# Pricing derivatives of American and game type in incomplete markets

## Author

Listed:
• Jan Kallsen

()

• Christoph Kühn

()

## 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

## Suggested Citation

• Jan Kallsen & Christoph Kühn, 2004. "Pricing derivatives of American and game type in incomplete markets," Finance and Stochastics, Springer, vol. 8(2), pages 261-284, May.
• Handle: RePEc:spr:finsto:v:8:y:2004:i:2:p:261-284 DOI: 10.1007/s00780-003-0110-7
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File URL: http://hdl.handle.net/10.1007/s00780-003-0110-7

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## References listed on IDEAS

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## Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
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Cited by:

1. Hsuan-Ku Liu, 2013. "The pricing formula for cancellable European options," Papers 1304.5962, arXiv.org, revised Sep 2014.
2. Ivan Guo & Marek Rutkowski, 2017. "Arbitrage-free pricing of multi-person game claims in discrete time," Finance and Stochastics, Springer, vol. 21(1), pages 111-155, January.
3. Gapeev Pavel V. & Kühn Christoph, 2005. "Perpetual convertible bonds in jump-diffusion models," Statistics & Risk Modeling, De Gruyter, vol. 23(1/2005), pages 15-31, January.
4. Kallsen Jan & Kühn Christoph, 2006. "On utility-based derivative pricing with and without intermediate trades," Statistics & Risk Modeling, De Gruyter, vol. 24(4/2006), pages 1-20, October.
5. Gapeev, Pavel V., 2008. "The integral option in a model with jumps," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2623-2631, November.
6. Said Hamadene & Jianfeng Zhang, 2008. "The Continuous Time Nonzero-sum Dynkin Game Problem and Application in Game Options," Papers 0810.5698, arXiv.org.
7. Yuri Kifer, 2012. "Dynkin Games and Israeli Options," Papers 1209.1791, arXiv.org.
8. Jan Kallsen & Johannes Muhle-Karbe, 2009. "Utility maximization in models with conditionally independent increments," Papers 0911.3608, arXiv.org.
9. Baurdoux, Erik J. & Kyprianou, Andreas E., 2004. "Further calculations for Israeli options," LSE Research Online Documents on Economics 23916, London School of Economics and Political Science, LSE Library.
10. repec:wsi:afexxx:v:12:y:2017:i:03:n:s2010495217500154 is not listed on IDEAS
11. Mark Owen & Gordan Zitkovic, 2007. "Optimal Investment with an Unbounded Random Endowment and Utility-Based Pricing," Papers 0706.0478, arXiv.org, revised Sep 2007.
12. Johannes Gerer & Gregor Dorfleitner, 2016. "A Note On Utility Indifference Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(06), pages 1-17, September.
13. Haishi Huang, 2009. "Convertible Bonds: Risks and Optimal Strategies," Bonn Econ Discussion Papers bgse07_2010, University of Bonn, Germany.
14. Hamadène, S. & Wang, H., 2009. "BSDEs with two RCLL reflecting obstacles driven by Brownian motion and Poisson measure and a related mixed zero-sum game," Stochastic Processes and their Applications, Elsevier, vol. 119(9), pages 2881-2912, September.
15. Klebert Kentia & Christoph Kuhn, 2017. "Nash equilibria for game contingent claims with utility-based hedging," Papers 1707.09351, arXiv.org.
16. Haishi Huang, 2009. "Convertible Bonds: Default Risk and Uncertain Volatility," Bonn Econ Discussion Papers bgse09_2010, University of Bonn, Germany.

### Keywords

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

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