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Exit problems for spectrally negative Levy processes and applications to (Canadized) Russian options


Reference:

Avram, F., Kyprianou, A. E. and Pistorius, M. R., 2004. Exit problems for spectrally negative Levy processes and applications to (Canadized) Russian options. Annals of Applied Probability, 14 (1), p. 215.

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Official URL:

http://dx.doi.org/10.1214/aoap/1075828052

Abstract

We consider spectrally negative Lévy process and determine the joint Laplace transform of the exit time and exit position from an interval containing the origin of the process reflected in its supremum. In the literature of fluid models, this stopping time can be identified as the time to buffer-overflow. The Laplace transform is determined in terms of the scale functions that appear in the two-sided exit problem of the given Lévy process. The obtained results together with existing results on two sided exit problems are applied to solving optimal stopping problems associated with the pricing of Russian options and their Canadized versions.

Details

Item Type Articles
CreatorsAvram, F., Kyprianou, A. E. and Pistorius, M. R.
DOI10.1214/aoap/1075828052
DepartmentsFaculty of Science > Mathematical Sciences
RefereedYes
StatusPublished
ID Code7275

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