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study
Learning Resource Type Article