Esscher transform and the duality principle for multidimensional semimartingales

Esscher transform and the duality principle for multidimensional semimartingales

Ernst Eberlein, Antonis Papapantoleon, and Albert N. Shiryaev

Source: Ann. Appl. Probab. Volume 19, Number 5 (2009), 1944-1971.

Abstract

The duality principle in option pricing aims at simplifying valuation problems that depend on several variables by associating them to the corresponding dual option pricing problem. Here, we analyze the duality principle for options that depend on several assets. The asset price processes are driven by general semimartingales, and the dual measures are constructed via an Esscher transformation. As an application, we can relate swap and quanto options to standard call and put options. Explicit calculations for jump models are also provided.

Primary Subjects: 91B28, 60G48

Keywords: Duality principle; options on several assets; multidimensional semimartingales; Esscher transform; swap option; quanto option

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Permanent link to this document: http://projecteuclid.org/euclid.aoap/1255699549
Digital Object Identifier: doi:10.1214/09-AAP600
Mathematical Reviews number (MathSciNet): MR2569813

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