Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
979319 | Physica A: Statistical Mechanics and its Applications | 2009 | 14 Pages |
Abstract
In this paper, we assume that the log return of the underlying asset follows a semi-Markov process, then from the knowledge of the kernel we derive an explicit expression for the value of the option and for the bare risk in the case of the European call (put) option and, by means of a recursive system, we derive the value and the bare risk in the case of the American option. The prices and risks we obtained depend explicitly on the waiting-time distributions of the asset and they are duration dependent. The link with models based on Markov Chains and Continuous Time Random Walks is debated.
Keywords
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Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Guglielmo D’Amico, Jacques Janssen, Raimondo Manca,