Comparison results for path-dependent options

Abstract

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.