Journal article
Pricing Perpetual Options for Jump Processes
North American actuarial journal, Vol.2(3), pp.101-107
07/01/1998
DOI: 10.1080/10920277.1998.10595736
Abstract
We consider two models in which the logarithm of the price of an asset is a shifted compound Poisson process. Explicit results are obtained for prices and optimal exercise strategies of certain perpetual American options on the asset, in particular for the perpetual put option. In the first model in which the jumps of the asset price are upwards, the results are obtained by the martingale approach and the smooth junction condition. In the second model in which the jumps are downwards, we show that the value of the strategy corresponding to a constant option-exercise boundary satisfies a certain renewal equation. Then the optimal exercise strategy is obtained from the continuous junction condition. Furthermore, the same model can be used to price certain reset options. Finally, we show how the classical model of geometric Brownian motion can be obtained as a limit and also how it can be integrated in the two models.
Details
- Title: Subtitle
- Pricing Perpetual Options for Jump Processes
- Creators
- Hans U. Gerber - University of LausanneElias S.W. Shiu - University of Iowa
- Resource Type
- Journal article
- Publication Details
- North American actuarial journal, Vol.2(3), pp.101-107
- Publisher
- Taylor & Francis Group
- DOI
- 10.1080/10920277.1998.10595736
- ISSN
- 1092-0277
- eISSN
- 2325-0453
- Language
- English
- Date published
- 07/01/1998
- Academic Unit
- Statistics and Actuarial Science
- Record Identifier
- 9984257742702771
Metrics
84 Record Views