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Publicly Available Published by De Gruyter (A) September 25, 2009

Comparison results for path-dependent options

  • Jan Bergenthum and Ludger Rüschendorf
From the journal Statistics & Decisions

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.


* Correspondence address: University of Freiburg, Department of Mathematics, Eckerstraße 1, 79104 Freiburg, Deutschland,

Published Online: 2009-09-25
Published in Print: 2008-03

© by Oldenbourg Wissenschaftsverlag, Freiburg, Germany

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