On the Optimal Super- and Sub-Hedging Strategies
This paper proposes optimal super-hedging and sub-hedging strategies for a derivative on two underlying assets without any specification of the underlying processes. Moreover, the strategies are free from any model of the dependency between the underlying asset prices. We derive the optimal pricing bounds by finding a joint distribution under which the derivative price is equal to the hedging portfolio's value; the portfolio consists of liquid derivatives on each of the underlying assets. As examples, we obtain new super-hedging and sub-hedging strategies for several exotic options such as quanto options, exchange options, basket options, forward starting options, and knock-out options.
|Date of creation:||Nov 2012|
|Date of revision:||Aug 2013|
|Contact details of provider:|| Postal: Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033|
Web page: http://www.carf.e.u-tokyo.ac.jp/english/
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- Umberto Cherubini & Elisa Luciano, 2002. "Multivariate Option Pricing with Copulas," ICER Working Papers - Applied Mathematics Series 05-2002, ICER - International Centre for Economic Research.
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- David Hobson & Peter Laurence & Tai-Ho Wang, 2005. "Static-arbitrage upper bounds for the prices of basket options," Quantitative Finance, Taylor & Francis Journals, vol. 5(4), pages 329-342.
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- Laurence, Peter & Wang, Tai-Ho, 2009. "Sharp distribution free lower bounds for spread options and the corresponding optimal subreplicating portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 35-47, February.
- Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: theory," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 3-33, August.
- Chen, X. & Deelstra, G. & Dhaene, J. & Vanmaele, M., 2008. "Static super-replicating strategies for a class of exotic options," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1067-1085, June.
- Hobson, David & Laurence, Peter & Wang, Tai-Ho, 2005. "Static-arbitrage optimal subreplicating strategies for basket options," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 553-572, December.
- Jan Baldeaux & Marek Rutkowski, 2010. "Static Replication of Forward-Start Claims and Realized Variance Swaps," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(2), pages 99-131.
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