# Pricing derivatives of American and game type in incomplete markets

## Author Info

• Jan Kallsen

()

• Christoph Kühn

()

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## Abstract

In this paper the neutral valuation approach is applied to American and game options in incomplete markets. Neutral prices occur if investors are utility maximizers and if derivative supply and demand are balanced. Game contingent claims are derivative contracts that can be terminated by both counterparties at any time before expiration. They generalize American options where this right is limited to the buyer of the claim. It turns out that as in the complete case, the price process of American and game contingent claims corresponds to a Snell envelope or to the value of a Dynkin game, respectively. On the technical level, an important role is played by $\sigma$ -sub- and $\sigma$ -supermartingales. We characterize these processes in terms of semimartingale characteristics. Copyright Springer-Verlag Berlin/Heidelberg 2004

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File URL: http://hdl.handle.net/10.1007/s00780-003-0110-7

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## Bibliographic Info

Article provided by Springer in its journal Finance and Stochastics.

Volume (Year): 8 (2004)
Issue (Month): 2 (05)
Pages: 261-284

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Handle: RePEc:spr:finsto:v:8:y:2004:i:2:p:261-284

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## Related research

Keywords: American options; game contingent claims; neutral derivative pricing; incomplete markets; Dynkin game; $\sigma$ -supermartingales;

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## Citations

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Cited by:
1. Haishi Huang, 2009. "Convertible Bonds: Default Risk and Uncertain Volatility," Bonn Econ Discussion Papers bgse09_2010, University of Bonn, Germany.
2. Yuri Kifer, 2012. "Dynkin Games and Israeli Options," Papers 1209.1791, arXiv.org.
3. Jan Kallsen & Johannes Muhle-Karbe, 2009. "Utility maximization in models with conditionally independent increments," Papers 0911.3608, arXiv.org.
4. Mark Owen & Gordan Zitkovic, 2007. "Optimal Investment with an Unbounded Random Endowment and Utility-Based Pricing," Papers 0706.0478, arXiv.org, revised Sep 2007.
5. Hsuan-Ku Liu, 2013. "The pricing formula for cancellable European options," Papers 1304.5962, arXiv.org, revised May 2013.
6. Haishi Huang, 2009. "Convertible Bonds: Risks and Optimal Strategies," Bonn Econ Discussion Papers bgse07_2010, University of Bonn, Germany.
7. Gapeev, Pavel V., 2008. "The integral option in a model with jumps," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2623-2631, November.
8. Said Hamadene & Jianfeng Zhang, 2008. "The Continuous Time Nonzero-sum Dynkin Game Problem and Application in Game Options," Papers 0810.5698, arXiv.org.

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