The Annals of Applied Probability

Esscher transform and the duality principle for multidimensional semimartingales

Ernst Eberlein, Antonis Papapantoleon, and Albert N. Shiryaev

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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.

Article information

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

Dates
First available in Project Euclid: 16 October 2009

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1255699549

Digital Object Identifier
doi:10.1214/09-AAP600

Mathematical Reviews number (MathSciNet)
MR2569813

Zentralblatt MATH identifier
1233.91268

Subjects
Primary: 91B28 60G48: Generalizations of martingales

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

Citation

Eberlein, Ernst; Papapantoleon, Antonis; Shiryaev, Albert N. Esscher transform and the duality principle for multidimensional semimartingales. Ann. Appl. Probab. 19 (2009), no. 5, 1944--1971. doi:10.1214/09-AAP600. https://projecteuclid.org/euclid.aoap/1255699549


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