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On the regularity of American options with regime-switching uncertainty

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  • Jacka, Saul D.
  • Ocejo, Adriana

Abstract

We study the regularity of the stochastic representation of the solution of a class of initial–boundary value problems related to a regime-switching diffusion. This representation is related to the value function of a finite-horizon optimal stopping problem such as the price of an American-style option in finance. We show continuity and smoothness of the value function using coupling and time-change techniques. As an application, we find the minimal payoff scenario for the holder of an American-style option in the presence of regime-switching uncertainty under the assumption that the transition rates are known to lie within level-dependent compact sets.

Suggested Citation

  • Jacka, Saul D. & Ocejo, Adriana, 2018. "On the regularity of American options with regime-switching uncertainty," Stochastic Processes and their Applications, Elsevier, vol. 128(3), pages 803-818.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:3:p:803-818
    DOI: 10.1016/j.spa.2017.06.007
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    References listed on IDEAS

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    1. David D. Yao & Qing Zhang & Xun Yu Zhou, 2006. "A Regime-Switching Model for European Options," International Series in Operations Research & Management Science, in: Houmin Yan & George Yin & Qing Zhang (ed.), Stochastic Processes, Optimization, and Control Theory: Applications in Financial Engineering, Queueing Networks, and Manufacturing Systems, chapter 0, pages 281-300, Springer.
    2. Filardo, Andrew J, 1994. "Business-Cycle Phases and Their Transitional Dynamics," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 299-308, July.
    3. Kanamura, Takashi & O[combining macron]hashi, Kazuhiko, 2008. "On transition probabilities of regime switching in electricity prices," Energy Economics, Elsevier, vol. 30(3), pages 1158-1172, May.
    4. John Buffington & Robert J. Elliott, 2002. "American Options With Regime Switching," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(05), pages 497-514.
    5. Alexander Cox & David Hobson, 2005. "Local martingales, bubbles and option prices," Finance and Stochastics, Springer, vol. 9(4), pages 477-492, October.
    6. Al-Anaswah, Nael & Wilfling, Bernd, 2011. "Identification of speculative bubbles using state-space models with Markov-switching," Journal of Banking & Finance, Elsevier, vol. 35(5), pages 1073-1086, May.
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    Cited by:

    1. Eisenberg, Julia & Krühner, Paul, 2022. "On Itô’s formula for semimartingales with jumps and non-C2 functions," Statistics & Probability Letters, Elsevier, vol. 184(C).
    2. Adriana Ocejo, 2018. "Explicit solutions to utility maximization problems in a regime-switching market model via Laplace transforms," Papers 1804.08442, arXiv.org.

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