European and American options: The semi-Markov case

D’Amico, Guglielmo, Jacques Janssen and Raimondo Manca

Physica A: Statistical Mechanics and its Applications, 2009, vol. 388, issue 15, 3181-3194

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: Semi-Markov processes; Backward recurrence time; European and American options; Wealth balance equation; Option value; Bare risk (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:388:y:2009:i:15:p:3181-3194

DOI: 10.1016/j.physa.2009.04.016

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