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Stochastic monotonicity and duality of kth order with application to put-call symmetry of powered options
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Kolokoltsov, V. N. (Vasiliĭ Nikitich) (2015) Stochastic monotonicity and duality of kth order with application to put-call symmetry of powered options. Journal of Applied Probability, 52 (1). pp. 82-101. doi:10.1239/jap/1429282608 ISSN 0021-9002.
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Official URL: http://dx.doi.org/10.1239/jap/1429282608
Abstract
We introduce a notion of kth order stochastic monotonicity and duality that allows one to unify the notion used in insurance mathematics (sometimes refereed to as Siegmund's duality) for the study of ruin probability and the duality responsible for the so-called put - call symmetries in option pricing. Our general kth order duality can be financially interpreted as put - call symmetry for powered options. The main objective of the present paper is to develop an effective analytic approach to the analysis of duality leading to the full characterization of kth order duality of Markov processes in terms of their generators, which is new even for the well-studied case of put -call symmetries.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
Journal or Publication Title: | Journal of Applied Probability | ||||
Publisher: | Applied Probability Trust | ||||
ISSN: | 0021-9002 | ||||
Official Date: | March 2015 | ||||
Dates: |
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Volume: | 52 | ||||
Number: | 1 | ||||
Page Range: | pp. 82-101 | ||||
DOI: | 10.1239/jap/1429282608 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published |
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