Kay Giesecke, Cornell University
Trends and compensation
Derivatives traders, geologists, and insurance companies
rely on mathematical models to forecast the likelihood of abruptly
occurring events such as corporate bankruptcies, earthquakes and
deaths.
We present a probabilistic framework in which to analyze event
risk. Our setup accounts for the evolution of relevant
information over time as well as the uncertainty surrounding that
information. The need for event risk models that incorporate these
features is highlighted by the recent accounting scandals at
Enron, WorldCom, and Tyco. In each of these cases, management
withheld and misrepresented the facts.
The mathematical underpinnings of the model are submartingales,
which are stochastic processes that have an average upward trend.
We explore the interesting relationship between the analytical
attributes of the trend and the probabilistic nature of events. We
then isolate the trend and use it to estimate event arrival
probabilities and to value securities with event-contingent
payoffs.
Many of the elements of our model are found in the work of
Paul-Andre Meyer, Claude Dellacherie and Marc Yor from the 1970's.