ESSCHER TRANSFORM AND THE DUALITY PRINCIPLE FOR MULTIDIMENSIONAL SEMIMARTINGALES

• 成果类型: Article
• 署名作者: Eberlein, Ernst; Papapantoleon, Antonis; Shiryaev, Albert N.
• 署名单位: University of Freiburg; Technische Universitat Wien; Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/09-AAP600
• 发表日期: 2009
• 页码: 1944-1971
• 关键词: option; numeraire

摘要

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.