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October 2009 Esscher transform and the duality principle for multidimensional semimartingales
Ernst Eberlein, Antonis Papapantoleon, Albert N. Shiryaev
Ann. Appl. Probab. 19(5): 1944-1971 (October 2009). DOI: 10.1214/09-AAP600

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.

Citation

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Ernst Eberlein. Antonis Papapantoleon. Albert N. Shiryaev. "Esscher transform and the duality principle for multidimensional semimartingales." Ann. Appl. Probab. 19 (5) 1944 - 1971, October 2009. https://doi.org/10.1214/09-AAP600

Information

Published: October 2009
First available in Project Euclid: 16 October 2009

zbMATH: 1233.91268
MathSciNet: MR2569813
Digital Object Identifier: 10.1214/09-AAP600

Subjects:
Primary: 60G48 , 91B28

Keywords: duality principle , Esscher transform , multidimensional semimartingales , options on several assets , quanto option , swap option

Rights: Copyright © 2009 Institute of Mathematical Statistics

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Vol.19 • No. 5 • October 2009
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