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Perpetual convertible bonds in jump-diffusion models

Listed author(s):
  • Gapeev Pavel V.
  • Kühn Christoph
Registered author(s):

    A 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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    File URL: https://www.degruyter.com/view/j/stnd.2005.23.issue-1/stnd.2005.23.1.15/stnd.2005.23.1.15.xml?format=INT
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    Article provided by De Gruyter in its journal Statistics & Risk Modeling.

    Volume (Year): 23 (2005)
    Issue (Month): 1/2005 (January)
    Pages: 15-31

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    Handle: RePEc:bpj:strimo:v:23:y:2005:i:1/2005:p:15-31:n:2
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    1. Ernesto Mordecki, 1999. "Optimal stopping for a diffusion with jumps," Finance and Stochastics, Springer, vol. 3(2), pages 227-236.
    2. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    3. Ingersoll, Jonathan E, Jr, 1977. "An Examination of Corporate Call Policies on Convertible Securities," Journal of Finance, American Finance Association, vol. 32(2), pages 463-478, May.
    4. 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, 05.
    5. Ernesto Mordecki, 2002. "Optimal stopping and perpetual options for Lévy processes," Finance and Stochastics, Springer, vol. 6(4), pages 473-493.
    6. S. G. Kou & Hui Wang, 2004. "Option Pricing Under a Double Exponential Jump Diffusion Model," Management Science, INFORMS, vol. 50(9), pages 1178-1192, September.
    7. Brennan, M J & Schwartz, Eduardo S, 1977. "Convertible Bonds: Valuation and Optimal Strategies for Call and Conversion," Journal of Finance, American Finance Association, vol. 32(5), pages 1699-1715, December.
    8. Yuri Kifer, 2000. "Game options," Finance and Stochastics, Springer, vol. 4(4), pages 443-463.
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