Perpetual convertible bonds in jump-diffusion models
AbstractA convertible (callable) bond is a security that the holder can convert into a specified number of underlying shares. In addition, the issuer can recall the bond, paying some compensation, or force the holder to convert it immediately. We give an explicit solution to the corresponding optimal stopping game in the context of a reduced form model driven by a Brownian motion and a compound Poisson process with exponential jumps. It turns out that the occurrence of jumps leads to optimal stopping strategies whose structure differs from the results for continuous models.
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Bibliographic InfoArticle provided by De Gruyter in its journal Statistics & Risk Modeling.
Volume (Year): 23 (2005)
Issue (Month): 1/2005 (January)
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Web page: http://www.degruyter.com
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- Yuri Kifer, 2006. "Error estimates for binomial approximations of game options," Papers math/0607123, arXiv.org.
- Pavel V. Gapeev, 2006. "On Maximal Inequalities for some Jump Processes," SFB 649 Discussion Papers SFB649DP2006-060, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
- Pavel V. Gapeev, 2006. "Integral Options in Models with Jumps," SFB 649 Discussion Papers SFB649DP2006-068, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
- Gapeev, Pavel V., 2008. "The integral option in a model with jumps," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2623-2631, November.
- Pavel V. Gapeev, 2006. "Discounted Optimal Stopping for Maxima of some Jump-Diffusion Processes," SFB 649 Discussion Papers SFB649DP2006-059, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
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