Comparison results for path-dependent options

Bergenthum Jan and Rüschendorf Ludger
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Bergenthum Jan: Universität Freiburg, Department of Mathematical Stochastics, Freiburg

Statistics & Risk Modeling, 2008, vol. 26, issue 1, 53-72

Abstract: In this paper comparison results of convex type are established for several path-dependent options in some classes of semimartingale models. The options considered are some classes of lookback options, Asian and American options and barrier options. Comparison of the path-dependent options is based on ordering properties of the local characteristics of the underlying processes as well as on suitable propagation of convexity property. These properties allow a stochastic analysis of the basic linking process which establishes a link between the value processes in the underlying models. The linking process gives a unified tool to obtain comparison results for these path-dependent options. This paper extends and unifies several results in the literature.

Keywords: path dependent options; lookback option; convex order; Levy process; semimartingale (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1524/stnd.2008.0912

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